diff --git a/.travis/test_package.sh b/.travis/test_package.sh
index f91f9982916..7b01d24ceb4 100644
--- a/.travis/test_package.sh
+++ b/.travis/test_package.sh
@@ -5,11 +5,17 @@
 
 DO_IGNORE=FALSE
 cd $1
-if [ ! -f "$2/package_info/$2/dependencies" ];then 
+
+if [ ! -d "$2" ]; then
+  echo "$2 : MISSING PACKAGE. Ignoring."
+  DO_IGNORE=TRUE
+  exit 1
+fi
+  
+  
+if [ ! -f "$2/package_info/$2/dependencies" ];then
   echo "No dependencies found for $2"
-  bash Scripts/developer_scripts/cgal_check_dependencies.sh --check_headers /usr/bin/doxygen
-  
-  
+  bash Scripts/developer_scripts/cgal_check_dependencies.sh --check_headers /usr/bin/doxygen	
   exit 1
 fi
 LIST_OF_FILES=$(git diff --name-only origin/master... |cut -d/ -f1 |uniq |sort)
diff --git a/Apollonius_graph_2/doc/Apollonius_graph_2/Apollonius_graph_2.txt b/Apollonius_graph_2/doc/Apollonius_graph_2/Apollonius_graph_2.txt
index 8f29331cbfb..196fc8451f1 100644
--- a/Apollonius_graph_2/doc/Apollonius_graph_2/Apollonius_graph_2.txt
+++ b/Apollonius_graph_2/doc/Apollonius_graph_2/Apollonius_graph_2.txt
@@ -369,9 +369,9 @@ concept. The second template parameter is a tag that indicates what
 operations are allowed in the computations that take place within the
 traits class.
 The two possible values of the `Method_tag` parameter are
-`Ring_tag` and `Sqrt_field_tag`. When
-`Ring_tag` is used, only ring operations are used during the
-evaluation of the predicates, whereas if `Sqrt_field_tag` is
+`Integral_domain_without_division_tag` and `Field_with_sqrt_tag`. When
+`Integral_domain_without_division_tag` is used, only ring operations are used during the
+evaluation of the predicates, whereas if `Field_with_sqrt_tag` is
 chosen, all four field operations, as well as square roots, are used
 during the predicate evaluation.
 
@@ -379,32 +379,22 @@ The `Apollonius_graph_traits_2<K,Method_tag>` class provides exact
 predicates if the number type in the kernel `K` is an exact number
 type. This is to be associated with the type of operations allowed for
 the predicate evaluation. For example `MP_Float` as number
-type, with `Ring_tag` as tag will give exact predicates,
-whereas `MP_Float` with `Sqrt_field_tag` will give
+type, with `Integral_domain_without_division_tag` as tag will give exact predicates,
+whereas `MP_Float` with `Field_with_sqrt_tag` will give
 inexact predicates.
 
-Since using an exact number type may be too slow, the
-`Apollonius_graph_traits_2<K,Method_tag>` class is designed to
-support the dynamic filtering of \cgal through the
-`Filtered_exact<CT,ET>` mechanism. In particular if `CT`
-is an inexact number type that supports the operations denoted by the
-tag `Method_tag` and `ET` is an exact number type for these
-operations, then kernel with number type
-`Filtered_exact<CT,ET>` will yield exact predicates for the
-Apollonius graph traits. To give a concrete example,
-`CGAL::Filtered_exact<double,CGAL::MP_Float>` with 
-`Ring_tag` will produce exact predicates.
-
-Another possibility for fast and exact predicate evaluation is to use
-the
-`Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>`
-class. This class is the analog of a filtered kernel. It takes a
+Although exact number types provide exact predicates and constructions,
+their use often results in unacceptably large runtimes.
+The class `Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>`
+aims to paliate this shortcoming. Similar to a filtered kernel, it takes a
 constructions kernel `CK`, a filtering kernel `FK` and an
 exact kernel `EK`, as well as the corresponding tags
 (`CM`, `FM` and `EM`, respectively).
-It evaluates the predicates by first using the filtering kernel, and
-if this fails the evaluation is performed using the exact kernel. The
-constructions are done using the kernel `CK`, which means that
+Predicates are evaluated by first using the filtering kernel, and
+if this fails the evaluation is performed using the exact kernel,
+thus yielding exact predicates at a generally much cheaper cost
+than directly using an exact number type. The constructions
+are done using the kernel `CK`, which means that
 they are not necessarily exact. All template parameters except
 `CK` have default values, which are explained in the reference
 manual.
diff --git a/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_filtered_traits_2.h b/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_filtered_traits_2.h
index a1b4a8003d5..c49c4a0bb76 100644
--- a/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_filtered_traits_2.h
+++ b/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_filtered_traits_2.h
@@ -20,8 +20,8 @@ This class has six template parameters. The first, third and fifth
 template parameters must be a models of the `Kernel` concept. The 
 second, fourth and sixth template parameters correspond to how 
 predicates are evaluated. There are two predefined possible values for 
-`Method_tag`, namely `CGAL::Sqrt_field_tag` and 
-`CGAL::Ring_tag`. The first one must be used when the number type 
+`Method_tag`, namely `CGAL::Field_with_sqrt_tag` and
+`CGAL::Integral_domain_without_division_tag`. The first one must be used when the number type
 used in the representation supports the exact evaluation of signs of 
 expressions involving all four basic operations and square roots, 
 whereas the second one requires the exact evaluation of signs of 
@@ -31,7 +31,7 @@ The way the predicates are evaluated is discussed in
 \cgalCite{cgal:ke-ppawv-02}, \cgalCite{cgal:ke-rctac-03}. 
 
 The default values for the template parameters are as follows: 
-`CM = CGAL::Ring_tag`, 
+`CM = CGAL::Integral_domain_without_division_tag`,
 `EK = CGAL::Simple_cartesian<CGAL::MP_Float>`, 
 `EM = CM`, 
 `FK = CGAL::Simple_cartesian<CGAL::Interval_nt<false> >`, 
@@ -41,8 +41,8 @@ The default values for the template parameters are as follows:
 
 \sa `Kernel` 
 \sa `ApolloniusGraphTraits_2` 
-\sa `CGAL::Ring_tag` 
-\sa `CGAL::Sqrt_field_tag` 
+\sa `CGAL::Integral_domain_without_division_tag`
+\sa `CGAL::Field_with_sqrt_tag`
 \sa `CGAL::Apollonius_graph_2<Gt,Agds>` 
 \sa `CGAL::Apollonius_graph_traits_2<K,Method_tag>` 
 
diff --git a/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_traits_2.h b/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_traits_2.h
index 6f3d11a7517..2b9ebca5625 100644
--- a/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_traits_2.h
+++ b/Apollonius_graph_2/doc/Apollonius_graph_2/CGAL/Apollonius_graph_traits_2.h
@@ -10,13 +10,13 @@ This class has two template parameters. The first template parameter
 must be a model of the `Kernel` concept. The second template 
 parameter corresponds to how predicates are evaluated. There are two 
 predefined possible values for `Method_tag`, namely 
-`CGAL::Sqrt_field_tag` and `CGAL::Ring_tag`. The first one 
+`CGAL::Field_with_sqrt_tag` and `CGAL::Integral_domain_without_division_tag`. The first one
 must be used when the number type used in the representation supports 
 the exact evaluation of signs of expressions involving all four basic 
 operations and square roots, whereas the second one requires the exact 
 evaluation of signs of ring-type expressions, i.e., expressions 
 involving only additions, subtractions and multiplications. The 
-default value for `Method_tag` is `CGAL::Ring_tag`. 
+default value for `Method_tag` is `CGAL::Integral_domain_without_division_tag`.
 The way the predicates are evaluated is discussed in 
 \cgalCite{cgal:ke-ppawv-02}, \cgalCite{cgal:ke-rctac-03}. 
 
@@ -24,8 +24,8 @@ The way the predicates are evaluated is discussed in
 
 \sa `Kernel` 
 \sa `ApolloniusGraphTraits_2` 
-\sa `CGAL::Ring_tag` 
-\sa `CGAL::Sqrt_field_tag` 
+\sa `CGAL::Integral_domain_without_division_tag`
+\sa `CGAL::Field_with_sqrt_tag`
 \sa `CGAL::Apollonius_graph_2<Gt,Agds>` 
 \sa `CGAL::Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>` 
 
diff --git a/Apollonius_graph_2/doc/Apollonius_graph_2/dependencies b/Apollonius_graph_2/doc/Apollonius_graph_2/dependencies
index 49ad6034b25..6270b1d0d3b 100644
--- a/Apollonius_graph_2/doc/Apollonius_graph_2/dependencies
+++ b/Apollonius_graph_2/doc/Apollonius_graph_2/dependencies
@@ -5,5 +5,6 @@ Algebraic_foundations
 Circulator
 Stream_support
 Voronoi_diagram_2
+Number_types
 TDS_2
 Triangulation_2
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/check_filter.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/check_filter.h
deleted file mode 100644
index d2395df4880..00000000000
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/check_filter.h
+++ /dev/null
@@ -1,38 +0,0 @@
-// Copyright (c) 2003,2004  INRIA Sophia-Antipolis (France).
-// All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org).
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
-// 
-//
-// Author(s)     : Menelaos Karavelas <mkaravel@iacm.forth.gr>
-
-
-
-#ifndef CGAL_CHECK_FILTER_H
-#define CGAL_CHECK_FILTER_H
-
-#include <CGAL/license/Apollonius_graph_2.h>
-
-
-#undef CGAL_IA_NEW_FILTERS
-
-namespace CGAL {
-
-template < class T>
-void must_be_filtered(const T&)
-{}
-
-#if defined CGAL_ARITHMETIC_FILTER_H
-template < class CT, class ET, class Type, bool Protection, class Cache>
-void must_be_filtered(const Filtered_exact<CT, ET, Type, Protection,
-		      Cache> &)
-{ dont_compile(CT(), ET()); }
-#endif
-
-}
-
-#endif
diff --git a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag2.cpp b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag2.cpp
index 22c23e75145..9b338b30edb 100644
--- a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag2.cpp
+++ b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag2.cpp
@@ -3,76 +3,31 @@
 #include <fstream>
 #include <cassert>
 
-#define DONT_USE_FILTERED_EXACT
 
 // choose number type
 #include <CGAL/MP_Float.h>
-#ifndef DONT_USE_FILTERED_EXACT
-#  include <CGAL/Filtered_exact.h>
-#endif
 
 typedef double         inexact_type;
 typedef CGAL::MP_Float exact_type;
 
-#ifndef DONT_USE_FILTERED_EXACT
-typedef CGAL::Filtered_exact<inexact_type,exact_type>  number_t;
-#endif
-
 #include <CGAL/Simple_cartesian.h>
 
-#ifndef DONT_USE_FILTERED_EXACT
-typedef CGAL::Simple_cartesian<number_t> Kernel;
-#endif
-
 typedef CGAL::Integral_domain_without_division_tag Method_tag;
 
 #include "./include/test.h"
 
-
 typedef CGAL::Simple_cartesian<inexact_type> CK;
 typedef CGAL::Simple_cartesian<exact_type> EK;
 
-
 int main()
 {
-#ifndef DONT_USE_FILTERED_EXACT
-  {
-    std::ifstream ifs_algo("./data/algo.dat");
+  std::ifstream ifs_algo("./data/algo.dat");
+  assert( ifs_algo );
 
-    assert( ifs_algo );
-
-    std::cout << "testing the Apollonius graph class..." << std::flush;
-    bool algo_ok =
-      CGAL::test_algo<Kernel,Method_tag,std::ifstream>(ifs_algo);
-
-    assert( algo_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_algo.close();
-
-    std::cout << std::endl;
-  }
-#endif
-  //------------------------------------------------------------------------
-
-  {
-    std::ifstream ifs_algo("./data/algo.dat");
-
-    assert( ifs_algo );
-
-    std::cout << "testing the Apollonius graph class"
-	      << " with filtered traits..." << std::flush;
-    bool algo_ok =
-      CGAL::test_filtered_traits_algo<CK,Method_tag,EK,Method_tag,
-      std::ifstream>(ifs_algo);
-
-    assert( algo_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_algo.close();
-
-    std::cout << std::endl;
-  }
+  std::cout << "testing the Apollonius graph class" << " with filtered traits..." << std::flush;
+  bool algo_ok = CGAL::test_filtered_traits_algo<CK,Method_tag,EK,Method_tag,std::ifstream>(ifs_algo);
+  assert( algo_ok );
+  std::cout << " done!" << std::endl;
 
   return 0;
 }
diff --git a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_hierarchy_2.cpp b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_hierarchy_2.cpp
index 51baa1a0cab..9bb7f335333 100644
--- a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_hierarchy_2.cpp
+++ b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_hierarchy_2.cpp
@@ -3,79 +3,31 @@
 #include <fstream>
 #include <cassert>
 
-#define DNOT_USE_FILTERED_EXACT
-
 // choose number type
 #include <CGAL/MP_Float.h>
 
-#ifndef DNOT_USE_FILTERED_EXACT
-#  include <CGAL/Filtered_exact.h>
-#endif
-
 typedef double         inexact_type;
 typedef CGAL::MP_Float exact_type;
 
-#ifndef DNOT_USE_FILTERED_EXACT
-typedef CGAL::Filtered_exact<inexact_type,exact_type>  number_t;
-#endif
-
 #include <CGAL/Simple_cartesian.h>
 
-#ifndef DNOT_USE_FILTERED_EXACT
-typedef CGAL::Simple_cartesian<number_t> K;
-#endif
-
 typedef CGAL::Integral_domain_without_division_tag Method_tag;
 
 #include "./include/test.h"
 
-
 typedef CGAL::Simple_cartesian<inexact_type> CK;
 typedef CGAL::Simple_cartesian<exact_type> EK;
 
-
 int main()
 {
-#ifndef DNOT_USE_FILTERED_EXACT
-  {
-    std::ifstream ifs_hierarchy("./data/hierarchy.dat");
+  std::ifstream ifs_hierarchy("./data/hierarchy.dat");
+  assert( ifs_hierarchy );
 
-    assert( ifs_hierarchy );
+  std::cout << "testing the Apollonius graph hierarchy class" << " with filtered traits..." << std::flush;
+  bool hierarchy_ok = CGAL::test_filtered_traits_hierarchy_algo<CK,Method_tag,EK,Method_tag,std::ifstream>(ifs_hierarchy);
 
-    std::cout << "testing the Apollonius graph hierarchy class..."
-	      << std::flush;
-    bool hierarchy_ok = 
-      CGAL::test_hierarchy_algo<Kernel,Method_tag,
-      std::ifstream>(ifs_hierarchy);
-
-    assert( hierarchy_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_hierarchy.close();
-
-    std::cout << std::endl;
-  }
-#endif
-  //------------------------------------------------------------------------
-
-  {
-    std::ifstream ifs_hierarchy("./data/hierarchy.dat");
-
-    assert( ifs_hierarchy );
-
-    std::cout << "testing the Apollonius graph hierarchy class"
-	      << " with filtered traits..." << std::flush;
-    bool hierarchy_ok = 
-      CGAL::test_filtered_traits_hierarchy_algo<CK,Method_tag,EK,
-      Method_tag,std::ifstream>(ifs_hierarchy);
-
-    assert( hierarchy_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_hierarchy.close();
-
-    std::cout << std::endl;
-  }
+  assert( hierarchy_ok );
+  std::cout << " done!" << std::endl;
 
   return 0;
 }
diff --git a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_traits_2.cpp b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_traits_2.cpp
index 3739b77cad4..1a8d4781bd9 100644
--- a/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_traits_2.cpp
+++ b/Apollonius_graph_2/test/Apollonius_graph_2/test_ag_traits_2.cpp
@@ -2,79 +2,33 @@
 #include <fstream>
 #include <cassert>
 
-#define DONT_USE_FILTERED_EXACT
-
 // choose number type
 #include <CGAL/MP_Float.h>
-#ifndef DONT_USE_FILTERED_EXACT
-#  include <CGAL/Filtered_exact.h>
-#endif
 
 typedef double         inexact_type;
 typedef CGAL::MP_Float exact_type;
 
-#ifndef DONT_USE_FILTERED_EXACT
-typedef CGAL::Filtered_exact<inexact_type,exact_type>  number_t;
-#endif
-
 #include <CGAL/Simple_cartesian.h>
 
-#ifndef DONT_USE_FILTERED_EXACT
-typedef CGAL::Simple_cartesian<number_t> Kernel;
-#endif
-
 typedef CGAL::Integral_domain_without_division_tag Method_tag;
 
 #include "./include/test.h"
 
-
 typedef CGAL::Simple_cartesian<double> CK;
 typedef CGAL::Simple_cartesian<CGAL::MP_Float> EK;
 
-
 int main()
 {
-#ifndef DONT_USE_FILTERED_EXACT
-  {
-    std::ifstream ifs_traits("./data/traits.dat");
+  std::ifstream ifs_traits("./data/traits.dat");
+  assert( ifs_traits );
 
-    assert( ifs_traits );
+  std::cout << "testing the filtered traits class..." << std::flush;
 
-    //  bool is_ok =
-    //    CGAL::test_traits<Kernel,CGAL::Integral_domain_without_division_tag,std::ifstream>(ifs_traits);
+  CGAL::Filtered_traits_tester<CK,Method_tag,EK,Method_tag> test_traits;
+  bool traits_ok = test_traits();
+  assert( traits_ok );
 
-    std::cout << "testing the traits class..." << std::flush;
-
-    CGAL::Traits_tester<Kernel,Method_tag> test_traits;
-    bool traits_ok = test_traits();
-
-    assert( traits_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_traits.close();
-
-    std::cout << std::endl;
-  }
-#endif
-  //------------------------------------------------------------------------
-
-  {
-    std::ifstream ifs_traits("./data/traits.dat");
-
-    assert( ifs_traits );
-
-    std::cout << "testing the filtered traits class..." << std::flush;
-
-    CGAL::Filtered_traits_tester<CK,Method_tag,EK,Method_tag> test_traits;
-    bool traits_ok = test_traits();
-
-    assert( traits_ok );
-    std::cout << " done!" << std::endl;
-
-    ifs_traits.close();
-
-    std::cout << std::endl;
-  }
+  std::cout << " done!" << std::endl;
 
   return 0;
 }
diff --git a/BGL/doc/BGL/CGAL/HalfedgeDS_face_max_base_with_id.h b/BGL/doc/BGL/CGAL/HalfedgeDS_face_max_base_with_id.h
index 446481b9fc4..0006a4332e8 100644
--- a/BGL/doc/BGL/CGAL/HalfedgeDS_face_max_base_with_id.h
+++ b/BGL/doc/BGL/CGAL/HalfedgeDS_face_max_base_with_id.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `HalfedgeDS_face_max_base_with_id` is a model of the `HalfedgeDSFace` 
 concept. 
diff --git a/BGL/doc/BGL/CGAL/HalfedgeDS_halfedge_max_base_with_id.h b/BGL/doc/BGL/CGAL/HalfedgeDS_halfedge_max_base_with_id.h
index 6e597c7d346..b9d7f4142eb 100644
--- a/BGL/doc/BGL/CGAL/HalfedgeDS_halfedge_max_base_with_id.h
+++ b/BGL/doc/BGL/CGAL/HalfedgeDS_halfedge_max_base_with_id.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `HalfedgeDS_halfedge_max_base_with_id` is a model of the `HalfedgeDSHalfedge` 
 concept. 
diff --git a/BGL/doc/BGL/CGAL/HalfedgeDS_vertex_max_base_with_id.h b/BGL/doc/BGL/CGAL/HalfedgeDS_vertex_max_base_with_id.h
index 0839d254c8f..565236d880e 100644
--- a/BGL/doc/BGL/CGAL/HalfedgeDS_vertex_max_base_with_id.h
+++ b/BGL/doc/BGL/CGAL/HalfedgeDS_vertex_max_base_with_id.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `HalfedgeDS_vertex_max_base_with_id` is a model of the `HalfedgeDSVertex` 
 concept.  It is 
diff --git a/BGL/doc/BGL/CGAL/Linear_cell_complex_bgl_min_items.h b/BGL/doc/BGL/CGAL/Linear_cell_complex_bgl_min_items.h
index 0c9ab30a613..611ff3cd88b 100644
--- a/BGL/doc/BGL/CGAL/Linear_cell_complex_bgl_min_items.h
+++ b/BGL/doc/BGL/CGAL/Linear_cell_complex_bgl_min_items.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `Linear_cell_complex_bgl_min_items` defines `void` as the information associated with darts, darts have ids and 0- and 2-attributes are enabled and have ids.
 
diff --git a/BGL/doc/BGL/CGAL/Linear_cell_complex_for_bgl_combinatorial_map_helper.h b/BGL/doc/BGL/CGAL/Linear_cell_complex_for_bgl_combinatorial_map_helper.h
index 72ba704077c..8bebd8f9e53 100644
--- a/BGL/doc/BGL/CGAL/Linear_cell_complex_for_bgl_combinatorial_map_helper.h
+++ b/BGL/doc/BGL/CGAL/Linear_cell_complex_for_bgl_combinatorial_map_helper.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `Linear_cell_complex_for_bgl_combinatorial_map_helper` defines a `CGAL::Linear_cell_complex_for_combinatorial_map` as inner type, named `type`, having `CGAL::Linear_cell_complex_bgl_min_items` as items class. With this item class, no information are associated with darts, darts have ids and 0- and 2-attributes are enabled and have ids.
 
diff --git a/BGL/doc/BGL/CGAL/Polyhedron_items_with_id_3.h b/BGL/doc/BGL/CGAL/Polyhedron_items_with_id_3.h
index fdfee46c400..a64795aaa74 100644
--- a/BGL/doc/BGL/CGAL/Polyhedron_items_with_id_3.h
+++ b/BGL/doc/BGL/CGAL/Polyhedron_items_with_id_3.h
@@ -2,7 +2,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `Polyhedron_items_with_id_3` is a model of the `PolyhedronItems_3` 
 concept. It provides definitions for vertices with points, halfedges, 
@@ -63,7 +63,7 @@ public:
 
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 Given a `CGAL::Polyhedron_3`,
 for each simplex type (vertex, halfedge, facet) associates an index from
diff --git a/BGL/doc/BGL/CGAL/Triangulation_face_base_with_id_2.h b/BGL/doc/BGL/CGAL/Triangulation_face_base_with_id_2.h
index 83e14e58af7..15827d6758b 100644
--- a/BGL/doc/BGL/CGAL/Triangulation_face_base_with_id_2.h
+++ b/BGL/doc/BGL/CGAL/Triangulation_face_base_with_id_2.h
@@ -1,15 +1,16 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `Triangulation_face_base_with_id_2` is a model of the
 concept `TriangulationFaceBase_2`, the base face of a
-2D-triangulation.  It provides an integer field that can be used to
+2D-triangulation. It provides an integer field that can be used to
 index faces for \sc{Bgl} algorithms.
 
 Note that the user is in charge of setting indices correctly before
-running a graph algorithm.
+running a graph algorithm, by calling the function
+`CGAL::set_triangulation_ids(Triangulation&)`.
 
 \tparam TriangulationTraits_2 is the geometric traits class
 and must be a model of `TriangulationTraits_2`.
@@ -42,4 +43,19 @@ int& id();
 /// @}
 
 }; /* end Triangulation_face_base_with_id_2 */
+
+/// \ingroup BGLGraphExternalIndices
+///
+/// This function initializes vertex, edge, and face indices of the triangulation `tr` and must
+/// be called prior to using `tr` as a BGL graph in an algorithm that requires
+/// vertex, halfedge, edge, or face indices.
+///
+/// \tparam Triangulation a 2D triangulation of \cgal, whose combinatorial data structure
+///         has been initialized with the vertex and face classes `Triangulation_vertex_base_with_id_2`
+///         and `Triangulation_face_base_with_id_2`.
+///
+/// \sa the \ref PkgTriangulation2 package
+template <typename Triangulation>
+void set_triangulation_ids(Triangulation& tr);
+
 } /* end namespace CGAL */
diff --git a/BGL/doc/BGL/CGAL/Triangulation_vertex_base_with_id_2.h b/BGL/doc/BGL/CGAL/Triangulation_vertex_base_with_id_2.h
index a93691aa0b4..bc156657b30 100644
--- a/BGL/doc/BGL/CGAL/Triangulation_vertex_base_with_id_2.h
+++ b/BGL/doc/BGL/CGAL/Triangulation_vertex_base_with_id_2.h
@@ -1,7 +1,7 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgBGLHelper
+\ingroup BGLGraphExternalIndices
 
 The class `Triangulation_vertex_base_with_id_2` is a model of the
 concept `TriangulationVertexBase_2`, the base vertex of a
@@ -9,7 +9,8 @@ concept `TriangulationVertexBase_2`, the base vertex of a
 index vertices for \sc{Bgl} algorithms.
 
 Note that the user is in charge of setting indices correctly before
-running a graph algorithm.
+running a graph algorithm, by calling the function
+`CGAL::set_triangulation_ids(Triangulation&)`.
 
 \tparam TriangulationTraits_2 is the geometric traits class
 and must be a model of `TriangulationTraits_2`.
diff --git a/BGL/doc/BGL/CGAL/boost/graph/properties.h b/BGL/doc/BGL/CGAL/boost/graph/properties.h
index cbd4d4f960f..a7416d53eae 100644
--- a/BGL/doc/BGL/CGAL/boost/graph/properties.h
+++ b/BGL/doc/BGL/CGAL/boost/graph/properties.h
@@ -1,14 +1,9 @@
-/// Boost Namespace
-namespace boost {
+/// CGAL Namespace
+namespace CGAL {
 
 /// \ingroup PkgBGLProperties
 /// @{
 
-/// The constant `edge_index` is a property tag which identifies the <i>index</i> property of an edge of a \sc{Bgl}
-/// <a href="https://www.boost.org/libs/graph/doc/Graph.html"><code>Graph</code></a>.
-/// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
-enum edge_index_t { edge_index};
-
 /// The constant `vertex_index` is a property tag which identifies the <i>index</i> property of a vertex of a \sc{Bgl}
 /// <a href="https://www.boost.org/libs/graph/doc/Graph.html"><code>Graph</code></a>.
 /// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
@@ -20,13 +15,17 @@ enum vertex_index_t { vertex_index };
 /// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
 enum halfedge_index_t { halfedge_index };
 
+/// The constant `edge_index` is a property tag which identifies the <i>index</i> property of an edge of a \sc{Bgl}
+/// <a href="https://www.boost.org/libs/graph/doc/Graph.html"><code>Graph</code></a>.
+/// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
+enum edge_index_t { edge_index };
+
 /// The constant `face_index` is a property tag which identifies the <i>index</i> property of a face of a `FaceGraph`.
 ///
 /// This is a property tag introduced by \cgal.
 /// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
 enum face_index_t { face_index };
 
-
 /// The constant `vertex_point` is a property tag which refers to the  geometric embedding property of
 /// a vertex of a `HalfedgeGraph`.
 ///
@@ -34,12 +33,22 @@ enum face_index_t { face_index };
 /// \cgalModels <a href="https://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
 enum vertex_point_t { vertex_point };
 
-
 /// @}
-} // namespace boost
-
-namespace CGAL {
 
+/// \ingroup PkgBGLProperties
+///
+/// \brief graph_has_property is used to indicate if a model of `HalfedgeGraph` or `FaceGraph`
+/// has an internal property associated with the given `PropertyTag`.
+///
+/// It inherits from \link Tag_true `CGAL::Tag_true` \endlink if there is a
+/// default internal property map for the corresponding property tag and from
+/// \link Tag_false `CGAL::Tag_false` \endlink otherwise.
+///
+/// \tparam Graph a model of `HalfedgeGraph` or `FaceGraph`
+/// \tparam PropertyTag the type of a property tag referring to the property of interest.
+///
+template<typename Graph, typename PropertyTag>
+struct graph_has_property;
 
 /// @{
 
diff --git a/BGL/doc/BGL/NamedParameters.txt b/BGL/doc/BGL/NamedParameters.txt
index ce3be60f8f4..47c1d3f866a 100644
--- a/BGL/doc/BGL/NamedParameters.txt
+++ b/BGL/doc/BGL/NamedParameters.txt
@@ -38,38 +38,51 @@ a \cgal point type as value type. \n
 \cgalNPEnd
 
 \cgalNPBegin{vertex_index_map} \anchor BGL_vertex_index_map
-is the property map containing the index of each vertex of the input polygon mesh.\n
+is the property map associating a unique index to each vertex of a polygon mesh `g`,
+between `0` and `num_vertices(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a vertex index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and the value type
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::vertex_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::vertex_index, pmesh)\endcode
+<b>Default:</b> an initialized vertex index property map
 \cgalNPEnd
 
 \cgalNPBegin{halfedge_index_map} \anchor BGL_halfedge_index_map
-is the property map containing the index of each halfedge of the input polygon mesh.\n
+is the property map associating a unique index to each halfedge of a polygon mesh,
+between `0` and `num_halfedges(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a halfedge index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%halfedge_descriptor` as key type and the value type:
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::halfedge_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::halfedge_index, pmesh)\endcode
-If this internal property map exists, its values should be initialized.
+<b>Default:</b> an initialized halfedge index property map
 \cgalNPEnd
 
 \cgalNPBegin{edge_index_map} \anchor BGL_edge_index_map
-is the property map containing the index of each edge of the input polygon mesh.\n
+is the property map associating a unique index to each edge of a polygon mesh,
+between `0` and `num_edges(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a edge index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%edge_descriptor` as key type and the value type:
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::edge_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::edge_index, pmesh)\endcode
-If this internal property map exists, its values should be initialized.
+<b>Default:</b> an initialized edge index property map
 \cgalNPEnd
 
 \cgalNPBegin{face_index_map} \anchor BGL_face_index_map
-is the property map containing the index of each face of the input polygon mesh.\n
+is the property map associating a unique index to each face of a polygon mesh,
+between `0` and `num_faces(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a face index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%face_descriptor` as key type and the value type:
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::face_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::face_index, pmesh)\endcode
-If this internal property map exists, its values should be initialized.
+<b>Default:</b> an initialized face index property map
 \cgalNPEnd
 
 \cgalNPBegin{edge_is_constrained_map} \anchor BGL_edge_is_constrained_map
diff --git a/BGL/doc/BGL/PackageDescription.txt b/BGL/doc/BGL/PackageDescription.txt
index 287b2662399..6f85bafbf06 100644
--- a/BGL/doc/BGL/PackageDescription.txt
+++ b/BGL/doc/BGL/PackageDescription.txt
@@ -443,7 +443,7 @@ the requirement for traversal of all faces in a graph.
 /// \defgroup PkgBGLPropertiesDynamic Dynamic Properties
 /// \ingroup PkgBGLRef
 
-/// \defgroup PkgBGLHelper Helper Classes
+/// \defgroup PkgBGLGraphExternalIndices External Indices
 /// \ingroup PkgBGLRef
 
 /// \defgroup PkgBGLHelperFct Helper Functions
@@ -473,8 +473,11 @@ The dynamic property tags enable to associate information to simplices of a `Fac
 */
 
 /*!
-\addtogroup PkgBGLHelper
-Several classes that enable to store ids in vertices/halfedges/faces of a `CGAL::Polyhedron_3`, as well as adapters such as `CGAL::Dual`.
+\addtogroup BGLGraphExternalIndices
+A number of BGL and \cgal algorithms require the graph to have (initialized) integer-like indices
+for its vertices, edges, or faces. However, not all graphs intrinsically offer a natural way
+to attach a unique ID to each element. The following classes and functions paliate this
+by attaching and initializing external IDs to the elements of the graph.
 */
 
 /*!
@@ -574,25 +577,25 @@ Methods to read and write graphs.
 - `MutableFaceGraph`
 
 \cgalCRPSection{Properties}
-- `boost::vertex_index_t`
-- `boost::halfedge_index_t`
-- `boost::edge_index_t`
-- `boost::face_index_t`
-- `boost::vertex_point_t`
+- `CGAL::vertex_index_t`
+- `CGAL::halfedge_index_t`
+- `CGAL::edge_index_t`
+- `CGAL::face_index_t`
+- `CGAL::vertex_point_t`
 
 \cgalCRPSection{%CGAL Classes Adapted for the Graph API}
 
-Different \cgal types have been adapted as graphs for the \sc{Bgl}. All
+A number of \cgal structures have been adapted as graphs for the \sc{Bgl}. All
 adapted types are listed here. The pages document which concepts they
 model, the properties they support, and any possible caveats that a
 user might encounter.
 
-- \link BGLSMGT  `boost::graph_traits< CGAL::Surface_mesh<P> >` \endlink
-- \link BGLPolyGT  `boost::graph_traits< CGAL::Polyhedron_3<T> >` \endlink
-- \link BGLLCCGT `boost::graph_traits< CGAL::Linear_cell_complex_for_combinatorial_map<...> >` \endlink
-- \link BGLSeam_meshGT `boost::graph_traits< CGAL::Seam_mesh<T> >` \endlink
-- \link BGLT2GT `boost::graph_traits< CGAL::Triangulation_2<GT, TDS> >` \endlink
-- \link BGLArgtGT `boost::graph_traits< CGAL::Arrangement_2<T,DC> >` \endlink
+- \link BGLSMGT `boost::graph_traits<CGAL::Surface_mesh<P> >` \endlink
+- \link BGLPolyGT `boost::graph_traits<CGAL::Polyhedron_3<T> >` \endlink
+- \link BGLLCCGT `boost::graph_traits<CGAL::Linear_cell_complex_for_combinatorial_map<...> >` \endlink
+- \link BGLSeam_meshGT `boost::graph_traits<CGAL::Seam_mesh<T> >` \endlink
+- \link BGLT2GT `boost::graph_traits<CGAL::Triangulation_2<GT, TDS> >` \endlink and other 2D triangulations
+- \link BGLArgtGT `boost::graph_traits<CGAL::Arrangement_2<T, DC> >` \endlink
 - \link BGLOMPAK `boost::graph_traits<OpenMesh::PolyMesh_ArrayKernelT<K> >` \endlink
 - \link BGLOMTMAK `boost::graph_traits<OpenMesh::TriMesh_ArrayKernelT<K> >` \endlink
 
@@ -642,6 +645,8 @@ user might encounter.
 - `CGAL::clear()`
 - `CGAL::copy_face_graph()`
 
+- `CGAL::set_triangulation_ids()`
+
 \cgalCRPSection{Iterators}
 - `CGAL::Halfedge_around_source_iterator`
 - `CGAL::Halfedge_around_target_iterator`
diff --git a/BGL/include/CGAL/boost/graph/Euler_operations.h b/BGL/include/CGAL/boost/graph/Euler_operations.h
index 12e6ed25252..f362aef6e17 100644
--- a/BGL/include/CGAL/boost/graph/Euler_operations.h
+++ b/BGL/include/CGAL/boost/graph/Euler_operations.h
@@ -702,19 +702,35 @@ add_face(const VertexRange& vr, Graph& g)
         break;
 
       case 3: // both are new
-        if (halfedge(v, g) == boost::graph_traits<Graph>::null_halfedge())
         {
-          set_halfedge(v, outer_prev, g);
-          next_cache.push_back(NextCacheEntry(outer_prev, outer_next));
+          // try to pick a border halfedge with v as target
+          halfedge_descriptor hv = halfedge(v, g);
+          if (hv != boost::graph_traits<Graph>::null_halfedge() && !is_border(hv, g))
+          {
+            for(halfedge_descriptor h_around_v : halfedges_around_target(hv, g))
+              if (is_border(h_around_v, g))
+              {
+                hv = h_around_v;
+                break;
+              }
+            if (!is_border(hv, g))
+              hv = boost::graph_traits<Graph>::null_halfedge();
+          }
+
+          if (hv == boost::graph_traits<Graph>::null_halfedge())
+          {
+            set_halfedge(v, outer_prev, g);
+            next_cache.push_back(NextCacheEntry(outer_prev, outer_next));
+          }
+          else
+          {
+            border_prev = hv;
+            border_next = next(border_prev, g);
+            next_cache.push_back(NextCacheEntry(border_prev, outer_next));
+            next_cache.push_back(NextCacheEntry(outer_prev, border_next));
+          }
+          break;
         }
-        else
-        {
-          border_prev = halfedge(v, g);
-          border_next = next(border_prev, g);
-          next_cache.push_back(NextCacheEntry(border_prev, outer_next));
-          next_cache.push_back(NextCacheEntry(outer_prev, border_next));
-        }
-        break;
       }
 
       // set inner link
@@ -1323,7 +1339,7 @@ flip_edge(typename boost::graph_traits<Graph>::halfedge_descriptor h,
 template<typename Graph>
 bool
 does_satisfy_link_condition(typename boost::graph_traits<Graph>::edge_descriptor e,
-                            Graph& g)
+                            const Graph& g)
 {
   typedef typename boost::graph_traits<Graph>::vertex_descriptor vertex_descriptor;
   typedef typename boost::graph_traits<Graph>::halfedge_descriptor halfedge_descriptor;
@@ -1423,7 +1439,7 @@ does_satisfy_link_condition(typename boost::graph_traits<Graph>::edge_descriptor
 template<typename Graph>
 bool
   satisfies_link_condition(typename boost::graph_traits<Graph>::edge_descriptor e,
-                           Graph& g)
+                           const Graph& g)
 {
   return does_satisfy_link_condition(e, g);
 }
diff --git a/BGL/include/CGAL/boost/graph/Face_filtered_graph.h b/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
index ffd943fb9c4..875eb7f3e73 100644
--- a/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
+++ b/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
@@ -16,23 +16,24 @@
 #include <CGAL/boost/graph/properties.h>
 #include <CGAL/boost/graph/iterator.h>
 #include <CGAL/boost/graph/Named_function_parameters.h>
+#include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/boost/graph/helpers.h>
-#include <CGAL/Dynamic_property_map.h>
-#include <CGAL/assertions.h>
-#include <boost/unordered_set.hpp>
-#include <boost/graph/graph_traits.hpp>
 #include <CGAL/boost/iterator/transform_iterator.hpp>
-#include <boost/iterator/filter_iterator.hpp>
+#include <CGAL/Default.h>
+#include <CGAL/Dynamic_property_map.h>
+
 #include <boost/dynamic_bitset.hpp>
+#include <boost/graph/graph_traits.hpp>
+#include <boost/iterator/filter_iterator.hpp>
 #include <boost/range/has_range_iterator.hpp>
+#include <boost/unordered_set.hpp>
 
 #ifdef DOXYGEN_RUNNING
 #define CGAL_BGL_NP_TEMPLATE_PARAMETERS NamedParameters
 #define CGAL_BGL_NP_CLASS NamedParameters
 #endif
 
-namespace CGAL
-{
+namespace CGAL {
 
   /*!
    * \ingroup PkgBGLAdaptors
@@ -62,18 +63,18 @@ namespace CGAL
    * missing if the default is fine.
    *
    * \tparam Graph must be a model of a `FaceListGraph`, `HalfedgeListGraph`, and \bgllink{VertexListGraph}.
-   * \tparam FIMap a model of `ReadablePropertyMap` with `face_descriptor` as key and `graph_traits<Graph>::%faces_size_type` as value
-   * \tparam VIMap a model of `ReadablePropertyMap` with `vertex_descriptor` as key and `graph_traits<Graph>::%vertices_size_type` as value
-   * \tparam HIMap a model of `ReadablePropertyMap` with `halfedge_descriptor` as key and `graph_traits<Graph>::%halfedges_size_type` as value
+   * \tparam FIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%face_descriptor` as key and `graph_traits<Graph>::%faces_size_type` as value
+   * \tparam VIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%vertex_descriptor` as key and `graph_traits<Graph>::%vertices_size_type` as value
+   * \tparam HIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%halfedge_descriptor` as key and `graph_traits<Graph>::%halfedges_size_type` as value
    *
    * \cgalModels `FaceListGraph`
    * \cgalModels `HalfedgeListGraph`
    * \cgalModels \bgllink{VertexListGraph}
    */
 template<typename Graph,
-         typename FIMap = typename boost::property_map<Graph, CGAL::face_index_t>::type,
-         typename VIMap = typename boost::property_map<Graph, boost::vertex_index_t>::type,
-         typename HIMap = typename boost::property_map<Graph, CGAL::halfedge_index_t>::type>
+         typename FIMap = Default,
+         typename VIMap = Default,
+         typename HIMap = Default>
 struct Face_filtered_graph
 {
   typedef boost::graph_traits<Graph>                  gt;
@@ -93,10 +94,15 @@ struct Face_filtered_graph
   #endif
 
   // non documented types
-  typedef typename boost::property_traits< FIMap >::value_type face_index_type;
-  typedef typename boost::property_traits< VIMap >::value_type vertex_index_type;
-  typedef typename boost::property_traits< HIMap >::value_type halfedge_index_type;
-  typedef Face_filtered_graph<Graph, FIMap, VIMap, HIMap>   Self;
+  typedef typename Default::Get<FIMap, typename CGAL::GetInitializedFaceIndexMap<Graph>::const_type>::type FIM;
+  typedef typename Default::Get<VIMap, typename CGAL::GetInitializedVertexIndexMap<Graph>::const_type>::type VIM;
+  typedef typename Default::Get<HIMap, typename CGAL::GetInitializedHalfedgeIndexMap<Graph>::const_type>::type HIM;
+
+  typedef typename boost::property_traits<FIM>::value_type face_index_type;
+  typedef typename boost::property_traits<VIM>::value_type vertex_index_type;
+  typedef typename boost::property_traits<HIM>::value_type halfedge_index_type;
+
+  typedef Face_filtered_graph<Graph, FIMap, VIMap, HIMap> Self;
 
   /*!
    * \brief Constructor where the set of selected faces is specified as a range of patch ids.
@@ -115,31 +121,31 @@ struct Face_filtered_graph
    *
    * \cgalNamedParamsBegin
    *   \cgalParamBegin{face_index_map}
-   *     a property map containing an index for each face initialized from 0 to `num_vertices(graph)`
+   *     a property map containing for each face of `graph` a unique index between `0` and `num_faces(graph)-1`
    *   \cgalParamEnd
    *   \cgalParamBegin{vertex_index_map}
-   *     a property map containing an index for each vertex initialized 0 to `num_vertices(graph)`
+   *     a property map containing for each vertex of `graph` a unique index between `0` and `num_vertices(graph)-1`
    *   \cgalParamEnd
    *   \cgalParamBegin{halfedge_index_map}
-   *     a property map containing an index for each halfedge initialized 0 to `num_halfedges(graph)`
+   *     a property map containing for each halfedge of `graph` a unique index between `0` and `num_halfedges(graph)-1`
    *   \cgalParamEnd
    * \cgalNamedParamsEnd
    */
   template <typename FacePatchIndexMap, class FacePatchIndexRange, class CGAL_BGL_NP_TEMPLATE_PARAMETERS>
   Face_filtered_graph(const Graph& graph,
                       const FacePatchIndexRange& selected_face_patch_indices,
-                            FacePatchIndexMap face_patch_index_map,
-                            const CGAL_BGL_NP_CLASS& np
-                           #ifndef DOXYGEN_RUNNING
-                              , typename boost::enable_if<
-                                  typename boost::has_range_const_iterator<FacePatchIndexRange>::type
-                                >::type* = 0
-                           #endif
-                             )
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index), get_const_property_map(face_index, graph)))
-    , vimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_index), get_const_property_map(boost::vertex_index, graph)))
-    , himap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::halfedge_index), get_const_property_map(halfedge_index, graph)))
+                      FacePatchIndexMap face_patch_index_map,
+                      const CGAL_BGL_NP_CLASS& np
+#ifndef DOXYGEN_RUNNING
+                    , typename boost::enable_if<
+                        typename boost::has_range_const_iterator<FacePatchIndexRange>::type
+                      >::type* = 0
+#endif
+                      )
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph, np)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
   {
     set_selected_faces(selected_face_patch_indices, face_patch_index_map);
   }
@@ -152,10 +158,10 @@ struct Face_filtered_graph
                       typename boost::has_range_const_iterator<FacePatchIndexRange>::type
                       >::type* = 0
                       )
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(get(CGAL::face_index, graph))
-    , vimap(get(boost::vertex_index, graph))
-    , himap(get(CGAL::halfedge_index, graph))
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph))
   {
     set_selected_faces(selected_face_patch_indices, face_patch_index_map);
   }
@@ -175,38 +181,37 @@ struct Face_filtered_graph
    *
    * \cgalNamedParamsBegin
    *   \cgalParamBegin{face_index_map}
-   *     a property map containing an index for each face initialized from 0 to `num_vertices(graph)`
+   *     a property map containing for each face of `graph` a unique index between `0` and `num_faces(graph)-1`
    *   \cgalParamEnd
    *   \cgalParamBegin{vertex_index_map}
-   *     a property map containing an index for each vertex initialized 0 to `num_vertices(graph)`
+   *     a property map containing for each vertex of `graph` a unique index between `0` and `num_vertices(graph)-1`
    *   \cgalParamEnd
    *   \cgalParamBegin{halfedge_index_map}
-   *     a property map containing an index for each halfedge initialized 0 to `num_halfedges(graph)`
+   *     a property map containing for each halfedge of `graph` a unique index between `0` and `num_halfedges(graph)-1`
    *   \cgalParamEnd
    * \cgalNamedParamsEnd
    */
   template <typename FacePatchIndexMap, class CGAL_BGL_NP_TEMPLATE_PARAMETERS>
   Face_filtered_graph(const Graph& graph,
-                            typename boost::property_traits<FacePatchIndexMap>::value_type selected_face_patch_index,
-                            FacePatchIndexMap face_patch_index_map,
-                            const CGAL_BGL_NP_CLASS& np
-                             )
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index), get_const_property_map(face_index, graph)))
-    , vimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_index), get_const_property_map(boost::vertex_index, graph)))
-    , himap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::halfedge_index), get_const_property_map(halfedge_index, graph)))
+                      typename boost::property_traits<FacePatchIndexMap>::value_type selected_face_patch_index,
+                      FacePatchIndexMap face_patch_index_map,
+                      const CGAL_BGL_NP_CLASS& np)
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph, np)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
   {
     set_selected_faces(selected_face_patch_index, face_patch_index_map);
   }
 
   template <typename FacePatchIndexMap>
   Face_filtered_graph(const Graph& graph,
-                            typename boost::property_traits<FacePatchIndexMap>::value_type pid,
-                            FacePatchIndexMap face_patch_index_map)
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(get(CGAL::face_index, graph))
-    , vimap(get(boost::vertex_index, graph))
-    , himap(get(CGAL::halfedge_index, graph))
+                      typename boost::property_traits<FacePatchIndexMap>::value_type pid,
+                      FacePatchIndexMap face_patch_index_map)
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph))
   {
     set_selected_faces(pid, face_patch_index_map);
   }
@@ -236,10 +241,10 @@ struct Face_filtered_graph
   Face_filtered_graph(const Graph& graph,
                       const FaceRange& selected_faces,
                       const CGAL_BGL_NP_CLASS& np)
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index), get_const_property_map(face_index, graph)))
-    , vimap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_index), get_const_property_map(boost::vertex_index, graph)))
-    , himap(parameters::choose_parameter(parameters::get_parameter(np, internal_np::halfedge_index), get_const_property_map(halfedge_index, graph)))
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph, np)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
   {
     set_selected_faces(selected_faces);
   }
@@ -247,10 +252,10 @@ struct Face_filtered_graph
   template <typename FaceRange>
   Face_filtered_graph(const Graph& graph,
                       const FaceRange& selected_faces)
-    : _graph(const_cast<Graph&>(graph))
-    , fimap(get(CGAL::face_index, graph))
-    , vimap(get(boost::vertex_index, graph))
-    , himap(get(CGAL::halfedge_index, graph))
+    : _graph(const_cast<Graph&>(graph)),
+      fimap(CGAL::get_initialized_face_index_map(graph)),
+      vimap(CGAL::get_initialized_vertex_index_map(graph)),
+      himap(CGAL::get_initialized_halfedge_index_map(graph))
   {
     set_selected_faces(selected_faces);
   }
@@ -293,12 +298,12 @@ struct Face_filtered_graph
   template<class FacePatchIndexRange, class FacePatchIndexMap>
   void set_selected_faces(const FacePatchIndexRange& selected_face_patch_indices,
                           FacePatchIndexMap face_patch_index_map
-  #ifndef DOXYGEN_RUNNING
+#ifndef DOXYGEN_RUNNING
                           , typename boost::enable_if<
                               typename boost::has_range_const_iterator<FacePatchIndexRange>::type
                             >::type* = 0
-  #endif
-  )
+#endif
+                          )
   {
     face_indices.clear();
     vertex_indices.clear();
@@ -407,7 +412,7 @@ struct Face_filtered_graph
     return selected_halfedges.count();
   }
 
-  Property_map_binder< FIMap, typename Pointer_property_map< typename boost::property_traits< FIMap >::value_type >::type >
+  Property_map_binder<FIM, typename Pointer_property_map<typename boost::property_traits<FIM>::value_type>::type>
   get_face_index_map() const
   {
     if (face_indices.empty())
@@ -422,7 +427,7 @@ struct Face_filtered_graph
     return bind_property_maps(fimap, make_property_map(face_indices) );
   }
 
-  Property_map_binder< VIMap, typename Pointer_property_map< typename boost::property_traits< VIMap >::value_type >::type >
+  Property_map_binder<VIM, typename Pointer_property_map<typename boost::property_traits<VIM>::value_type>::type>
   get_vertex_index_map() const
   {
     if (vertex_indices.empty())
@@ -437,7 +442,7 @@ struct Face_filtered_graph
     return bind_property_maps(vimap, make_property_map(vertex_indices) );
   }
 
-  Property_map_binder< HIMap, typename Pointer_property_map< typename boost::property_traits< HIMap >::value_type >::type >
+  Property_map_binder<HIM, typename Pointer_property_map<typename boost::property_traits<HIM>::value_type >::type>
   get_halfedge_index_map() const
   {
     if (halfedge_indices.empty())
@@ -510,9 +515,9 @@ struct Face_filtered_graph
 
 private:
   Graph& _graph;
-  FIMap fimap;
-  VIMap vimap;
-  HIMap himap;
+  FIM fimap;
+  VIM vimap;
+  HIM himap;
   boost::dynamic_bitset<> selected_faces;
   boost::dynamic_bitset<> selected_vertices;
   boost::dynamic_bitset<> selected_halfedges;
@@ -1142,38 +1147,40 @@ CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(dynamic_face_property_t)
 
 #undef CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION
 
-
-
 //specializations for indices
-template<typename Graph,
-         typename FIMap,
-         typename VIMap,
-         typename HIMap>
-struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, CGAL::face_index_t>{
-  typedef typename CGAL::Property_map_binder< FIMap,
-  typename CGAL::Pointer_property_map< typename boost::property_traits< FIMap >::value_type >::type > type;
-  typedef type const_type;
+template<typename Graph, typename FIMap, typename VIMap, typename HIMap>
+struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, CGAL::face_index_t>
+{
+  typedef typename CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::FIM         FIM;
+  typedef typename CGAL::Property_map_binder<FIM,
+                     typename CGAL::Pointer_property_map<
+                       typename boost::property_traits<FIM>::value_type>::type>       type;
+  typedef type                                                                        const_type;
+};
+
+template<typename Graph, typename FIMap, typename VIMap, typename HIMap>
+struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::vertex_index_t>
+{
+  typedef typename CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::VIM         VIM;
+  typedef typename CGAL::Property_map_binder<VIM,
+                     typename CGAL::Pointer_property_map<
+                       typename boost::property_traits<VIM>::value_type>::type>       type;
+  typedef type                                                                        const_type;
 };
 
 template<typename Graph,
          typename FIMap,
          typename VIMap,
          typename HIMap>
-struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::vertex_index_t>{
-  typedef typename CGAL::Property_map_binder< VIMap,
-  typename CGAL::Pointer_property_map< typename boost::property_traits< VIMap >::value_type >::type > type;
-  typedef type const_type;
+struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, CGAL::halfedge_index_t>
+{
+  typedef typename CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::HIM         HIM;
+  typedef typename CGAL::Property_map_binder<HIM,
+                     typename CGAL::Pointer_property_map<
+                       typename boost::property_traits<HIM>::value_type>::type>       type;
+  typedef type                                                                        const_type;
 };
 
-template<typename Graph,
-         typename FIMap,
-         typename VIMap,
-         typename HIMap>
+} // namespace boost
 
-struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, CGAL::halfedge_index_t>{
-  typedef typename CGAL::Property_map_binder< HIMap,
-  typename CGAL::Pointer_property_map< typename boost::property_traits< HIMap >::value_type >::type > type;
-  typedef type const_type;
-};
-}// namespace boost
 #endif // CGAL_BOOST_GRAPH_FACE_FILTERED_GRAPH_H
diff --git a/BGL/include/CGAL/boost/graph/METIS/partition_dual_graph.h b/BGL/include/CGAL/boost/graph/METIS/partition_dual_graph.h
index 50c0bcf7e37..d11a426b5e1 100644
--- a/BGL/include/CGAL/boost/graph/METIS/partition_dual_graph.h
+++ b/BGL/include/CGAL/boost/graph/METIS/partition_dual_graph.h
@@ -42,17 +42,14 @@ void partition_dual_graph(const TriangleMesh& tm,
   CGAL_precondition(CGAL::is_triangle_mesh(tm));
   CGAL_precondition_msg(nparts > 1, ("Partitioning requires a number of parts > 1"));
 
-  using parameters::choose_parameter;
   using parameters::get_parameter;
 
   typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor   vertex_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::face_iterator       face_iterator;
 
-  // vertex index map
-  typedef typename CGAL::GetVertexIndexMap<TriangleMesh, NamedParameters>::type Indices;
-  Indices indices = choose_parameter(get_parameter(np, internal_np::vertex_index),
-                                 get_const_property_map(boost::vertex_index, tm));
+  typedef typename CGAL::GetInitializedVertexIndexMap<TriangleMesh, NamedParameters>::type Indices;
+  Indices indices = CGAL::get_initialized_vertex_index_map(tm, np);
 
   idx_t nn = static_cast<idx_t>(num_vertices(tm));
   idx_t ne = static_cast<idx_t>(num_faces(tm));
@@ -136,9 +133,6 @@ void partition_dual_graph(const TriangleMesh& tm, int nparts,
 /// based on the mesh's dual graph. The resulting partition is stored in the vertex and/or face
 /// property maps that are passed as parameters using \ref bgl_namedparameters "Named Parameters".
 ///
-/// Property map for `CGAL::vertex_index_t` should be either available
-/// as an internal property map to `tm` or provided as \ref bgl_namedparameters "Named Parameters".
-///
 /// \param tm a triangle mesh
 /// \param nparts the number of parts in the final partition
 /// \param np optional \ref bgl_namedparameters "Named Parameters" described below
@@ -148,7 +142,7 @@ void partition_dual_graph(const TriangleMesh& tm, int nparts,
 ///
 /// \cgalNamedParamsBegin
 ///   \cgalParamBegin{vertex_index_map}
-///     is a property map containing the index of each vertex of `tm` intialized from `0` to `num_vertices(tm)-1`.
+///     is a property map containing for each vertex of `tm` a unique index between `0` and `num_vertices(tm)-1`.
 ///   \cgalParamEnd
 ///   \cgalParamBegin{METIS_options}
 ///     is a parameter used in to pass options to the METIS mesh
diff --git a/BGL/include/CGAL/boost/graph/METIS/partition_graph.h b/BGL/include/CGAL/boost/graph/METIS/partition_graph.h
index ec60ecbc11a..4ef813efcc6 100644
--- a/BGL/include/CGAL/boost/graph/METIS/partition_graph.h
+++ b/BGL/include/CGAL/boost/graph/METIS/partition_graph.h
@@ -77,17 +77,14 @@ void partition_graph(const TriangleMesh& tm,
   CGAL_precondition(CGAL::is_triangle_mesh(tm));
   CGAL_precondition_msg(nparts > 1, ("Partitioning requires a number of parts > 1"));
 
-  using parameters::choose_parameter;
   using parameters::get_parameter;
 
   typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor   vertex_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::face_iterator       face_iterator;
 
-  //Vertex index map
-  typedef typename CGAL::GetVertexIndexMap<TriangleMesh, NamedParameters>::type Indices;
-  Indices indices = choose_parameter(get_parameter(np, internal_np::vertex_index),
-                                 get_const_property_map(boost::vertex_index, tm));
+  typedef typename CGAL::GetInitializedVertexIndexMap<TriangleMesh, NamedParameters>::type Indices;
+  Indices indices = CGAL::get_initialized_vertex_index_map(tm, np);
 
   idx_t nn = static_cast<idx_t>(num_vertices(tm));
   idx_t ne = static_cast<idx_t>(num_faces(tm));
@@ -168,9 +165,6 @@ void partition_graph(const TriangleMesh& tm, int nparts,
 /// mesh's nodal graph. The resulting partition is stored in the vertex and/or face
 /// property maps that are passed as parameters using \ref bgl_namedparameters "Named Parameters".
 ///
-/// Property map for `CGAL::vertex_index_t` should be either available
-/// as an internal property map to `tm` or provided as \ref bgl_namedparameters "Named Parameters".
-///
 /// \param tm a triangle mesh
 /// \param nparts the number of parts in the final partition
 /// \param np optional \ref bgl_namedparameters "Named Parameters" described below
@@ -180,7 +174,7 @@ void partition_graph(const TriangleMesh& tm, int nparts,
 ///
 /// \cgalNamedParamsBegin
 ///   \cgalParamBegin{vertex_index_map}
-///     is a property map containing the index of each vertex of `tm` intialized from `0` to `num_vertices(tm)-1`.
+///     is a property map containing for each vertex of `tm` a unique index between `0` and `num_vertices(tm)-1`.
 ///   \cgalParamEnd
 ///   \cgalParamBegin{METIS_options}
 ///     is a parameter used in to pass options to the METIS mesh
diff --git a/BGL/include/CGAL/boost/graph/Seam_mesh.h b/BGL/include/CGAL/boost/graph/Seam_mesh.h
index 33a995dba43..07ed312307f 100644
--- a/BGL/include/CGAL/boost/graph/Seam_mesh.h
+++ b/BGL/include/CGAL/boost/graph/Seam_mesh.h
@@ -124,8 +124,8 @@ public:
   /// The type for the objects used to identify halfedges in the underlying mesh.
   typedef typename boost::graph_traits<TM>::halfedge_descriptor   TM_halfedge_descriptor;
 
- /// The type for the iterators that traverse through the complete halfedge set of the underlying mesh.
- typedef typename boost::graph_traits<TM>::halfedge_iterator     TM_halfedge_iterator;
+  /// The type for the iterators that traverse through the complete halfedge set of the underlying mesh.
+  typedef typename boost::graph_traits<TM>::halfedge_iterator     TM_halfedge_iterator;
 
   /// The type for the objects used to identify edges in the underlying mesh.
   typedef typename boost::graph_traits<TM>::edge_descriptor       TM_edge_descriptor;
@@ -439,6 +439,11 @@ public:
     {
       return ! (e1 == e2);
     }
+
+    friend std::size_t hash_value(const edge_descriptor& ed)
+    {
+      return hash_value((std::min)(ed.hd, ed.mesh_->opposite(ed.hd)));
+    }
   };
 
 #ifndef DOXYGEN_RUNNING
diff --git a/BGL/include/CGAL/boost/graph/copy_face_graph.h b/BGL/include/CGAL/boost/graph/copy_face_graph.h
index 5eafa161533..4e0dc04cd93 100644
--- a/BGL/include/CGAL/boost/graph/copy_face_graph.h
+++ b/BGL/include/CGAL/boost/graph/copy_face_graph.h
@@ -199,13 +199,8 @@ void copy_face_graph(const SourceMesh& sm, TargetMesh& tm,
   typedef typename boost::graph_traits<TargetMesh>::halfedge_descriptor tm_halfedge_descriptor;
   std::vector<tm_halfedge_descriptor> hedges(num_halfedges(sm));
 
-  // init halfedge index map
-  /// \TODO shall we keep that?
-  helpers::init_halfedge_indices(const_cast<SourceMesh&>(sm),
-                                 get(boost::halfedge_index, sm));
-
   copy_face_graph_impl(sm, tm,
-                       bind_property_maps(get(boost::halfedge_index, sm),
+                       bind_property_maps(get_initialized_halfedge_index_map(sm),
                                           make_property_map(hedges)),
                        v2v, h2h, f2f,
                        sm_vpm, tm_vpm);
diff --git a/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h b/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h
new file mode 100644
index 00000000000..e392ff064a0
--- /dev/null
+++ b/BGL/include/CGAL/boost/graph/internal/initialized_index_maps_helpers.h
@@ -0,0 +1,307 @@
+// Copyright (c) 2020 GeometryFactory (France).  All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org)
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
+// 
+// Author(s) : Mael Rouxel-Labbé
+//             Maxime Gimeno
+
+#ifndef CGAL_BOOST_GRAPH_INITIALIZED_INTERNAL_INDEX_MAPS_HELPERS
+#define CGAL_BOOST_GRAPH_INITIALIZED_INTERNAL_INDEX_MAPS_HELPERS
+
+#include <CGAL/assertions.h>
+#include <CGAL/boost/graph/Named_function_parameters.h>
+#include <CGAL/boost/graph/properties.h>
+#include <CGAL/Dynamic_property_map.h>
+#include <CGAL/use.h>
+
+#include <vector>
+#include <type_traits>
+
+namespace CGAL {
+namespace BGL {
+namespace internal {
+
+// Check that an index map has been correctly initialized
+template <typename DescriptorRange, typename IndexMap>
+bool is_index_map_valid(IndexMap idmap,
+                        const std::size_t num_simplices,
+                        const DescriptorRange& range)
+{
+  typedef typename boost::property_traits<IndexMap>::value_type Id_type;
+
+  Id_type max_id = static_cast<Id_type>(num_simplices);
+  std::vector<bool> indices(max_id);
+  for(const auto& d : range)
+  {
+    const Id_type id = get(idmap, d);
+    if(id >= 0 && id < max_id && !indices[id])
+    {
+      indices[id] = true;
+    }
+    else
+    {
+#ifdef CGAL_BGL_INDEX_MAP_DEBUG
+      std::cerr << "Invalid ID: " << id << " num_simplices: " << num_simplices << std::endl;
+#endif
+      return false;
+    }
+  }
+
+  return true;
+}
+
+template <typename VertexIndexPropertyMap, typename Graph>
+bool is_index_map_valid(const CGAL::internal_np::vertex_index_t, VertexIndexPropertyMap vertex_index_map, const Graph& g)
+{
+  return is_index_map_valid(vertex_index_map, num_vertices(g), vertices(g));
+}
+
+template <typename HalfedgeIndexPropertyMap, typename Graph>
+bool is_index_map_valid(const CGAL::internal_np::halfedge_index_t, HalfedgeIndexPropertyMap halfedge_index_map, const Graph& g)
+{
+  return is_index_map_valid(halfedge_index_map, num_halfedges(g), halfedges(g));
+}
+
+template <typename EdgeIndexPropertyMap, typename Graph>
+bool is_index_map_valid(const CGAL::internal_np::edge_index_t, EdgeIndexPropertyMap edge_index_map, const Graph& g)
+{
+  return is_index_map_valid(edge_index_map, num_edges(g), edges(g));
+}
+
+template <typename FaceIndexPropertyMap, typename Graph>
+bool is_index_map_valid(const CGAL::internal_np::face_index_t, FaceIndexPropertyMap face_index_map, const Graph& g)
+{
+  return is_index_map_valid(face_index_map, num_faces(g), faces(g));
+}
+
+template <typename PropertyTag, typename IndexPropertyMap, typename Graph>
+void initialize_index_map(const PropertyTag, IndexPropertyMap, const Graph&)
+{
+  // Unknown parameter; should never be here.
+  CGAL_assertion(false);
+}
+
+template <typename IndexPropertyMap,
+          typename Graph,
+          bool is_writable = CGAL::internal::Is_writable_property_map<IndexPropertyMap>::value>
+struct Index_map_initializer
+{
+  void operator()(const CGAL::internal_np::vertex_index_t, IndexPropertyMap vertex_index_map, const Graph& g)
+  {
+    typename boost::property_traits<IndexPropertyMap>::value_type i = 0;
+    for(typename boost::graph_traits<Graph>::vertex_descriptor vd : vertices(g))
+      put(vertex_index_map, vd, i++);
+  }
+
+  void operator()(const CGAL::internal_np::halfedge_index_t, IndexPropertyMap halfedge_index_map, const Graph& g)
+  {
+    typename boost::property_traits<IndexPropertyMap>::value_type i = 0;
+    for(typename boost::graph_traits<Graph>::halfedge_descriptor hd : halfedges(g))
+      put(halfedge_index_map, hd, i++);
+  }
+
+  void operator()(const CGAL::internal_np::edge_index_t, IndexPropertyMap edge_index_map, const Graph& g)
+  {
+    typename boost::property_traits<IndexPropertyMap>::value_type i = 0;
+    for(typename boost::graph_traits<Graph>::edge_descriptor ed : edges(g))
+      put(edge_index_map, ed, i++);
+  }
+
+  void operator()(const CGAL::internal_np::face_index_t, IndexPropertyMap face_index_map, const Graph& g)
+  {
+    typename boost::property_traits<IndexPropertyMap>::value_type i = 0;
+    for(typename boost::graph_traits<Graph>::face_descriptor fd : faces(g))
+      put(face_index_map, fd, i++);
+  }
+
+  template <typename PropertyTag>
+  void operator()(const PropertyTag, IndexPropertyMap, const Graph&)
+  {
+    // Unknown parameter; should never be here.
+    CGAL_assertion(false);
+  }
+};
+
+template <typename IndexPropertyMap, typename Graph>
+struct Index_map_initializer<IndexPropertyMap, Graph, false>
+{
+  template <typename PropertyTag>
+  void operator()(const PropertyTag, IndexPropertyMap, const Graph&)
+  {
+    // The property map is not writable; should never be here.
+    CGAL_assertion_msg(false, "You are trying to initialize a non-writable property map");
+  }
+};
+
+// Just for convenience, define the following functions:
+//
+// BGL::internal::initialize_vertex_index_map()
+// BGL::internal::initialize_halfedge_index_map()
+// BGL::internal::initialize_edge_index_map()
+// BGL::internal::initialize_face_index_map()
+
+#define CGAL_DEF_INITIALIZE_ID_MAP_FUNCTION(TYPE)                                                  \
+template <typename WritableIndexPropertyMap, typename Graph>                                       \
+void initialize_##TYPE##_index_map(WritableIndexPropertyMap index_map,                             \
+                                   const Graph& g)                                                 \
+{                                                                                                  \
+  Index_map_initializer<WritableIndexPropertyMap, Graph> initializer;                              \
+  initializer(CGAL::internal_np::TYPE##_index_t{}, index_map, g);                                  \
+}
+
+CGAL_DEF_INITIALIZE_ID_MAP_FUNCTION(vertex)
+CGAL_DEF_INITIALIZE_ID_MAP_FUNCTION(halfedge)
+CGAL_DEF_INITIALIZE_ID_MAP_FUNCTION(edge)
+CGAL_DEF_INITIALIZE_ID_MAP_FUNCTION(face)
+
+#undef CGAL_DEF_INITIALIZE_ID_FUCNTION
+
+// Using the pmap passed in named parameters -------------------------------------------------------
+template <typename IndexMap, typename PropertyTag, typename Tag, typename DynamicTag, typename Graph>
+IndexMap get_initialized_index_map_const(const IndexMap index_map,
+                                         const PropertyTag p, Tag, DynamicTag,
+                                         const Graph& g)
+{
+  CGAL_USE(g);
+  CGAL_USE(p);
+
+  // If you are passing a pmap via NPs, it must be initialized
+  CGAL_assertion(is_index_map_valid(p, index_map, g));
+
+  return index_map;
+}
+
+template <typename IndexMap, typename PropertyTag, typename Tag, typename DynamicTag, typename Graph>
+IndexMap get_initialized_index_map(const IndexMap index_map,
+                                   const PropertyTag p, Tag, DynamicTag,
+                                   Graph& g)
+{
+  CGAL_USE(g);
+  CGAL_USE(p);
+
+  // If you are passing a pmap via NPs, it must be initialized
+  CGAL_assertion(is_index_map_valid(p, index_map, g));
+
+  return index_map;
+}
+
+// Using the internal to the mesh ------------------------------------------------------------------
+template <typename InternalIndexMap, typename PropertyTag, typename Graph>
+InternalIndexMap
+get_initialized_internal_index_map(InternalIndexMap index_map,
+                                   const PropertyTag p,
+                                   const Graph& g)
+{
+  if(CGAL::internal::Is_writable_property_map<InternalIndexMap>::value)
+  {
+    if(!is_index_map_valid(p, index_map, g))
+      Index_map_initializer<InternalIndexMap, Graph>{}(p, index_map, g);
+  }
+  else // not writable
+  {
+    CGAL_assertion(is_index_map_valid(p, index_map, g));
+  }
+
+  return index_map;
+}
+
+template <typename PropertyTag, typename Tag, typename DynamicTag, typename Graph>
+typename boost::property_map<Graph, Tag>::const_type
+get_initialized_index_map_const(CGAL::internal_np::Param_not_found,
+                                const PropertyTag p, const Tag tag, DynamicTag,
+                                const Graph& g)
+{
+  return get_initialized_internal_index_map(get(tag, g), p, g);
+}
+
+// same as above, non-const graph overload
+template <typename PropertyTag, typename Tag, typename DynamicTag, typename Graph>
+typename boost::property_map<Graph, Tag>::type
+get_initialized_index_map(CGAL::internal_np::Param_not_found,
+                          const PropertyTag p, const Tag tag, DynamicTag,
+                          Graph& g)
+{
+  // From now on the correct property map has been acquired
+  // and there is no need to distinguish between const and non-const mesh
+  return get_initialized_internal_index_map(get(tag, g), p, g);
+}
+
+// Create a dynamic property and initialize it -----------------------------------------------------
+template <typename DynamicIndexMap, typename PropertyTag, typename Graph>
+DynamicIndexMap
+get_initialized_dynamic_index_map(DynamicIndexMap index_map,
+                                  const PropertyTag p,
+                                  const Graph& g)
+{
+#ifdef CGAL_PERFORMANCE_WARNINGS
+  std::cerr << "Warning: the automatically selected index map is a dynamic property map,"
+            << " which might not have constant-time access complexity." << std::endl;
+#endif
+
+  Index_map_initializer<DynamicIndexMap, Graph>{}(p, index_map, g);
+  return index_map;
+}
+
+template <typename PropertyTag, typename DynamicTag, typename Graph>
+typename boost::property_map<Graph, DynamicTag>::const_type
+get_initialized_index_map_const(CGAL::internal_np::Param_not_found,
+                                const PropertyTag p, const DynamicTag dtag, DynamicTag,
+                                const Graph& g)
+{
+  return get_initialized_dynamic_index_map(get(dtag, g), p, g);
+}
+
+// same as above, non-const graph overload
+template <typename PropertyTag, typename DynamicTag, typename Graph>
+typename boost::property_map<Graph, DynamicTag>::type
+get_initialized_index_map(CGAL::internal_np::Param_not_found,
+                          const PropertyTag p, const DynamicTag dtag, DynamicTag,
+                          Graph& g)
+{
+  // From now on the correct property map has been acquired
+  // and there is no need to distinguish between const and non-const mesh
+  return get_initialized_dynamic_index_map(get(dtag, g), p, g);
+}
+
+template <typename PropertyTag, typename Tag, typename DynamicTag,
+          typename Graph,
+          typename NamedParameters = Named_function_parameters<bool, internal_np::all_default_t> >
+class GetInitializedIndexMap
+{
+public:
+  // Check if there is an internal property map; if not, we must a dynamic property map
+  typedef typename boost::mpl::if_c<
+      CGAL::graph_has_property<Graph, Tag>::value, Tag, DynamicTag>::type    Final_tag;
+
+  typedef typename internal_np::Lookup_named_param_def<
+      PropertyTag,
+      NamedParameters,
+      typename boost::property_map<Graph, Final_tag>::const_type>::type      const_type;
+
+  typedef typename internal_np::Lookup_named_param_def<
+      PropertyTag,
+      NamedParameters,
+      typename boost::property_map<Graph, Final_tag>::type>::type            type;
+
+  static const_type get_const(const PropertyTag p, const Graph& g, const NamedParameters& np)
+  {
+    return BGL::internal::get_initialized_index_map_const(parameters::get_parameter(np, p),
+                                                          p, Final_tag{}, DynamicTag{}, g);
+  }
+
+  static type get(const PropertyTag p, Graph& g, const NamedParameters& np)
+  {
+    return BGL::internal::get_initialized_index_map(parameters::get_parameter(np, p),
+                                                    p, Final_tag{}, DynamicTag{}, g);
+  }
+};
+
+} // namespace internal
+} // namespace BGL
+} // namespace CGAL
+
+#endif // CGAL_BOOST_GRAPH_INITIALIZED_INTERNAL_INDEX_MAPS_HELPERS
diff --git a/BGL/include/CGAL/boost/graph/io.h b/BGL/include/CGAL/boost/graph/io.h
index f8e91ea49c2..dd41b28a65f 100644
--- a/BGL/include/CGAL/boost/graph/io.h
+++ b/BGL/include/CGAL/boost/graph/io.h
@@ -417,13 +417,9 @@ write_polys(std::ostream& os,
 {
   typedef typename boost::graph_traits<Mesh>::vertex_descriptor vertex_descriptor;
   typedef typename boost::graph_traits<Mesh>::face_iterator face_iterator;
-  typedef typename CGAL::GetVertexIndexMap<Mesh, NamedParameters>::type Vimap;
 
-  using parameters::get_parameter;
-  using parameters::choose_parameter;
-
-  Vimap V = choose_parameter(get_parameter(np, internal_np::vertex_index),
-                             get_const_property_map(boost::vertex_index, mesh));
+  typedef typename CGAL::GetInitializedVertexIndexMap<Mesh, NamedParameters>::const_type Vimap;
+  Vimap V = CGAL::get_initialized_vertex_index_map(mesh, np);
 
   std::vector<std::size_t> connectivity_table;
   std::vector<std::size_t> offsets;
@@ -456,13 +452,9 @@ write_polys_tag(std::ostream& os,
 {
   typedef typename boost::graph_traits<Mesh>::vertex_descriptor vertex_descriptor;
   typedef typename boost::graph_traits<Mesh>::face_iterator face_iterator;
-  typedef typename CGAL::GetVertexIndexMap<Mesh, NamedParameters>::type Vimap;
 
-  using parameters::get_parameter;
-  using parameters::choose_parameter;
-
-  Vimap V = choose_parameter(get_parameter(np, internal_np::vertex_index),
-                             get_const_property_map(boost::vertex_index, mesh));
+  typedef typename CGAL::GetInitializedVertexIndexMap<Mesh, NamedParameters>::const_type Vimap;
+  Vimap V = CGAL::get_initialized_vertex_index_map(mesh, np);
 
   std::string formatattribute =
     binary ? " format=\"appended\"" : " format=\"ascii\"";
@@ -638,8 +630,7 @@ write_polys_points(std::ostream& os,
  *       `CGAL::vertex_point_t` must be available in `TriangleMesh`.
  *     \cgalParamEnd
  *    \cgalParamBegin{vertex_index_map} the property map with the indices associated to
- * the vertices of `mesh`. If this parameter is omitted, an internal property map for
- *       `CGAL::vertex_index_t` must be available in `TriangleMesh`.
+ * the vertices of `mesh`.
  *     \cgalParamEnd
  * \cgalNamedParamsEnd
  */
diff --git a/BGL/include/CGAL/boost/graph/named_params_helper.h b/BGL/include/CGAL/boost/graph/named_params_helper.h
index 4c432a311c6..297c93e0f18 100644
--- a/BGL/include/CGAL/boost/graph/named_params_helper.h
+++ b/BGL/include/CGAL/boost/graph/named_params_helper.h
@@ -19,18 +19,19 @@
 #ifndef CGAL_BOOST_GRAPH_NAMED_PARAMETERS_HELPERS_H
 #define CGAL_BOOST_GRAPH_NAMED_PARAMETERS_HELPERS_H
 
+#include <CGAL/boost/graph/internal/initialized_index_maps_helpers.h>
 #include <CGAL/boost/graph/Named_function_parameters.h>
-
+#include <CGAL/boost/graph/properties.h>
+#include <CGAL/Dynamic_property_map.h>
 #include <CGAL/Kernel_traits.h>
 #include <CGAL/Origin.h>
-
 #include <CGAL/property_map.h>
-#include <CGAL/boost/graph/properties.h>
+
 #include <boost/mpl/if.hpp>
 #include <boost/mpl/has_xxx.hpp>
-
 #include <boost/type_traits/is_same.hpp>
 
+#include <type_traits>
 
 namespace CGAL {
 
@@ -40,8 +41,8 @@ namespace CGAL {
   class Eigen_svd;
   class Lapack_svd;
   //
-  
-  
+
+
   //helper classes
   template<typename PolygonMesh, typename PropertyTag>
   class property_map_selector
@@ -104,7 +105,8 @@ namespace CGAL {
     property_map_selector<PolygonMesh, PropertyTag> pms;
     return pms.get_const_pmap(p, pmesh);
   }
-// shortcut for accessing the value type of the property map
+
+  // Shortcut for accessing the value type of the property map
   template <class Graph, class Property>
   class property_map_value {
     typedef typename boost::property_map<Graph, Property>::const_type PMap;
@@ -175,37 +177,105 @@ namespace CGAL {
     > ::type  type;
   };
 
-  template<typename PolygonMesh, typename NamedParameters>
-  class GetFaceIndexMap
-  {
-    typedef typename property_map_selector<PolygonMesh, boost::face_index_t>::type DefaultMap;
-    typedef typename property_map_selector<PolygonMesh, boost::face_index_t>::const_type DefaultMap_const;
-  public:
-    typedef typename internal_np::Lookup_named_param_def <
-    internal_np::face_index_t,
-    NamedParameters,
-    DefaultMap
-    > ::type  type;
-    typedef typename internal_np::Lookup_named_param_def <
-      internal_np::face_index_t,
-      NamedParameters,
-      DefaultMap_const
-      > ::type  const_type;
-    typedef typename boost::is_same<type, DefaultMap>::type Is_internal_map;
-    typedef typename boost::is_same<const_type, DefaultMap_const>::type Is_internal_map_const;
-  };
+// Define the following structs:
+//
+// GetInitializedVertexIndexMap
+// GetInitializedHalfedgeIndexMap
+// GetInitializedEdgeIndexMap
+// GetInitializedFaceIndexMap
 
-  template<typename PolygonMesh, typename NamedParameters>
-  class GetVertexIndexMap
-  {
-    typedef typename property_map_selector<PolygonMesh, boost::vertex_index_t>::type DefaultMap;
-  public:
-    typedef typename internal_np::Lookup_named_param_def <
-    internal_np::vertex_index_t,
-    NamedParameters,
-    DefaultMap
-    > ::type  type;
-  };
+#define CGAL_DEF_GET_INDEX_TYPE(CTYPE, DTYPE, STYPE)                                               \
+template <typename Graph,                                                                          \
+          typename NamedParameters =                                                               \
+            CGAL::Named_function_parameters<bool, CGAL::internal_np::all_default_t> >              \
+struct GetInitialized##CTYPE##IndexMap                                                             \
+  : public BGL::internal::GetInitializedIndexMap<internal_np::DTYPE##_index_t,                     \
+                                                 boost::DTYPE##_index_t,                           \
+                                                 CGAL::dynamic_##DTYPE##_property_t<STYPE>,        \
+                                                 Graph, NamedParameters>                           \
+{ };
+
+CGAL_DEF_GET_INDEX_TYPE(Vertex, vertex, typename boost::graph_traits<Graph>::vertices_size_type)
+CGAL_DEF_GET_INDEX_TYPE(Halfedge, halfedge, typename boost::graph_traits<Graph>::halfedges_size_type)
+CGAL_DEF_GET_INDEX_TYPE(Edge, edge, typename boost::graph_traits<Graph>::edges_size_type)
+CGAL_DEF_GET_INDEX_TYPE(Face, face, typename boost::graph_traits<Graph>::faces_size_type)
+
+#undef CGAL_DEF_GET_INDEX_TYPE
+
+// Define the following functions:
+//
+// get_initialized_vertex_index_map()
+// get_initialized_halfedge_index_map()
+// get_initialized_edge_index_map()
+// get_initialized_face_index_map()
+//
+// The function returns:
+// - the index property map passed in the NPs, if passed in the NPs; it must be initialized by the user;
+// - the internal index property map if it is the graph has one. It is initialized if needed and possible;
+// - an initialized dynamic pmap otherwise.
+
+#define CGAL_DEF_GET_INITIALIZED_INDEX_MAP(DTYPE, STYPE)                                           \
+template <typename Graph,                                                                          \
+          typename NamedParameters>                                                                \
+typename BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                 \
+                                               boost::DTYPE##_index_t,                             \
+                                               CGAL::dynamic_##DTYPE##_property_t<STYPE>,          \
+                                               Graph, NamedParameters>::const_type                 \
+get_initialized_##DTYPE##_index_map(const Graph& g,                                                \
+                                   const NamedParameters& np)                                      \
+{                                                                                                  \
+  typedef BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                \
+                                                boost::DTYPE##_index_t,                            \
+                                                CGAL::dynamic_##DTYPE##_property_t<STYPE>,         \
+                                                Graph, NamedParameters>          Index_map_getter; \
+  return Index_map_getter::get_const(CGAL::internal_np::DTYPE##_index_t{}, g, np);                 \
+}                                                                                                  \
+template <typename Graph>                                                                          \
+typename BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                 \
+                                               boost::DTYPE##_index_t,                             \
+                                               CGAL::dynamic_##DTYPE##_property_t<STYPE>,          \
+                                               Graph>::const_type                                  \
+get_initialized_##DTYPE##_index_map(const Graph& g)                                                \
+{                                                                                                  \
+  return get_initialized_##DTYPE##_index_map(g, CGAL::parameters::all_default());                  \
+}                                                                                                  \
+/* same as above, non-const version*/                                                              \
+template <typename Graph,                                                                          \
+          typename NamedParameters,                                                                \
+          /*otherwise compilers will try to use 'Graph := const PM' and things will go badly*/     \
+          std::enable_if_t<                                                                        \
+            !std::is_const<typename std::remove_reference<Graph>::type>::value, int> = 0>          \
+typename BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                 \
+                                               boost::DTYPE##_index_t,                             \
+                                               CGAL::dynamic_##DTYPE##_property_t<STYPE>,          \
+                                               Graph, NamedParameters>::type                       \
+get_initialized_##DTYPE##_index_map(Graph& g,                                                      \
+                                   const NamedParameters& np)                                      \
+{                                                                                                  \
+  typedef BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                \
+                                                boost::DTYPE##_index_t,                            \
+                                                CGAL::dynamic_##DTYPE##_property_t<STYPE>,         \
+                                                Graph, NamedParameters>          Index_map_getter; \
+  return Index_map_getter::get(CGAL::internal_np::DTYPE##_index_t{}, g, np);                       \
+}                                                                                                  \
+template <typename Graph,                                                                          \
+          std::enable_if_t<                                                                        \
+            !std::is_const<typename std::remove_reference<Graph>::type>::value, int> = 0>          \
+typename BGL::internal::GetInitializedIndexMap<CGAL::internal_np::DTYPE##_index_t,                 \
+                                               boost::DTYPE##_index_t,                             \
+                                               CGAL::dynamic_##DTYPE##_property_t<STYPE>,          \
+                                               Graph>::type                                        \
+get_initialized_##DTYPE##_index_map(Graph& g)                                                      \
+{                                                                                                  \
+  return get_initialized_##DTYPE##_index_map(g, CGAL::parameters::all_default());                  \
+}
+
+CGAL_DEF_GET_INITIALIZED_INDEX_MAP(vertex, typename boost::graph_traits<Graph>::vertices_size_type)
+CGAL_DEF_GET_INITIALIZED_INDEX_MAP(halfedge, typename boost::graph_traits<Graph>::halfedges_size_type)
+CGAL_DEF_GET_INITIALIZED_INDEX_MAP(edge, typename boost::graph_traits<Graph>::edges_size_type)
+CGAL_DEF_GET_INITIALIZED_INDEX_MAP(face, typename boost::graph_traits<Graph>::faces_size_type)
+
+#undef CGAL_DEF_GET_INITIALIZED_INDEX_MAP
 
   template<typename PolygonMesh, typename NamedParameters>
   class GetFaceNormalMap
@@ -244,7 +314,7 @@ namespace CGAL {
         typedef std::random_access_iterator_tag iterator_category;
       };
     };
-    
+
     namespace parameters
     {
       template <typename PointRange>
@@ -258,7 +328,7 @@ namespace CGAL {
     namespace internal{
       BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(Has_nested_type_iterator, iterator, false)
     }
-    
+
     template<typename PointRange, typename NamedParameters,
              bool has_nested_iterator=internal::Has_nested_type_iterator<PointRange>::value>
     class GetPointMap
@@ -380,7 +450,7 @@ namespace CGAL {
       DefaultPMap
       > ::type  const_type;
     };
-    
+
     template<typename NamedParameters>
     class GetPlaneIndexMap
     {
@@ -428,7 +498,7 @@ namespace CGAL {
     };
 
   } // namespace Point_set_processing_3
-  
+
   template<typename NamedParameters, typename DefaultSolver>
   class GetSolver
   {
@@ -461,10 +531,10 @@ namespace CGAL {
       typedef int Matrix;
       static FT solve (const Matrix&, Vector&) { return 0.; }
     };
-    
+
   public:
     typedef DummySvdTraits NoTraits;
-    
+
     typedef typename internal_np::Lookup_named_param_def <
     internal_np::svd_traits_t,
     NamedParameters,
@@ -477,6 +547,7 @@ namespace CGAL {
 #endif
     > ::type type;
   };
+
 } //namespace CGAL
 
 
diff --git a/BGL/include/CGAL/boost/graph/parameters_interface.h b/BGL/include/CGAL/boost/graph/parameters_interface.h
index ebdce042e75..a65e2d99f07 100644
--- a/BGL/include/CGAL/boost/graph/parameters_interface.h
+++ b/BGL/include/CGAL/boost/graph/parameters_interface.h
@@ -93,7 +93,8 @@ CGAL_add_named_parameter(get_placement_policy_t, get_placement_policy, get_place
 //to be documented
 CGAL_add_named_parameter(face_normal_t, face_normal, face_normal_map)
 CGAL_add_named_parameter(random_seed_t, random_seed, random_seed)
-CGAL_add_named_parameter(tolerance_map_t, tolerance_map, tolerance_map)
+CGAL_add_named_parameter(do_lock_mesh_t, do_lock_mesh, do_lock_mesh)
+CGAL_add_named_parameter(do_simplify_border_t, do_simplify_border, do_simplify_border)
 
 //internal
 CGAL_add_named_parameter(weight_calculator_t, weight_calculator, weight_calculator)
diff --git a/BGL/include/CGAL/boost/graph/properties.h b/BGL/include/CGAL/boost/graph/properties.h
index 6460f9f88e6..589662ce0dc 100644
--- a/BGL/include/CGAL/boost/graph/properties.h
+++ b/BGL/include/CGAL/boost/graph/properties.h
@@ -14,72 +14,45 @@
 #define CGAL_BOOST_GRAPH_BGL_PROPERTIES_H
 
 #include <CGAL/property_map.h>
+#include <CGAL/Dynamic_property_map.h>
+#include <CGAL/basic.h>
+
 #include <boost/graph/properties.hpp>
 #include <boost/graph/graph_traits.hpp>
-#include <boost/type_traits/is_const.hpp>
-#include <boost/type_traits/remove_reference.hpp>
-#include <CGAL/Dynamic_property_map.h>
 
-#include <CGAL/basic.h>
 #include <string>
+#include <vector>
+#include <type_traits>
+
+namespace CGAL {
 
-namespace CGAL{
-/// \ingroup PkgBGLProperties
-/// \brief graph_has_property is used to indicate if
-/// a model of `HalfedgeGraph` or `FaceGraph`
-/// has an internal property associated with the
-/// given `PropertyTag`.
-///
-/// It inherits from `CGAL::Tag_true` if there is a
-/// default internal property map for the
-/// corresponding property tag and from
-/// `CGAL::Tag_false` otherwise.
-///
-/// \tparam Graph a model of `HalfedgeGraph` or `FaceGraph`
-/// \tparam PropertyTag the type of a property tag
-/// referring to the property of interest.
-///
 template<typename Graph, typename PropertyTag>
-struct graph_has_property
-#ifndef DOXYGEN_RUNNING
-    : CGAL::Tag_false
-#endif
-{};
-}
-/// Boost Namespace
+struct graph_has_property : CGAL::Tag_false { };
+
+} // namespace CGAL
+
 namespace boost {
 
-/// \ingroup PkgBGLProperties
-/// @{
-
-/// A property tag which refers to the geometric embedding property
-/// of a vertex of a \ref HalfedgeGraph.
 enum vertex_point_t          { vertex_point          };
-enum vertex_external_index_t { vertex_external_index } ;
 
-/// A property tag which refers to the property
-/// of a halfedge of being a border halfedge.
-enum edge_external_index_t   { edge_external_index   } ;
+// vertex_index_t is defined in boost
+enum vertex_external_index_t { vertex_external_index };
 
-/// A property tag which identifies the *index* property of
-/// a halfedge of a \ref HalfedgeGraph.
-enum halfedge_index_t        { halfedge_index        };
-enum halfedge_external_index_t   { halfedge_external_index   } ;
+enum halfedge_index_t          { halfedge_index };
+enum halfedge_external_index_t { halfedge_external_index };
+
+// edge_index_t is defined in boost
+enum edge_external_index_t   { edge_external_index   };
 
-/// A property tag which identifies the *index* property of
-/// a face of a \ref FaceGraph.
 enum face_index_t            { face_index            };
-enum face_external_index_t   { face_external_index   } ;
+enum face_external_index_t   { face_external_index   };
 
-  
 struct cgal_no_property
 {
   typedef bool type;
   typedef const bool const_type;
 };
 
-/// @}
-
 // Introduce those two tags so we can use BOOST_INSTALL_PROPERTY
 // macro. This is dangerous because we now rely on implementation
 // details.
@@ -97,12 +70,16 @@ BOOST_INSTALL_PROPERTY(face, external_index);
 namespace CGAL {
 using boost::vertex_point_t;
 using boost::vertex_point;
+using boost::vertex_index_t;
+using boost::vertex_index;
 using boost::vertex_external_index_t;
 using boost::vertex_external_index;
 using boost::halfedge_index_t;
 using boost::halfedge_index;
 using boost::halfedge_external_index_t;
 using boost::halfedge_external_index;
+using boost::edge_index_t;
+using boost::edge_index;
 using boost::edge_external_index_t;
 using boost::edge_external_index;
 using boost::face_index_t;
@@ -111,128 +88,7 @@ using boost::face_external_index_t;
 using boost::face_external_index;
 } // CGAL
 
-namespace CGAL{
-namespace helpers {
-
-// matches read-write property maps
-template <class PolygonMesh, class FaceIndexMap, class Tag>
-void init_face_indices(PolygonMesh& pm,
-                       FaceIndexMap& fid,
-                       boost::read_write_property_map_tag,
-                       Tag)
-{
-  typename boost::property_traits<FaceIndexMap>::value_type i = 0;
-  for(typename boost::graph_traits<PolygonMesh>::face_descriptor fd :
-                faces(pm))
-  {
-    put(fid, fd, i);
-    ++i;
-  }
-}
-template <class PolygonMesh, class VertexIndexMap, class Tag>
-void init_vertex_indices(PolygonMesh& pm,
-                         VertexIndexMap& vid,
-                         boost::read_write_property_map_tag,
-                         Tag)
-{
-  typename boost::property_traits<VertexIndexMap>::value_type i = 0;
-  for(typename boost::graph_traits<PolygonMesh>::vertex_descriptor vd :
-                vertices(pm))
-  {
-    put(vid, vd, i);
-    ++i;
-  }
-}
-template <class PolygonMesh, class HalfedgeIndexMap, class Tag>
-void init_halfedge_indices(PolygonMesh& pm,
-                           HalfedgeIndexMap& hid,
-                           boost::read_write_property_map_tag,
-                           Tag)
-{
-  typename boost::property_traits<HalfedgeIndexMap>::value_type i = 0;
-  for(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor hd :
-                halfedges(pm))
-  {
-    put(hid, hd, i);
-    ++i;
-  }
-}
-
-// matches mutable Lvalue property maps
-template <class PolygonMesh, class FaceIndexMap>
-void init_face_indices(PolygonMesh& pm,
-                       FaceIndexMap& fid,
-                       boost::lvalue_property_map_tag,
-                       boost::false_type)
-{
-  init_face_indices(pm, fid,
-    boost::read_write_property_map_tag(), boost::false_type());
-}
-template <class PolygonMesh, class VertexIndexMap>
-void init_vertex_indices(PolygonMesh& pm,
-                         VertexIndexMap& vid,
-                         boost::lvalue_property_map_tag,
-                         boost::false_type)
-{
-  init_vertex_indices(pm, vid,
-    boost::read_write_property_map_tag(), boost::false_type());
-}
-template <class PolygonMesh, class HalfedgeIndexMap>
-void init_halfedge_indices(PolygonMesh& pm,
-                         HalfedgeIndexMap& hid,
-                         boost::lvalue_property_map_tag,
-                         boost::false_type)
-{
-  init_halfedge_indices(pm, hid,
-    boost::read_write_property_map_tag(), boost::false_type());
-}
-
-// matches all other types of property map
-template <class PolygonMesh, class FaceIndexMap, class MapTag, class Tag>
-void init_face_indices(PolygonMesh&, FaceIndexMap, MapTag, Tag)
-{}
-template <class PolygonMesh, class VertexIndexMap, class MapTag, class Tag>
-void init_vertex_indices(PolygonMesh&, VertexIndexMap, MapTag, Tag)
-{}
-template <class PolygonMesh, class HalfedgeIndexMap, class MapTag, class Tag>
-void init_halfedge_indices(PolygonMesh&, HalfedgeIndexMap, MapTag, Tag)
-{}
-
-template <class PolygonMesh, class FaceIndexMap>
-void init_face_indices(PolygonMesh& pm, FaceIndexMap fid)
-{
-  init_face_indices(pm, fid,
-                    typename boost::property_traits<FaceIndexMap>::category(),
-                    typename boost::is_const<
-                      typename boost::remove_reference<
-                        typename boost::property_traits<FaceIndexMap>::reference
-                            >::type >::type() );
-}
-
-template <class PolygonMesh, class VertexIndexMap>
-void init_vertex_indices(PolygonMesh& pm, VertexIndexMap vid)
-{
-  init_vertex_indices(pm, vid,
-                      typename boost::property_traits<VertexIndexMap>::category(),
-                      typename boost::is_const<
-                        typename boost::remove_reference<
-                          typename boost::property_traits<VertexIndexMap>::reference
-                            >::type >::type() );
-}
-
-template <class PolygonMesh, class HalfedgeIndexMap>
-void init_halfedge_indices(PolygonMesh& pm, HalfedgeIndexMap hid)
-{
-  init_halfedge_indices(pm, hid,
-                        typename boost::property_traits<HalfedgeIndexMap>::category(),
-                        typename boost::is_const<
-                          typename boost::remove_reference<
-                            typename boost::property_traits<HalfedgeIndexMap>::reference
-                              >::type >::type() );
-}
-
-} //namespace helpers
-
+namespace CGAL {
 namespace internal {
   
   template<typename Polyhedron, typename Handle>
@@ -260,8 +116,8 @@ struct Edge_index_accessor
 };
 
 template<typename Handle, typename ValueType, typename Reference,
-         bool is_const = boost::is_const<
-                           typename boost::remove_reference<Reference>::type >::value>
+         bool is_const = std::is_const<
+                           typename std::remove_reference<Reference>::type >::value>
 struct Point_accessor
   : boost::put_get_helper< Reference, Point_accessor<Handle, ValueType, Reference> >
 {
@@ -293,6 +149,32 @@ struct Point_accessor<Handle, ValueType, ConstReference, true>
   reference operator[](Handle h) const { return h->point(); }
 };
 
+// this one is basically 'readable_property_map_tag'
+template <typename PropertyMap,
+          typename PropertyMapCategory = typename boost::property_traits<PropertyMap>::category>
+struct Is_writable_property_map : CGAL::Tag_false { };
+
+template <typename PropertyMap>
+struct Is_writable_property_map<PropertyMap, boost::writable_property_map_tag> : CGAL::Tag_true { };
+
+template <typename PropertyMap>
+struct Is_writable_property_map<PropertyMap, boost::read_write_property_map_tag> : CGAL::Tag_true { };
+
+// 'lvalue_pmap_tag' is annoying, because the property map is allowed to be non-mutable,
+// but boost::lvalue_property_map_tag is defined as:
+//   struct lvalue_property_map_tag : public read_write_property_map_tag
+// so we can't just check that 'writable_property_map_tag' is a base of the the lvalue tag.
+//
+// This checks if the reference is non-const, which is not completely correct: map[key] returning
+// a non-const reference doesn't mean that 'put(map, key, val)' exists, which is what a writable
+// property map must define.
+template <typename PropertyMap>
+struct Is_writable_property_map<PropertyMap, boost::lvalue_property_map_tag>
+  : boost::mpl::if_c<std::is_const<typename std::remove_reference<
+                       typename boost::property_traits<PropertyMap>::reference>::type>::value,
+                     CGAL::Tag_false, CGAL::Tag_true>::type
+{ };
+
 } // namespace internal
 
 // Needed by PMP::detec_features and Mesh_3
@@ -303,12 +185,12 @@ enum vertex_time_stamp_t        { vertex_time_stamp};
 enum halfedge_time_stamp_t      { halfedge_time_stamp};
 enum face_time_stamp_t          { face_time_stamp};
 
-template <typename ID>
+template<typename ID>
 struct vertex_incident_patches_t {
   typedef ID type;
 };
 
-template <typename ID>
+template<typename ID>
 struct face_patch_id_t {
   typedef ID type;
 };
diff --git a/BGL/include/CGAL/boost/graph/properties_Seam_mesh.h b/BGL/include/CGAL/boost/graph/properties_Seam_mesh.h
index 96bf18fa8ab..53acfbce101 100644
--- a/BGL/include/CGAL/boost/graph/properties_Seam_mesh.h
+++ b/BGL/include/CGAL/boost/graph/properties_Seam_mesh.h
@@ -112,6 +112,39 @@ struct property_map<CGAL::Seam_mesh<TM, SEM, SVM>, CGAL::vertex_point_t>
   typedef CGAL::Seam_mesh_point_map<TM, SEM, SVM>        type;
   typedef type                                           const_type;
 };
+
+template <class TM, class SEM, class SVM, typename T>
+struct property_map<CGAL::Seam_mesh<TM, SEM, SVM>, CGAL::dynamic_vertex_property_t<T> >
+{
+  typedef typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::vertex_descriptor vertex_descriptor;
+  typedef CGAL::internal::Dynamic_property_map<vertex_descriptor,T> type;
+  typedef type const_type;
+};
+
+template <class TM, class SEM, class SVM, typename T>
+struct property_map<CGAL::Seam_mesh<TM, SEM, SVM>, CGAL::dynamic_halfedge_property_t<T> >
+{
+  typedef typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::halfedge_descriptor halfedge_descriptor;
+  typedef CGAL::internal::Dynamic_property_map<halfedge_descriptor,T> type;
+  typedef type const_type;
+};
+
+
+template <class TM, class SEM, class SVM, typename T>
+struct property_map<CGAL::Seam_mesh<TM, SEM, SVM>, CGAL::dynamic_edge_property_t<T> >
+{
+  typedef typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::edge_descriptor edge_descriptor;
+  typedef CGAL::internal::Dynamic_property_map<edge_descriptor,T> type;
+  typedef type const_type;
+};
+
+template <class TM, class SEM, class SVM, typename T>
+struct property_map<CGAL::Seam_mesh<TM, SEM, SVM>, CGAL::dynamic_face_property_t<T> >
+{
+  typedef typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::face_descriptor face_descriptor;
+  typedef CGAL::internal::Dynamic_property_map<face_descriptor,T> type;
+  typedef type const_type;
+};
 } // namespace boost
 
 namespace CGAL {
diff --git a/BGL/include/CGAL/boost/graph/selection.h b/BGL/include/CGAL/boost/graph/selection.h
index 769561cd705..ae44f79c0fa 100644
--- a/BGL/include/CGAL/boost/graph/selection.h
+++ b/BGL/include/CGAL/boost/graph/selection.h
@@ -584,26 +584,38 @@ void expand_face_selection_for_removal(const FaceRange& faces_to_be_deleted,
     {
       // collect non-selected faces
       std::vector<halfedge_descriptor> faces_traversed;
+      bool non_selected_face_range_has_boundary = false; // handle non-manifold situations when crossing a border
       do
       {
         faces_traversed.push_back(next_around_vertex);
         next_around_vertex = opposite( next(next_around_vertex, tm), tm);
         if (is_border(next_around_vertex,tm))
+        {
           next_around_vertex = opposite( next(next_around_vertex, tm), tm);
+          if (!get(is_selected, face(next_around_vertex, tm) ))
+          {
+            non_selected_face_range_has_boundary=true; // always non-manifold after removal of the selection
+            break;
+          }
+        }
         CGAL_assertion(!is_border(next_around_vertex,tm));
       }
       while( !get(is_selected, face(next_around_vertex, tm) ) );
 
-      // go over the connected components of faces to remove
-      do{
+      if (!non_selected_face_range_has_boundary)
+      {
+        // go over the connected components of faces to remove
+        do{
+          if (next_around_vertex==start)
+            break;
+          next_around_vertex = opposite( next(next_around_vertex, tm), tm);
+        }
+        while(is_border(next_around_vertex,tm) || get(is_selected, face(next_around_vertex, tm) ) );
+
         if (next_around_vertex==start)
           break;
-        next_around_vertex = opposite( next(next_around_vertex, tm), tm);
       }
-      while(is_border(next_around_vertex,tm) || get(is_selected, face(next_around_vertex, tm) ) );
-
-      if (next_around_vertex==start)
-        break;
+      // else we simply mark the range of traversed faces and start a new range after the border
 
       for(halfedge_descriptor f_hd : faces_traversed)
       {
diff --git a/BGL/test/BGL/data/nm_selection_removal.off b/BGL/test/BGL/data/nm_selection_removal.off
new file mode 100644
index 00000000000..d9a07f81dba
--- /dev/null
+++ b/BGL/test/BGL/data/nm_selection_removal.off
@@ -0,0 +1,18 @@
+OFF
+9 7 0
+0 0 0
+1 0 0
+2 0 0
+2 1 0
+2 2 0
+1 2 0
+0 2 0
+0 1 0
+1 1 0
+3 0 1 8
+3 1 2 8
+3 2 3 8
+3 3 4 8
+3 5 6 8
+3 6 7 8
+3 7 0 8
diff --git a/BGL/test/BGL/test_Euler_operations.cpp b/BGL/test/BGL/test_Euler_operations.cpp
index 7b5439470a8..2edc8060d89 100644
--- a/BGL/test/BGL/test_Euler_operations.cpp
+++ b/BGL/test/BGL/test_Euler_operations.cpp
@@ -402,6 +402,44 @@ test_swap_edges()
   }
 }
 
+template <typename T>
+void
+add_face_bug()
+{
+  typedef boost::graph_traits<T> GT;
+  typedef typename GT::vertex_descriptor vertex_descriptor;
+  typedef typename GT::halfedge_descriptor halfedge_descriptor;
+
+  T g;
+
+  std::vector<vertex_descriptor> vs;
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(0,1,0)
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(4,1,0)
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(5,2,0)
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(4,0,0)
+
+  CGAL::Euler::add_face(CGAL::make_array(vs[0], vs[1], vs[2]), g);
+  CGAL::Euler::add_face(CGAL::make_array(vs[1], vs[3], vs[2]), g);
+
+  // force vertex halfedge to not be a border halfedge
+  for(vertex_descriptor v : vertices(g))
+  {
+    halfedge_descriptor h = halfedge(v, g);
+    if ( CGAL::is_border(h, g) )
+      set_halfedge(v, prev(opposite(h, g), g), g);
+    assert(target(halfedge(v, g), g)==v);
+  }
+
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(0,0,0)
+  vs.push_back( add_vertex(g) );  // Kernel::Point_3(1,0,0)
+  CGAL::Euler::add_face(CGAL::make_array(vs[4],vs[5],vs[0]), g);
+
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(2,0,0)
+  vs.push_back( add_vertex(g) ); // Kernel::Point_3(3,0,0)
+  CGAL::Euler::add_face(CGAL::make_array(vs[6],vs[7],vs[1]), g);
+  CGAL::Euler::add_face(CGAL::make_array(vs[7],vs[3],vs[1]), g);
+}
+
 template <typename Graph>
 void
 test_Euler_operations()
@@ -421,6 +459,7 @@ test_Euler_operations()
   join_split_inverse<Graph>();
   does_satisfy_link_condition<Graph>();
   test_swap_edges<Graph>();
+  add_face_bug<Graph>();
 }
 
 int main()
diff --git a/BGL/test/BGL/test_Face_filtered_graph.cpp b/BGL/test/BGL/test_Face_filtered_graph.cpp
index bbf57e5b2c2..0a579fe96cc 100644
--- a/BGL/test/BGL/test_Face_filtered_graph.cpp
+++ b/BGL/test/BGL/test_Face_filtered_graph.cpp
@@ -491,13 +491,13 @@ int main()
 
 
   typedef boost::graph_traits<Polyhedron> PolyTraits;
-  typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VPMap;
+  typedef boost::property_map<Polyhedron, boost::vertex_point_t>::const_type VPMap;
   typedef PolyTraits::face_descriptor poly_face_descriptor;
   typedef boost::associative_property_map< std::map<poly_face_descriptor,
       PolyTraits::faces_size_type> > FCMap;
-  typedef boost::property_map<Polyhedron, CGAL::face_external_index_t>::type FIMap;
-  typedef boost::property_map<Polyhedron, CGAL::vertex_external_index_t>::type VIMap;
-  typedef boost::property_map<Polyhedron, CGAL::halfedge_external_index_t>::type HIMap;
+  typedef boost::property_map<Polyhedron, CGAL::face_external_index_t>::const_type FIMap;
+  typedef boost::property_map<Polyhedron, CGAL::vertex_external_index_t>::const_type VIMap;
+  typedef boost::property_map<Polyhedron, CGAL::halfedge_external_index_t>::const_type HIMap;
   typedef CGAL::Face_filtered_graph<Polyhedron, FIMap, VIMap, HIMap> Poly_Adapter;
   auto poly = std::make_unique<Polyhedron>();
   CGAL::make_tetrahedron(
@@ -516,14 +516,14 @@ int main()
   FCMap poly_fccmap(fc_map);
 
   VPMap vpmap = get(boost::vertex_point, *poly);
-  CGAL::Polygon_mesh_processing::connected_components(*poly, poly_fccmap, CGAL::Polygon_mesh_processing::parameters::
-                                                      edge_is_constrained_map(Constraint<Polyhedron, VPMap >(*poly, vpmap)).
-                                                      face_index_map(poly_fimap));
+  CGAL::Polygon_mesh_processing::connected_components(*poly, poly_fccmap,
+                                                      CGAL::Polygon_mesh_processing::parameters::edge_is_constrained_map(Constraint<Polyhedron, VPMap >(*poly, vpmap))
+                                                                                                .face_index_map(poly_fimap));
   Poly_Adapter poly_adapter(*poly,
                             pids,
                             poly_fccmap,
-                            CGAL::parameters::face_index_map(poly_fimap).
-                            vertex_index_map(poly_vimap).
-                            halfedge_index_map(poly_himap));
+                            CGAL::parameters::face_index_map(poly_fimap)
+                                             .vertex_index_map(poly_vimap)
+                                             .halfedge_index_map(poly_himap));
   test_mesh<Polyhedron, FCMap, Poly_Adapter>(poly_adapter);
 }
diff --git a/BGL/test/BGL/test_Manifold_face_removal.cpp b/BGL/test/BGL/test_Manifold_face_removal.cpp
index 97ab16b3026..4e5e75dd0c8 100644
--- a/BGL/test/BGL/test_Manifold_face_removal.cpp
+++ b/BGL/test/BGL/test_Manifold_face_removal.cpp
@@ -14,6 +14,68 @@ typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef CGAL::Surface_mesh<Kernel::Point_3> SM;
 typedef boost::graph_traits<SM>::face_descriptor face_descriptor;
 
+void border_cases()
+{
+  SM sm_ref;
+  std::ifstream input("data/nm_selection_removal.off");
+  input >> sm_ref;
+
+  {
+    SM sm = sm_ref;
+    std::vector<SM::Face_index> faces_to_remove;
+    faces_to_remove.push_back(SM::Face_index(5));
+    faces_to_remove.push_back(SM::Face_index(6));
+    SM::Property_map<SM::Face_index, bool> is_selected = sm.add_property_map<SM::Face_index, bool>("f:is_selected", false).first;
+    is_selected[SM::Face_index(5)]=true;
+    is_selected[SM::Face_index(6)]=true;
+    CGAL::expand_face_selection_for_removal(faces_to_remove,
+                                            sm,
+                                            is_selected);
+    int i=0;
+    for(face_descriptor fh : sm.faces())
+      if(!is_selected[fh]) ++i;
+    assert(i==4);
+  }
+
+  {
+    SM sm = sm_ref;
+    std::vector<SM::Face_index> faces_to_remove;
+    faces_to_remove.push_back(SM::Face_index(4));
+    faces_to_remove.push_back(SM::Face_index(6));
+    SM::Property_map<SM::Face_index, bool> is_selected = sm.add_property_map<SM::Face_index, bool>("f:is_selected", false).first;
+    is_selected[SM::Face_index(4)]=true;
+    is_selected[SM::Face_index(6)]=true;
+    CGAL::expand_face_selection_for_removal(faces_to_remove,
+                                            sm,
+                                            is_selected);
+    int i=0;
+    for(face_descriptor fh : sm.faces())
+      if(!is_selected[fh]) ++i;
+
+    assert(i==1 || i==4); // depends on the start point
+  }
+
+  {
+    SM sm = sm_ref;
+    std::vector<SM::Face_index> faces_to_remove;
+    faces_to_remove.push_back(SM::Face_index(4));
+    faces_to_remove.push_back(SM::Face_index(5));
+    faces_to_remove.push_back(SM::Face_index(6));
+    SM::Property_map<SM::Face_index, bool> is_selected = sm.add_property_map<SM::Face_index, bool>("f:is_selected", false).first;
+    is_selected[SM::Face_index(4)]=true;
+    is_selected[SM::Face_index(5)]=true;
+    is_selected[SM::Face_index(6)]=true;
+    CGAL::expand_face_selection_for_removal(faces_to_remove,
+                                            sm,
+                                            is_selected);
+    int i=0;
+    for(face_descriptor fh : sm.faces())
+      if(!is_selected[fh]) ++i;
+    assert(i==4); // depends on the start point
+  }
+
+}
+
 int main()
 {
   SM sm;
@@ -60,6 +122,8 @@ int main()
   assert( sm.number_of_faces()+30 < nb_input_faces);
   assert(is_valid_polygon_mesh(sm));
 
+  border_cases();
+
   return 0;
 }
 
diff --git a/BGL/test/BGL/test_Prefix.h b/BGL/test/BGL/test_Prefix.h
index e5343a10659..4ca383561f1 100644
--- a/BGL/test/BGL/test_Prefix.h
+++ b/BGL/test/BGL/test_Prefix.h
@@ -38,6 +38,7 @@
 #include <CGAL/boost/graph/properties_Constrained_Delaunay_triangulation_2.h>
 #include <CGAL/boost/graph/graph_traits_Constrained_triangulation_plus_2.h>
 #include <CGAL/boost/graph/properties_Constrained_triangulation_plus_2.h>
+#include <CGAL/boost/graph/Seam_mesh.h>
 
 #include <CGAL/boost/graph/io.h>
 
@@ -57,6 +58,10 @@ typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map_helper
 
 typedef CGAL::Surface_mesh<Point_3> SM;
 
+typedef SM::Property_map<SM::Edge_index, bool>                  Seam_edge_pmap;
+typedef SM::Property_map<SM::Vertex_index, bool>                Seam_vertex_pmap;
+typedef CGAL::Seam_mesh<SM, Seam_edge_pmap, Seam_vertex_pmap>   Seam_mesh;
+
 #if defined(CGAL_USE_OPENMESH)
 
 #include <OpenMesh/Core/IO/MeshIO.hh>
@@ -73,6 +78,8 @@ typedef OpenMesh::PolyMesh_ArrayKernelT</* MyTraits*/> OMesh;
 typedef CGAL::Triangulation_vertex_base_with_id_2<Kernel>        Vbb;
 typedef CGAL::Triangulation_face_base_with_id_2<Kernel>          Fbb;
 
+typedef CGAL::Triangulation_2<Kernel>                            Triangulation_no_id_2;
+
 typedef CGAL::Triangulation_2<Kernel,
           CGAL::Triangulation_data_structure_2<Vbb, Fbb> >       Triangulation_2;
 typedef CGAL::Delaunay_triangulation_2<Kernel,
@@ -189,8 +196,6 @@ template <typename Tr>
 Tr build_dummy_triangulation()
 {
   typedef typename Tr::Point                                       Point;
-  typedef typename boost::graph_traits<Tr>::vertex_descriptor      vertex_descriptor;
-  typedef typename boost::graph_traits<Tr>::face_descriptor        face_descriptor;
 
   Tr t;
   t.insert(Point(0.1,0));
@@ -199,24 +204,25 @@ Tr build_dummy_triangulation()
   t.insert(Point(0,1));
   t.insert(Point(0,2));
 
-  int id = 0;
-  for(vertex_descriptor vd : vertices(t))
-    vd->id() = id++;
-
-  id = 0;
-  for(face_descriptor fd : faces(t))
-    fd->id() = id++;
-
   return t;
 }
 
-Triangulation_2 t2_data() { return build_dummy_triangulation<Triangulation_2>(); }
-Delaunay_triangulation_2 dt2_data() { return build_dummy_triangulation<Delaunay_triangulation_2>(); }
-Regular_triangulation_2 rt2_data() { return build_dummy_triangulation<Regular_triangulation_2>(); }
-Constrained_triangulation_2 ct2_data() { return build_dummy_triangulation<Constrained_triangulation_2>(); }
-Constrained_Delaunay_triangulation_2 cdt2_data() { return build_dummy_triangulation<Constrained_Delaunay_triangulation_2>(); }
-CDT_P2 cdtp2_data() { return build_dummy_triangulation<CDT_P2>(); }
-Triangulation_hierarchy_2 t2h_data() { return build_dummy_triangulation<Triangulation_hierarchy_2>(); }
+template <typename Tr>
+Tr build_dummy_triangulation_with_ids()
+{
+  Tr t = build_dummy_triangulation<Tr>();
+  CGAL::set_triangulation_ids(t);
+  return t;
+}
+
+Triangulation_no_id_2 t2_no_id_data() { return build_dummy_triangulation<Triangulation_no_id_2>(); }
+Triangulation_2 t2_data() { return build_dummy_triangulation_with_ids<Triangulation_2>(); }
+Delaunay_triangulation_2 dt2_data() { return build_dummy_triangulation_with_ids<Delaunay_triangulation_2>(); }
+Regular_triangulation_2 rt2_data() { return build_dummy_triangulation_with_ids<Regular_triangulation_2>(); }
+Constrained_triangulation_2 ct2_data() { return build_dummy_triangulation_with_ids<Constrained_triangulation_2>(); }
+Constrained_Delaunay_triangulation_2 cdt2_data() { return build_dummy_triangulation_with_ids<Constrained_Delaunay_triangulation_2>(); }
+CDT_P2 cdtp2_data() { return build_dummy_triangulation_with_ids<CDT_P2>(); }
+Triangulation_hierarchy_2 t2h_data() { return build_dummy_triangulation_with_ids<Triangulation_hierarchy_2>(); }
 
 template <typename Graph>
 struct Surface_fixture_1 {
diff --git a/BGL/test/BGL/test_Properties.cpp b/BGL/test/BGL/test_Properties.cpp
index 3ffd9d1720e..984891b4ca9 100644
--- a/BGL/test/BGL/test_Properties.cpp
+++ b/BGL/test/BGL/test_Properties.cpp
@@ -1,115 +1,459 @@
 #include "test_Prefix.h"
 
+#include <CGAL/boost/graph/Euler_operations.h>
+
 #include <boost/unordered_set.hpp>
 
-template< typename G,
-          typename ForwardRange,
-          typename IndexPropertyMap
-          >
-void index_uniqueness(const G&, 
-                      ForwardRange range,
-                      IndexPropertyMap pm)
+// #define CGAL_TEST_PROPERTIES_DEBUG
+
+namespace CGAL {
+
+template <typename Key, typename Value, typename Container>
+struct Non_mutable_property_map
 {
+  typedef Key                                     key_type;
+  typedef Value                                   value_type;
+  typedef value_type                              reference;
+  typedef boost::readable_property_map_tag        category;
+
+  Non_mutable_property_map(const Container& c) : m_c(c) { }
+
+  friend reference get(const Non_mutable_property_map<Key, Value, Container>& pmap, key_type k)
+  {
+    return pmap.m_c.at(k);
+  }
+
+private:
+  const Container& m_c;
+};
+
+template <typename Key, typename Value, typename Container>
+struct RW_property_map
+{
+  typedef Key                                     key_type;
+  typedef Value                                   value_type;
+  typedef value_type&                             reference;
+  typedef boost::read_write_property_map_tag      category;
+
+  RW_property_map(Container& c) : m_c(c) { }
+
+  friend void put(RW_property_map<Key, Value, Container>& pmap, const key_type& k, const value_type& val)
+  {
+    pmap.m_c[k] = val;
+  }
+
+  friend reference get(RW_property_map<Key, Value, Container>& pmap, const key_type& k)
+  {
+    return pmap.m_c[k];
+  }
+
+private:
+  Container& m_c;
+};
+
+} // namespace CGAL
+
+template<typename Graph,
+         typename ForwardRange,
+         typename IndexPropertyMap>
+void test_uniqueness(const Graph&,
+                     const ForwardRange& range,
+                     IndexPropertyMap index_map)
+{
+#ifdef CGAL_TEST_PROPERTIES_DEBUG
+  std::cout << std::endl
+            << "Checking the uniqueness of the property map of type: "
+            << typeid(IndexPropertyMap).name() << std::endl;
+  std::cout << "Element type: " << typeid(typename boost::range_value<ForwardRange>::type).name() << std::endl;
+#endif
+
   typename boost::range_iterator<ForwardRange>::type 
-    begin = boost::begin(range), 
+    begin = boost::begin(range),
     begin2 = boost::begin(range),
     end = boost::end(range);
 
   typedef boost::unordered_set<typename IndexPropertyMap::value_type> id_map;
   typedef std::pair<typename id_map::iterator, bool> resultp;
-  id_map m;
 
-  while(begin != end) {
-    resultp r = m.insert(get(pm, *begin));
+  id_map m;
+  while(begin != end)
+  {
+    resultp r = m.insert(get(index_map, *begin));
+#ifdef CGAL_TEST_PROPERTIES_DEBUG
+    std::cout << "id: " << get(index_map, *begin) << std::endl;
+#endif
     ++begin;
-    assert(r.second);
+    assert(r.second); // already seen that id
   }
 
   assert(std::distance(begin2, end) == static_cast<std::ptrdiff_t>(m.size()));
 }
 
-
-void index_uniqueness_poly(const Polyhedron& g)
+template<typename Graph,
+         typename NamedParameters>
+void test_vertex_index_map_uniqueness(const Graph& g,
+                                      const NamedParameters& np)
 {
-  index_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  typedef typename CGAL::GetInitializedVertexIndexMap<Graph, NamedParameters>::type       VIM;
+  typedef typename CGAL::GetInitializedVertexIndexMap<Graph, NamedParameters>::const_type CVIM;
 
-  index_uniqueness(g, edges(g) ,    get(boost::edge_external_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_external_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_external_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_external_index, g));
+  // in the case where the map is passed by NP, its type doesn't depend on whether the mesh is const or not
+  static_assert((std::is_same<VIM, CVIM>::value), "VIM, CVIM must be the same type");
+
+  VIM ivim = CGAL::get_initialized_vertex_index_map(g, np);
+
+  return test_uniqueness(g, vertices(g), ivim);
 }
 
-void index_uniqueness_lcc(const LCC& g)
+template<typename Graph,
+         typename NamedParameters>
+void test_halfedge_index_map_uniqueness(const Graph& g,
+                                        const NamedParameters& np)
 {
-  index_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  typedef typename CGAL::GetInitializedHalfedgeIndexMap<Graph, NamedParameters>::type       HIM;
+  typedef typename CGAL::GetInitializedHalfedgeIndexMap<Graph, NamedParameters>::const_type CHIM;
+
+  // in the case where the map is passed by NP, its type doesn't depend on whether the mesh is const or not
+  static_assert((std::is_same<HIM, CHIM>::value), "HIM, CHIM must be the same type");
+
+  HIM ihim = CGAL::get_initialized_halfedge_index_map(g, np);
+
+  return test_uniqueness(g, halfedges(g), ihim);
 }
 
-void index_uniqueness_sm(const SM& g)
+template<typename Graph,
+         typename NamedParameters>
+void test_edge_index_map_uniqueness(const Graph& g,
+                                    const NamedParameters& np)
 {
-  index_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  typedef typename CGAL::GetInitializedEdgeIndexMap<Graph, NamedParameters>::type       EIM;
+  typedef typename CGAL::GetInitializedEdgeIndexMap<Graph, NamedParameters>::const_type CEIM;
+
+  // in the case where the map is passed by NP, its type doesn't depend on whether the mesh is const or not
+  static_assert((std::is_same<EIM, CEIM>::value), "EIM, CEIM must be the same type");
+
+  EIM ieim = CGAL::get_initialized_edge_index_map(g, np);
+
+  return test_uniqueness(g, edges(g), ieim);
 }
 
-#if defined(CGAL_USE_OPENMESH)
-void index_uniqueness_omesh(const OMesh& g)
+template<typename Graph,
+         typename NamedParameters>
+void test_face_index_map_uniqueness(const Graph& g,
+                                    const NamedParameters& np)
 {
-  index_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  typedef typename CGAL::GetInitializedFaceIndexMap<Graph, NamedParameters>::type       FIM;
+  typedef typename CGAL::GetInitializedFaceIndexMap<Graph, NamedParameters>::const_type CFIM;
+
+  // in the case where the map is passed by NP, its type doesn't depend on whether the mesh is const or not
+  static_assert((std::is_same<FIM, CFIM>::value), "FIM, CFIM must be the same type");
+
+  FIM ifim = CGAL::get_initialized_face_index_map(g, np);
+
+  return test_uniqueness(g, faces(g), ifim);
 }
+
+////////////////////////////////////////// const ///////////////////////////////////////////////////
+
+template <typename Graph>
+void test_internal_index_maps_const(const Graph& g)
+{
+  test_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
+  test_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  test_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
+  test_uniqueness(g, faces(g),     get(boost::face_index, g));
+}
+
+template <typename Graph>
+void test_initialized_index_maps_const(const Graph& g)
+{
+  typedef typename CGAL::GetInitializedVertexIndexMap<Graph>::const_type      VIM;
+  VIM ivim = CGAL::get_initialized_vertex_index_map(g);
+  test_uniqueness(g, vertices(g), ivim);
+
+  typedef typename CGAL::GetInitializedHalfedgeIndexMap<Graph>::const_type    HIM;
+  HIM ihim = CGAL::get_initialized_halfedge_index_map(g);
+  test_uniqueness(g, halfedges(g), ihim);
+
+  typedef typename CGAL::GetInitializedEdgeIndexMap<Graph>::const_type        EIM;
+  EIM ieim = CGAL::get_initialized_edge_index_map(g);
+  test_uniqueness(g, edges(g), ieim);
+
+  typedef typename CGAL::GetInitializedFaceIndexMap<Graph>::const_type        FIM;
+  FIM ifim = CGAL::get_initialized_face_index_map(g);
+  test_uniqueness(g, faces(g), ifim);
+
+  // Passing an index map via NP
+  typedef typename boost::graph_traits<Graph>::vertex_descriptor        vertex_descriptor;
+  typedef std::map<vertex_descriptor, int>                              VertexIndexMap;
+  typedef boost::associative_property_map<VertexIndexMap>               VertexIdPropertyMap; // lvalue_pmap
+
+  int vi = static_cast<int>(num_vertices(g));
+  VertexIndexMap vim;
+  VertexIdPropertyMap external_vertex_index_map(vim);
+  for(vertex_descriptor v : vertices(g))
+    put(external_vertex_index_map, v, --vi);
+
+  test_vertex_index_map_uniqueness(g, CGAL::parameters::vertex_index_map(external_vertex_index_map));
+
+  // Read-only pmap
+  typedef typename boost::graph_traits<Graph>::halfedge_descriptor      halfedge_descriptor;
+  typedef std::map<halfedge_descriptor, int>                            HalfedgeIndexMap;
+  typedef CGAL::Non_mutable_property_map<halfedge_descriptor, int,
+                                         HalfedgeIndexMap>              HalfedgeIdPropertyMap;
+
+  int hi = 0;
+  HalfedgeIndexMap him;
+  HalfedgeIdPropertyMap external_halfedge_index_map(him);
+
+  // this should complain that the map is not writable (commented because it does assert)
+// CGAL::BGL::internal::initialize_halfedge_index_map(external_halfedge_index_map, g);
+
+  // forced to initialize the underlying map
+  for(halfedge_descriptor h : halfedges(g))
+    him[h] = hi++;
+
+  test_halfedge_index_map_uniqueness(g, CGAL::parameters::halfedge_index_map(external_halfedge_index_map));
+
+  // Writable pmap
+  typedef typename boost::graph_traits<Graph>::edge_descriptor          edge_descriptor;
+  typedef boost::unordered_map<edge_descriptor, int>                    EdgeIndexMap;
+  typedef CGAL::RW_property_map<edge_descriptor, int, EdgeIndexMap>     EdgeIdPropertyMap;
+
+  EdgeIndexMap eim;
+  EdgeIdPropertyMap external_edge_index_map(eim);
+  CGAL::BGL::internal::initialize_edge_index_map(external_edge_index_map, g);
+
+  test_edge_index_map_uniqueness(g, CGAL::parameters::edge_index_map(external_edge_index_map));
+
+  // Just so face_index_map don't feel excluded
+  typedef typename boost::graph_traits<Graph>::face_descriptor          face_descriptor;
+  typedef std::map<face_descriptor, int>                                FaceIndexMap;
+  typedef boost::const_associative_property_map<FaceIndexMap>           FaceIdPropertyMap;
+
+  FaceIndexMap fim;
+  FaceIdPropertyMap external_face_index_map(fim);
+
+  // 'const_associative_pmap' has category 'lvalue_property_map_tag' but it's not writable
+  // so below should complain (commented because it does assert)
+//  CGAL::BGL::internal::initialize_face_index_map(external_face_index_map, g);
+
+  // gotta initialize the underlying map
+  int fi = 0;
+  for(face_descriptor f : faces(g))
+    fim[f] = fi++;
+
+  test_face_index_map_uniqueness(g, CGAL::parameters::face_index_map(external_face_index_map));
+}
+
+template <typename Graph>
+void test_all_index_maps_const(const Graph& g)
+{
+#ifdef CGAL_TEST_PROPERTIES_DEBUG
+  std::cout << " ----------------------------  Const graph tests" << std::endl;
 #endif
 
-template <typename Triangulation>
-void index_uniqueness_tr(const Triangulation& g)
-{
-  index_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
-  index_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
-  index_uniqueness(g, faces(g),     get(boost::face_index, g));
-  index_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  test_internal_index_maps_const(g);
+  test_initialized_index_maps_const(g);
 }
 
-int main()
+///////////////////////////////////// non-const ////////////////////////////////////////////////////
+
+template <typename Graph>
+void test_internal_index_maps(Graph& g)
+{
+  test_uniqueness(g, vertices(g),  get(boost::vertex_index, g));
+  test_uniqueness(g, halfedges(g), get(boost::halfedge_index, g));
+  test_uniqueness(g, edges(g) ,    get(boost::edge_index, g));
+  test_uniqueness(g, faces(g),     get(boost::face_index, g));
+}
+
+template <typename Graph>
+void test_initialized_index_maps(Graph& g)
+{
+  typedef typename CGAL::GetInitializedVertexIndexMap<Graph>::type      VIM;
+  VIM ivim = CGAL::get_initialized_vertex_index_map(g);
+  test_uniqueness(g, vertices(g), ivim);
+
+  typedef typename CGAL::GetInitializedHalfedgeIndexMap<Graph>::type    HIM;
+  HIM ihim = CGAL::get_initialized_halfedge_index_map(g);
+  test_uniqueness(g, halfedges(g), ihim);
+
+  typedef typename CGAL::GetInitializedEdgeIndexMap<Graph>::type        EIM;
+  EIM ieim = CGAL::get_initialized_edge_index_map(g);
+  test_uniqueness(g, edges(g), ieim);
+
+  typedef typename CGAL::GetInitializedFaceIndexMap<Graph>::type        FIM;
+  FIM ifim = CGAL::get_initialized_face_index_map(g);
+  test_uniqueness(g, faces(g), ifim);
+
+  // Passing an index map via NP
+  typedef typename boost::graph_traits<Graph>::vertex_descriptor        vertex_descriptor;
+  typedef std::map<vertex_descriptor, int>                              VertexIndexMap;
+  typedef boost::associative_property_map<VertexIndexMap>               VertexIdPropertyMap; // lvalue_pmap
+
+  int vi = static_cast<int>(num_vertices(g));
+  VertexIndexMap vim;
+  VertexIdPropertyMap external_vertex_index_map(vim);
+  for(vertex_descriptor v : vertices(g))
+    put(external_vertex_index_map, v, --vi);
+
+  test_vertex_index_map_uniqueness(g, CGAL::parameters::vertex_index_map(external_vertex_index_map));
+
+  // Read-only pmap
+  typedef typename boost::graph_traits<Graph>::halfedge_descriptor      halfedge_descriptor;
+  typedef std::map<halfedge_descriptor, int>                            HalfedgeIndexMap;
+  typedef CGAL::Non_mutable_property_map<halfedge_descriptor, int,
+                                         HalfedgeIndexMap>              HalfedgeIdPropertyMap;
+
+  int hi = 0;
+  HalfedgeIndexMap him;
+  HalfedgeIdPropertyMap external_halfedge_index_map(him);
+
+  // this should complain that the map is not writable (commented because it does assert)
+// CGAL::BGL::internal::initialize_halfedge_index_map(external_halfedge_index_map, g);
+
+  // forced to initialize the underlying map
+  for(halfedge_descriptor h : halfedges(g))
+    him[h] = hi++;
+
+  test_halfedge_index_map_uniqueness(g, CGAL::parameters::halfedge_index_map(external_halfedge_index_map));
+
+  // Writable pmap
+  typedef typename boost::graph_traits<Graph>::edge_descriptor          edge_descriptor;
+  typedef boost::unordered_map<edge_descriptor, int>                    EdgeIndexMap;
+  typedef CGAL::RW_property_map<edge_descriptor, int, EdgeIndexMap>     EdgeIdPropertyMap;
+
+  EdgeIndexMap eim;
+  EdgeIdPropertyMap external_edge_index_map(eim);
+  CGAL::BGL::internal::initialize_edge_index_map(external_edge_index_map, g);
+
+  test_edge_index_map_uniqueness(g, CGAL::parameters::edge_index_map(external_edge_index_map));
+
+  // Just so face_index_map don't feel excluded
+  typedef typename boost::graph_traits<Graph>::face_descriptor          face_descriptor;
+  typedef std::map<face_descriptor, int>                                FaceIndexMap;
+  typedef boost::const_associative_property_map<FaceIndexMap>           FaceIdPropertyMap;
+
+  FaceIndexMap fim;
+  FaceIdPropertyMap external_face_index_map(fim);
+
+  // 'const_associative_pmap' has category 'lvalue_property_map_tag' but it's not writable
+  // so below should complain (commented because it does assert)
+//  CGAL::BGL::internal::initialize_face_index_map(external_face_index_map, g);
+
+  // gotta initialize the underlying map
+  int fi = 0;
+  for(face_descriptor f : faces(g))
+    fim[f] = fi++;
+
+  test_face_index_map_uniqueness(g, CGAL::parameters::face_index_map(external_face_index_map));
+}
+
+template <typename Graph>
+void test_all_index_maps(Graph& g)
+{
+#ifdef CGAL_TEST_PROPERTIES_DEBUG
+  std::cout << " ---------------------------- Non-const graph tests" << std::endl;
+#endif
+
+  test_internal_index_maps(g);
+  test_initialized_index_maps(g);
+}
+
+template <typename Graph>
+void test_graph(Graph& g)
+{
+#ifdef CGAL_TEST_PROPERTIES_DEBUG
+  std::cout << "Graph has:" << std::endl
+            << "\t" << num_vertices(g) << " vertices (actual: " << vertices(g).size() << ")" << std::endl
+            << "\t" << num_halfedges(g) << " halfedges (actual: " << halfedges(g).size() << ")" << std::endl
+            << "\t" << num_edges(g) << " edges (actual: " << edges(g).size() << ")" << std::endl
+            << "\t" << num_faces(g) << " faces (actual: " << faces(g).size() << ")" << std::endl;
+#endif
+
+  test_all_index_maps(g);
+  test_all_index_maps_const(g);
+}
+
+void test_poly(Polyhedron& g)
+{
+  test_graph(g);
+
+  test_uniqueness(g, edges(g) ,    get(boost::edge_external_index, g));
+  test_uniqueness(g, vertices(g),  get(boost::vertex_external_index, g));
+  test_uniqueness(g, faces(g),     get(boost::face_external_index, g));
+  test_uniqueness(g, halfedges(g), get(boost::halfedge_external_index, g));
+}
+
+int main(int, char**)
 {
   std::cout << "testing Polyhedron\n";
   std::vector<Polyhedron> polys = poly_data();
-  for(Polyhedron p : polys)
-    index_uniqueness_poly(p);
+  for(Polyhedron& p : polys)
+    test_poly(p);
 
   std::cout << "testing Linear_cell_complex\n";
   std::vector<LCC> lccs = lcc_data();
-  for(LCC p : lccs)
-    index_uniqueness_lcc(p);
+  for(LCC& p : lccs)
+    test_graph(p);
 
   std::cout << "testing Surface_mesh\n";
   std::vector<SM> sms = sm_data();
-  for(SM p : sms)
-    index_uniqueness_sm(p);
+  for(SM& sm : sms)
+  {
+    assert(!CGAL::is_empty(sm));
+
+    // Add some garbage
+    CGAL::Euler::join_vertex(*(halfedges(sm).begin()), sm);
+
+    test_graph(sm);
+
+    // Test on a mesh with no internal index maps
+    Seam_edge_pmap seam_edges = sm.add_property_map<SM::Edge_index, bool>("e:on_seam", false).first;
+    Seam_vertex_pmap seam_vertices = sm.add_property_map<SM::Vertex_index, bool>("v:on_seam", false).first;
+    Seam_mesh seam_mesh(sm, seam_edges, seam_vertices);
+
+    test_initialized_index_maps(seam_mesh);
+    test_initialized_index_maps_const(seam_mesh);
+  }
 
 #if defined(CGAL_USE_OPENMESH)
   std::cout << "testing OpenMesh\n";
   std::vector<OMesh> omeshs = omesh_data();
-  for(OMesh p : omeshs)
-    index_uniqueness_omesh(p);
+  for(OMesh& p : omeshs)
+    test_graph(p);
 #endif
 
   std::cout << "testing Triangulations\n";
-  index_uniqueness_tr(t2_data());
-  index_uniqueness_tr(dt2_data());
-  index_uniqueness_tr(rt2_data());
-  index_uniqueness_tr(ct2_data());
-  index_uniqueness_tr(cdt2_data());
-  index_uniqueness_tr(cdtp2_data());
-  index_uniqueness_tr(t2h_data());
 
-  std::cerr << "done\n";
-  return 0;
+  Triangulation_2 t2 = t2_data();
+  test_graph(t2);
+
+  Delaunay_triangulation_2 dt2 = dt2_data();
+  test_graph(dt2);
+
+  Regular_triangulation_2 rt2 = rt2_data();
+  test_graph(rt2);
+
+  Constrained_triangulation_2 ct2 = ct2_data();
+  test_graph(ct2);
+
+  Constrained_Delaunay_triangulation_2 cdt2 = cdt2_data();
+  test_graph(cdt2);
+
+  CDT_P2 cdtp2 = cdtp2_data();
+  test_graph(cdtp2);
+
+  Triangulation_hierarchy_2 t2h = t2h_data();
+  test_graph(t2h);
+
+  // no dynamic pmaps in triangulations (yet)
+//  Triangulation_no_id_2 t2_no_id = t2_no_id_data();
+//  test_initialized_index_maps(t2_no_id);
+//  test_initialized_index_maps_const(t2_no_id);
+
+  std::cout << "Done!" << std::endl;
+
+  return EXIT_SUCCESS;
 }
diff --git a/BGL/test/BGL/test_cgal_bgl_named_params.cpp b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
index c3a577f20e3..53c6c65adf1 100644
--- a/BGL/test/BGL/test_cgal_bgl_named_params.cpp
+++ b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
@@ -94,6 +94,8 @@ void test(const NamedParameters& np)
   assert(get_parameter(np, CGAL::internal_np::area_threshold).v == 57);
   assert(get_parameter(np, CGAL::internal_np::volume_threshold).v == 58);
   assert(get_parameter(np, CGAL::internal_np::dry_run).v == 59);
+  assert(get_parameter(np, CGAL::internal_np::do_lock_mesh).v == 60);
+  assert(get_parameter(np, CGAL::internal_np::do_simplify_border).v == 61);
 
     // Named parameters that we use in the package 'Surface Mesh Simplification'
   assert(get_parameter(np, CGAL::internal_np::get_cost_policy).v == 34);
@@ -181,6 +183,8 @@ void test(const NamedParameters& np)
   check_same_type<57>(get_parameter(np, CGAL::internal_np::area_threshold));
   check_same_type<58>(get_parameter(np, CGAL::internal_np::volume_threshold));
   check_same_type<59>(get_parameter(np, CGAL::internal_np::dry_run));
+  check_same_type<60>(get_parameter(np, CGAL::internal_np::do_lock_mesh));
+  check_same_type<61>(get_parameter(np, CGAL::internal_np::do_simplify_border));
 
     // Named parameters that we use in the package 'Surface Mesh Simplification'
   check_same_type<34>(get_parameter(np, CGAL::internal_np::get_cost_policy));
@@ -274,6 +278,8 @@ int main()
                          .area_threshold(A<57>(57))
                          .volume_threshold(A<58>(58))
                          .dry_run(A<59>(59))
+                         .do_lock_mesh(A<60>(60))
+                         .do_simplify_border(A<61>(61))
        );
 
   return EXIT_SUCCESS;
diff --git a/Bounding_volumes/examples/Approximate_min_ellipsoid_d/CMakeLists.txt b/Bounding_volumes/examples/Approximate_min_ellipsoid_d/CMakeLists.txt
index 8802463b72d..9e5c6bb914e 100644
--- a/Bounding_volumes/examples/Approximate_min_ellipsoid_d/CMakeLists.txt
+++ b/Bounding_volumes/examples/Approximate_min_ellipsoid_d/CMakeLists.txt
@@ -8,15 +8,16 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0 QUIET) #(3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
   
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     if(NOT (${cppfile} STREQUAL "ellipsoid.cpp") OR EIGEN3_FOUND)
       create_single_source_cgal_program( "${cppfile}" )
+      if (EIGEN3_FOUND)
+        get_filename_component(target ${cppfile} NAME_WE)
+        CGAL_target_use_Eigen(${target})
+      endif()
     endif()
   endforeach()
 
diff --git a/Bounding_volumes/test/Bounding_volumes/CMakeLists.txt b/Bounding_volumes/test/Bounding_volumes/CMakeLists.txt
index 403e652475c..dd6813bb97e 100644
--- a/Bounding_volumes/test/Bounding_volumes/CMakeLists.txt
+++ b/Bounding_volumes/test/Bounding_volumes/CMakeLists.txt
@@ -14,15 +14,16 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0 QUIET) #(3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
   
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     if(NOT (${cppfile} STREQUAL "Approximate_min_ellipsoid_d.cpp") OR EIGEN3_FOUND)
       create_single_source_cgal_program( "${cppfile}" )
+      if (EIGEN3_FOUND)
+        get_filename_component(target ${cppfile} NAME_WE)
+        CGAL_target_use_Eigen(${target})
+      endif()
     endif()
   endforeach()
 
diff --git a/CGAL_ImageIO/include/CGAL/read_vtk_image_data.h b/CGAL_ImageIO/include/CGAL/read_vtk_image_data.h
index a0e892fb416..3dee3352a19 100644
--- a/CGAL_ImageIO/include/CGAL/read_vtk_image_data.h
+++ b/CGAL_ImageIO/include/CGAL/read_vtk_image_data.h
@@ -76,6 +76,10 @@ read_vtk_image_data(vtkImageData* vtk_image, Image_3::Own owning = Image_3::OWN_
   image->wdim = imageio_type.wdim;
   image->wordKind = imageio_type.wordKind;
   image->sign = imageio_type.sign;
+  if (!vtk_image->GetPointData() || !vtk_image->GetPointData()->GetScalars()) {
+    ::_freeImage(image);
+    return Image_3();
+  }
   CGAL_assertion(vtk_image->GetPointData()->GetScalars()->GetNumberOfTuples() == dims[0]*dims[1]*dims[2]);
   if(owning == Image_3::OWN_THE_DATA) {
     image->data = ::ImageIO_alloc(dims[0]*dims[1]*dims[2]*image->wdim);
diff --git a/CGAL_ipelets/demo/CGAL_ipelets/CMakeLists.txt b/CGAL_ipelets/demo/CGAL_ipelets/CMakeLists.txt
index 64206c30223..a764689a9d9 100644
--- a/CGAL_ipelets/demo/CGAL_ipelets/CMakeLists.txt
+++ b/CGAL_ipelets/demo/CGAL_ipelets/CMakeLists.txt
@@ -27,9 +27,7 @@ if ( CGAL_FOUND )
   include(${CGAL_USE_FILE})
 
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  else()
+  if (NOT EIGEN3_FOUND)
     message(STATUS "NOTICE: This project requires the Eigen library, and will not be compiled.")
     return()
   endif()
@@ -143,6 +141,7 @@ if ( CGAL_FOUND )
       add_library(CGAL_${IPELET} MODULE ${IPELET}.cpp)
       add_to_cached_list(CGAL_EXECUTABLE_TARGETS CGAL_${IPELET})
       target_link_libraries(CGAL_${IPELET} PRIVATE CGAL::CGAL ${IPE_LIBRARIES})
+      CGAL_target_use_Eigen(CGAL_${IPELET})
       if ( IPELET_INSTALL_DIR )
         install(TARGETS CGAL_${IPELET} DESTINATION ${IPELET_INSTALL_DIR})
         if (WITH_IPE_7)
@@ -153,12 +152,13 @@ if ( CGAL_FOUND )
     endforeach(IPELET)
     if(CGAL_Core_FOUND)
       target_link_libraries(CGAL_cone_spanners PRIVATE CGAL::CGAL_Core)
+      CGAL_target_use_Eigen(CGAL_cone_spanners)
     endif()
     #example in doc not installed
     add_library(simple_triangulation MODULE simple_triangulation.cpp)
     add_to_cached_list(CGAL_EXECUTABLE_TARGETS simple_triangulation)
     target_link_libraries(simple_triangulation ${IPE_LIBRARIES})
-
+    CGAL_target_use_Eigen(simple_triangulation)
     cgal_add_compilation_test(simple_triangulation)
 
   else()
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
index 92985777bbb..028c772c102 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
@@ -50,6 +50,15 @@ public:
   PointC2(const FT &hx, const FT &hy, const FT &hw)
     : base(hx, hy, hw) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Vector_2_>)
+#endif
+  {
+    using std::swap;
+    swap(a.base, b.base);
+  }
+
   const FT& x() const
   {
       return base.x();
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
index 614ec31fcc5..b46ab99284b 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
@@ -24,6 +24,7 @@ namespace CGAL {
 template < class R_ >
 class PointC3
 {
+  typedef PointC3<R_>                       Self;
   typedef typename R_::Vector_3             Vector_3;
   typedef typename R_::Point_3              Point_3;
   typedef typename R_::Aff_transformation_3 Aff_transformation_3;
@@ -47,6 +48,15 @@ public:
   PointC3(const FT &x, const FT &y, const FT &z, const FT &w)
     : base(x, y, z, w) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Vector_3>)
+#endif
+  {
+    using std::swap;
+    swap(a.base, b.base);
+  }
+
   const FT & x() const
   {
       return base.x();
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
index 6331471dff7..01986b321a3 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
@@ -27,6 +27,7 @@ namespace CGAL {
 template < class R_ >
 class VectorC2
 {
+  typedef VectorC2<R_>                      Self;
   typedef typename R_::FT                   FT;
   typedef typename R_::Point_2              Point_2;
   typedef typename R_::Vector_2             Vector_2;
@@ -55,6 +56,15 @@ public:
     : base( hw != FT(1) ? CGAL::make_array<FT>(hx/hw, hy/hw)
                         : CGAL::make_array(hx, hy) ) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Base>)
+#endif
+  {
+    using std::swap;
+    swap(a.base, b.base);
+  }
+
   const FT & x() const
   {
       return CGAL::get_pointee_or_identity(base)[0];
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
index ccad6ad574c..72954931d0b 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
@@ -27,6 +27,7 @@ template < class R_ >
 class VectorC3
 {
 // https://doc.cgal.org/latest/Manual/devman_code_format.html#secprogramming_conventions
+  typedef VectorC3<R_>                      Self;
   typedef typename R_::FT                   FT_;
   typedef typename R_::Point_3              Point_3;
   typedef typename R_::Vector_3             Vector_3;
@@ -70,6 +71,15 @@ public:
     : base( w != FT_(1) ? CGAL::make_array<FT_>(x/w, y/w, z/w)
                        : CGAL::make_array(x, y, z) ) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Base>)
+#endif
+  {
+    using std::swap;
+    swap(a.base, b.base);
+  }
+
   const FT_ & x() const
   {
       return get_pointee_or_identity(base)[0];
diff --git a/Classification/examples/Classification/CMakeLists.txt b/Classification/examples/Classification/CMakeLists.txt
index 79ad8c5bf03..4cdfe2e2c08 100644
--- a/Classification/examples/Classification/CMakeLists.txt
+++ b/Classification/examples/Classification/CMakeLists.txt
@@ -5,7 +5,6 @@ cmake_minimum_required(VERSION 3.1...3.15)
 project( Classification_Examples )
 
 
-
 # CGAL and its components
 find_package( CGAL QUIET COMPONENTS  )
 
@@ -22,127 +21,73 @@ if ( NOT Boost_FOUND )
   return()  
 endif()
 
-find_package( Boost OPTIONAL_COMPONENTS serialization iostreams )
+set(Classification_dependencies_met TRUE)
 
-if( WIN32 )
-# to avoid a warning with old cmake 
-  set(_Boost_BZIP2_HEADERS             "boost/iostreams/filter/bzip2.hpp")
-  set(_Boost_ZLIB_HEADERS              "boost/iostreams/filter/zlib.hpp")
-  find_package( Boost OPTIONAL_COMPONENTS bzip2 zlib)
-else()
-  find_package(ZLIB QUIET)
+find_package( Boost OPTIONAL_COMPONENTS serialization iostreams )
+if (NOT Boost_SERIALIZATION_FOUND)
+  message(STATUS "NOTICE: This project requires Boost Serialization, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
+endif()
+if (NOT Boost_IOSTREAMS_FOUND)
+  message(STATUS "NOTICE: This project requires Boost IO Streams, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
+endif()
+
+find_package(OpenCV QUIET COMPONENTS core ml) # Need core + machine learning
+if (NOT OpenCV_FOUND)
+  message(STATUS "NOTICE: OpenCV was not found. OpenCV random forest predicate for classification won't be available.")
+endif()
+
+find_package(TensorFlow QUIET) 
+if (NOT TensorFlow_FOUND)
+  message(STATUS "NOTICE: TensorFlow was not found. TensorFlow neural network predicate for classification won't be available.")
+endif()
+
+find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+if (NOT EIGEN3_FOUND)
+  message(STATUS "This project requires the Eigen library, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
 endif()
 
 find_package(TBB QUIET)
 
-find_package(OpenCV QUIET COMPONENTS core ml) # Need core + machine learning
-
-# Use Eigen
-find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
-if (NOT EIGEN3_FOUND)
-  message(STATUS "This project requires the Eigen library, and will not be compiled.")
-  return()
-else()
-  include( ${EIGEN3_USE_FILE} )
-endif()
-
-
-# Creating entries for all C++ files with "main" routine
-# ##########################################################
-
-# Classification examples
-set(targets
-  example_classification
-  example_ethz_random_forest
-  example_feature
-  example_generation_and_training
-  example_mesh_classification
-  example_cluster_classification)
-
-# Classification requires some C++11 features
-set(needed_cxx_features cxx_rvalue_references cxx_variadic_templates)
-
-# Libraries and flags
-set(classification_linked_libraries)
-set(classification_compile_definitions)
-
-
-if (Boost_SERIALIZATION_FOUND AND Boost_IOSTREAMS_FOUND)
-  if(TARGET Boost::serialization AND TARGET Boost::iostreams)
-    set(classification_linked_libraries Boost::serialization Boost::iostreams)
-  else()
-    set(classification_linked_libraries ${classification_linked_libraries}
-      ${Boost_SERIALIZATION_LIBRARY}
-      ${Boost_IOSTREAMS_LIBRARY})
-  endif()
-else()
-  if (NOT Boost_SERIALIZATION_FOUND)
-    message(STATUS "NOTICE: This project requires Boost Serialization, and will not be compiled.")
-  endif()
-  if (NOT Boost_IOSTREAMS_FOUND)
-    message(STATUS "NOTICE: This project requires Boost IO Streams, and will not be compiled.")
-  endif()
+if (NOT Classification_dependencies_met)
   return()
 endif()
 
-if( WIN32 )
-  if (Boost_ZLIB_FOUND AND Boost_BZIP2_FOUND)
-    set(classification_linked_libraries ${classification_linked_libraries}
-      ${Boost_ZLIB_LIBRARY} ${Boost_BZIP2_LIBRARY})
-  else()
-    message(STATUS "NOTICE: This project requires Boost ZLIB and Boost BZIP2, and will not be compiled.")
-    return()
-  endif()
-else()
-  if(ZLIB_FOUND)
-    set(classification_linked_libraries ${classification_linked_libraries} ZLIB::ZLIB)
-  else()
-    message(STATUS "NOTICE: This project requires ZLIB, and will not be compiled.")
-    return()
-  endif()
-endif()
+create_single_source_cgal_program( "example_classification.cpp" )
+create_single_source_cgal_program( "example_ethz_random_forest.cpp" )
+create_single_source_cgal_program( "example_feature.cpp" )
+create_single_source_cgal_program( "example_generation_and_training.cpp" )
+create_single_source_cgal_program( "example_mesh_classification.cpp" )
+create_single_source_cgal_program( "example_cluster_classification.cpp" )
 
 if (OpenCV_FOUND)
-  message(STATUS "Found OpenCV ${OpenCV_VERSION}")
-  include_directories(${OpenCV_INCLUDE_DIRS})
-  set(classification_linked_libraries ${classification_linked_libraries}
-    ${OpenCV_LIBS})
-  set(classification_compile_definitions ${classification_compile_definitions}
-    "-DCGAL_LINKED_WITH_OPENCV")
-
-  set(targets ${targets} example_opencv_random_forest)
-else()
-  message(STATUS "NOTICE: OpenCV was not found. OpenCV random forest predicate for classification won't be available.")
+  create_single_source_cgal_program( "example_opencv_random_forest.cpp" )
+  CGAL_target_use_OpenCV(example_opencv_random_forest)
 endif()
 
-find_package(TensorFlow QUIET)
 if (TensorFlow_FOUND)
-  message(STATUS "Found TensorFlow")
-  include_directories( ${TensorFlow_INCLUDE_DIR} )
-  set(classification_linked_libraries ${classification_linked_libraries}
-    ${TensorFlow_LIBRARY})
-  set(classification_compile_definitions ${classification_compile_definitions}
-    "-DCGAL_LINKED_WITH_TENSORFLOW")
-  
-  set(targets ${targets} example_tensorflow_neural_network)
-else()
-  message(STATUS "NOTICE: TensorFlow not found, Neural Network predicate for classification won't be available.")
+  create_single_source_cgal_program( "example_tensorflow_neural_network.cpp" )
+  CGAL_target_use_TensorFlow(example_tensorflow_neural_network)
 endif()
 
-
-# Creating targets with correct libraries and flags
-foreach(target ${targets})
-  create_single_source_cgal_program( "${target}.cpp" CXX_FEATURES ${needed_cxx_features} )
+foreach(target
+    example_classification
+    example_ethz_random_forest
+    example_feature
+    example_generation_and_training
+    example_mesh_classification
+    example_cluster_classification
+    example_opencv_random_forest
+    example_tensorflow_neural_network)
   if(TARGET ${target})
-    target_link_libraries(${target} PUBLIC ${classification_linked_libraries})
-    target_compile_definitions(${target} PUBLIC ${classification_compile_definitions})
+    CGAL_target_use_Eigen(${target})
+    CGAL_target_use_Boost_IOStreams(${target})
+    CGAL_target_use_Boost_Serialization(${target})
     if(TBB_FOUND)
       CGAL_target_use_TBB(${target})
     endif()
   endif()
 endforeach()
 
-
-
-
-
diff --git a/Classification/test/Classification/CMakeLists.txt b/Classification/test/Classification/CMakeLists.txt
index ae7699281d1..c108ca45a56 100644
--- a/Classification/test/Classification/CMakeLists.txt
+++ b/Classification/test/Classification/CMakeLists.txt
@@ -5,7 +5,6 @@ cmake_minimum_required(VERSION 3.1...3.15)
 project( Classification_Tests )
 
 
-
 # CGAL and its components
 find_package( CGAL QUIET COMPONENTS  )
 
@@ -22,88 +21,39 @@ if ( NOT Boost_FOUND )
   return()  
 endif()
 
+set(Classification_dependencies_met TRUE)
+
 find_package( Boost OPTIONAL_COMPONENTS serialization iostreams )
-
-if( WIN32 )
-# to avoid a warning with old cmake 
-  set(_Boost_BZIP2_HEADERS             "boost/iostreams/filter/bzip2.hpp")
-  set(_Boost_ZLIB_HEADERS              "boost/iostreams/filter/zlib.hpp")
-  find_package( Boost OPTIONAL_COMPONENTS bzip2 zlib)
-else()
-  find_package(ZLIB QUIET)
+if (NOT Boost_SERIALIZATION_FOUND)
+  message(STATUS "NOTICE: This project requires Boost Serialization, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
+endif()
+if (NOT Boost_IOSTREAMS_FOUND)
+  message(STATUS "NOTICE: This project requires Boost IO Streams, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
 endif()
 
-# Use Eigen
-find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
+find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+if (NOT EIGEN3_FOUND)
+  message(STATUS "This project requires the Eigen library, and will not be compiled.")
+  set(Classification_dependencies_met FALSE)
 endif()
 
-find_package( TBB )
+find_package(TBB QUIET)
 
-# include for local directory
-include_directories( BEFORE include )
-
-# include for local package
-
-# Creating entries for all C++ files with "main" routine
-# ##########################################################
-
-#add_definitions("-DCGAL_DO_NOT_USE_BOYKOV_KOLMOGOROV_MAXFLOW_SOFTWARE")
-
-# Classification requires some C++11 features
-set(needed_cxx_features cxx_rvalue_references cxx_variadic_templates)
-
-# Libraries and flags
-set(classification_linked_libraries)
-
-if (Boost_SERIALIZATION_FOUND AND Boost_IOSTREAMS_FOUND)
-  if(TARGET Boost::serialization AND TARGET Boost::iostreams)
-    set(classification_linked_libraries Boost::serialization Boost::iostreams)
-  else()
-    set(classification_linked_libraries ${classification_linked_libraries}
-      ${Boost_SERIALIZATION_LIBRARY}
-      ${Boost_IOSTREAMS_LIBRARY})
-  endif()
-else()
-  if (NOT Boost_SERIALIZATION_FOUND)
-    message(STATUS "NOTICE: This project requires Boost Serialization, and will not be compiled.")
-  endif()
-  if (NOT Boost_IOSTREAMS_FOUND)
-    message(STATUS "NOTICE: This project requires Boost IO Streams, and will not be compiled.")
-  endif()
+if (NOT Classification_dependencies_met)
   return()
 endif()
 
-if( WIN32 )
-  if (Boost_ZLIB_FOUND AND Boost_BZIP2_FOUND)
-    set(classification_linked_libraries ${classification_linked_libraries}
-      ${Boost_ZLIB_LIBRARY} ${Boost_BZIP2_LIBRARY})
-  else()
-    message(STATUS "NOTICE: This project requires Boost ZLIB and Boost BZIP2, and will not be compiled.")
-    return()
-  endif()
-else()
-  if(ZLIB_FOUND)
-    set(classification_linked_libraries ${classification_linked_libraries} ZLIB::ZLIB)
-  else()
-    message(STATUS "NOTICE: This project requires ZLIB, and will not be compiled.")
-    return()
-  endif()
-endif()
+create_single_source_cgal_program( "test_classification_point_set.cpp" )
+create_single_source_cgal_program( "test_classification_io.cpp" )
 
-create_single_source_cgal_program( "test_classification_point_set.cpp" CXX_FEATURES ${needed_cxx_features} )
-if(TARGET test_classification_point_set)
-  target_link_libraries(test_classification_point_set PUBLIC ${classification_linked_libraries})
-  if (TBB_FOUND)
-    CGAL_target_use_TBB( test_classification_point_set )
+foreach(target test_classification_point_set test_classification_io)
+  CGAL_target_use_Eigen(${target})
+  CGAL_target_use_Boost_IOStreams(${target})
+  CGAL_target_use_Boost_Serialization(${target})
+  if(TBB_FOUND)
+    CGAL_target_use_TBB(${target})
   endif()
-endif()
+endforeach()
 
-create_single_source_cgal_program( "test_classification_io.cpp" CXX_FEATURES ${needed_cxx_features} )
-if(TARGET test_classification_io)
-  target_link_libraries(test_classification_io PUBLIC ${classification_linked_libraries})
-  if (TBB_FOUND)
-    CGAL_target_use_TBB( test_classification_io )
-  endif()
-endif()
diff --git a/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h b/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
index bc83e1d13a0..78e5d46a00f 100644
--- a/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
@@ -21,7 +21,7 @@ is a kernel with exact predicates but inexact constructions
 (in practice we check `R::Has_filtered_predicates_tag` is `Tag_true` and `R::FT` is a floating point type),
 then the default traits class of `::convex_hull_3()` is `Convex_hull_traits_3<R>`, and `R` otherwise.
 
-\attention The user must include the header file of the `Polygon_mesh` type.
+\attention The user must include the header file of the `PolygonMesh` type.
 
 \cgalHeading{Implementation}
 
@@ -34,6 +34,36 @@ Barnard <I>et al.</I> \cgalCite{bdh-qach-96}.
 template <class InputIterator, class PolygonMesh, class Traits>
 void convex_hull_3(InputIterator first, InputIterator last, PolygonMesh& pm, const Traits& ch_traits = Default_traits);
 
+
+/*!
+\ingroup PkgConvexHull3Functions
+ * \brief computes the convex hull of the points associated to the vertices of `g`.
+ * The polygon mesh `pm` is cleared, then
+ * the convex hull is stored in `pm`. Note that the convex hull will be triangulated,
+ * that is `pm` will contain only triangular faces.
+ * if the convex hull is a point or a segment, endpoints will be added in `pm` as isolated vertices.
+ * 
+ * \tparam VertexListGraph a model of `VertexListGraph`.
+ * \tparam PolygonMesh must be a model of `MutableFaceGraph`.
+ * \tparam NamedParameters a sequence of named parameters
+ * 
+ * \param g the graph
+ * \param pm the `PolygonMesh` that will contain the convex hull
+ * \param np optional sequence of named parameters among the ones listed below
+ *
+ * \cgalNamedParamsBegin
+ *    \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of `g`.
+ *   If this parameter is omitted, an internal property map for
+ *   `CGAL::vertex_point_t` must be available in `VertexListGraph`
+ * \cgalParamEnd
+* \cgalNamedParamsEnd
+ * \attention The user must include the header file of the `PolygonMesh` and `VertexListGraph` types.
+ */
+template <class VertexListGraph, class PolygonMesh, class NamedParameters>
+void convex_hull_3(const VertexListGraph& g,
+                   PolygonMesh& pm,
+                   const NamedParameters& np);
+
 /*!
 \ingroup PkgConvexHull3Functions
 
@@ -47,7 +77,7 @@ that is the polygon mesh will contain only triangular facets.
 \tparam Traits must be model of the concept `ConvexHullTraits_3`.
 For the purposes of checking the postcondition that the convex hull
 is valid, `Traits` must also be a model of the concept
-`IsStronglyConvexTraits_3`.   Furthermore, `Traits` must define a type `Polygon_mesh` that is a model of
+`IsStronglyConvexTraits_3`.   Furthermore, `Traits` must define a type `PolygonMesh` that is a model of
 `MutableFaceGraph`.
 
 If the kernel `R` of the points determined by the value type  of `InputIterator`
@@ -55,7 +85,7 @@ is a kernel with exact predicates but inexact constructions
 (in practice we check `R::Has_filtered_predicates_tag` is `Tag_true` and `R::FT` is a floating point type),
 then the default traits class of `convex_hull_3()` is `Convex_hull_traits_3<R>`, and `R` otherwise.
 
-\attention The user must include the header file of the `Polygon_mesh` type.
+\attention The user must include the header file of the `PolygonMesh` type.
 */
 
 template <class InputIterator, class Traits>
diff --git a/Convex_hull_3/doc/Convex_hull_3/Doxyfile.in b/Convex_hull_3/doc/Convex_hull_3/Doxyfile.in
index a114b807a2b..860593ed992 100644
--- a/Convex_hull_3/doc/Convex_hull_3/Doxyfile.in
+++ b/Convex_hull_3/doc/Convex_hull_3/Doxyfile.in
@@ -1,3 +1,9 @@
 @INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
 
 PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 3D Convex Hulls"
+
+\# macros to be used inside the code
+ALIASES += "cgalNamedParamsBegin=<dl class=\"params\"><dt>Named Parameters</dt><dd> <table class=\"params\">"
+ALIASES += "cgalNamedParamsEnd=</table> </dd> </dl>"
+ALIASES += "cgalParamBegin{1}=<tr><td class=\"paramname\">\ref BGL_\1 \"\1\"</td><td>"
+ALIASES += "cgalParamEnd=</td></tr>"
diff --git a/Convex_hull_3/examples/Convex_hull_3/CMakeLists.txt b/Convex_hull_3/examples/Convex_hull_3/CMakeLists.txt
index 18d983da969..a5b3583a751 100644
--- a/Convex_hull_3/examples/Convex_hull_3/CMakeLists.txt
+++ b/Convex_hull_3/examples/Convex_hull_3/CMakeLists.txt
@@ -54,6 +54,9 @@ create_single_source_cgal_program( "lloyd_algorithm.cpp" )
 
 create_single_source_cgal_program( "quickhull_3.cpp" )
 
+create_single_source_cgal_program( "graph_hull_3.cpp" )
+
+
 create_single_source_cgal_program( "quickhull_any_dim_3.cpp" )
 
 create_single_source_cgal_program( "extreme_points_3_sm.cpp" )
diff --git a/Convex_hull_3/examples/Convex_hull_3/graph_hull_3.cpp b/Convex_hull_3/examples/Convex_hull_3/graph_hull_3.cpp
new file mode 100644
index 00000000000..1769315fe5b
--- /dev/null
+++ b/Convex_hull_3/examples/Convex_hull_3/graph_hull_3.cpp
@@ -0,0 +1,31 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polyhedron_3.h>
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/convex_hull_3.h>
+#include <vector>
+#include <fstream>
+
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel  K;
+typedef K::Point_3                                Point_3;
+typedef CGAL::Surface_mesh<Point_3>               Surface_mesh;
+
+
+int main(int argc, char* argv[])
+{
+  std::ifstream in( (argc>1)? argv[1] : "data/star.off");
+  
+  Surface_mesh poly;
+  if(!(in >> poly))
+  {
+    std::cerr<<"Could not find input file."<<std::endl;
+    return 1;
+  }
+  
+  Surface_mesh chull;
+  // compute convex hull
+  CGAL::convex_hull_3(poly, chull);
+
+  std::cout << "The convex hull contains " << chull.number_of_vertices() << " vertices" << std::endl;
+  return 0;
+}
diff --git a/Convex_hull_3/include/CGAL/convex_hull_3.h b/Convex_hull_3/include/CGAL/convex_hull_3.h
index 7c69f1fa26f..15dd55705fd 100644
--- a/Convex_hull_3/include/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/include/CGAL/convex_hull_3.h
@@ -37,6 +37,7 @@
 #include <memory>
 #include <list>
 #include <vector>
+#include <type_traits>
 #include <boost/bind.hpp>
 #include <boost/next_prior.hpp>
 #include <boost/type_traits/is_floating_point.hpp>
@@ -49,6 +50,9 @@
 #include <CGAL/boost/graph/properties_Triangulation_data_structure_2.h>
 #include <CGAL/Polyhedron_3_fwd.h>
 #include <CGAL/boost/graph/Euler_operations.h>
+#include <CGAL/boost/iterator/transform_iterator.hpp>
+#include <CGAL/boost/graph/named_params_helper.h>
+#include <CGAL/is_iterator.h>
 
 #include <boost/unordered_map.hpp>
 
@@ -1036,7 +1040,10 @@ void convex_hull_3(InputIterator first, InputIterator beyond,
 
 template <class InputIterator, class Polyhedron_3>
 void convex_hull_3(InputIterator first, InputIterator beyond,
-                   Polyhedron_3& polyhedron)
+                   Polyhedron_3& polyhedron,
+                   typename std::enable_if<
+                     CGAL::is_iterator<InputIterator>::value
+                   >::type* =0) //workaround to avoid ambiguity with next overload.
 {
    typedef typename std::iterator_traits<InputIterator>::value_type Point_3;
    typedef typename internal::Convex_hull_3::Default_traits_for_Chull_3<Point_3, Polyhedron_3>::type Traits;
@@ -1044,6 +1051,29 @@ void convex_hull_3(InputIterator first, InputIterator beyond,
 }
 
 
+template <class VertexListGraph, class PolygonMesh, class NamedParameters>
+void convex_hull_3(const VertexListGraph& g,
+                   PolygonMesh& pm, 
+                   const NamedParameters& np)
+{
+  typedef typename GetVertexPointMap<VertexListGraph, NamedParameters>::const_type Vpmap;
+  typedef CGAL::Property_map_to_unary_function<Vpmap> Vpmap_fct;
+  Vpmap vpm = CGAL::parameters::choose_parameter(
+        CGAL::parameters::get_parameter(np, internal_np::vertex_point),
+        get_const_property_map(boost::vertex_point, g));
+  
+  Vpmap_fct v2p(vpm);
+  convex_hull_3(boost::make_transform_iterator(vertices(g).begin(), v2p),
+                boost::make_transform_iterator(vertices(g).end(), v2p), pm);
+}
+
+template <class VertexListGraph, class PolygonMesh>
+void convex_hull_3(const VertexListGraph& g,
+                   PolygonMesh& pm)
+{
+  convex_hull_3(g,pm,CGAL::parameters::all_default());
+}
+
 template <class InputRange, class OutputIterator, class Traits>
 OutputIterator
 extreme_points_3(const InputRange& range,
diff --git a/Convex_hull_3/test/Convex_hull_3/test_ch_3_ambiguity.cpp b/Convex_hull_3/test/Convex_hull_3/test_ch_3_ambiguity.cpp
new file mode 100644
index 00000000000..0b67fa73bdc
--- /dev/null
+++ b/Convex_hull_3/test/Convex_hull_3/test_ch_3_ambiguity.cpp
@@ -0,0 +1,32 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polyhedron_3.h>
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/convex_hull_3.h>
+#include <vector>
+#include <fstream>
+
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel  K;
+typedef CGAL::Polyhedron_3<K>                     Polyhedron_3;
+typedef K::Point_3                                Point_3;
+typedef CGAL::Surface_mesh<Point_3>               Surface_mesh;
+
+
+int main(int argc, char* argv[])
+{
+  std::ifstream in( (argc>1)? argv[1] : "data/cross.off");
+  
+  Surface_mesh poly;
+  if(!in || !(in >> poly))
+  {
+    std::cerr<<"Could not find a correct input file."<<std::endl;
+    return 1;
+  }
+  
+  Surface_mesh chull;
+  // compute convex hull
+  auto np = CGAL::parameters::all_default();
+  CGAL::convex_hull_3(poly, chull, np);
+  std::cout << "The convex hull contains " << chull.number_of_vertices() << " vertices" << std::endl;
+  return 0;
+}
diff --git a/Documentation/doc/Documentation/Third_party.txt b/Documentation/doc/Documentation/Third_party.txt
index e0220b92691..c431b428da5 100644
--- a/Documentation/doc/Documentation/Third_party.txt
+++ b/Documentation/doc/Documentation/Third_party.txt
@@ -126,10 +126,14 @@ The exhaustive list of \sc{Qt}5 components used in demos is:
 \sc{Eigen} is a `C++` template library for linear algebra. \sc{Eigen} supports all
 matrix sizes, various matrix decomposition methods and sparse linear solvers.
 
-In \cgal, \sc{Eigen} is used in many packages such as \ref PkgPoissonSurfaceReconstruction3
-or \ref PkgJetFitting3, providing sparse linear solvers and singular value decompositions.
-A package dependency over \sc{Eigen} is marked on the
-<a href="https://doc.cgal.org/latest/Manual/packages.html">Package Overview</a> page.
+In \cgal, \sc{Eigen} is used in many packages such as \ref
+PkgPoissonSurfaceReconstruction3 or \ref PkgJetFitting3, providing
+sparse linear solvers and singular value decompositions.  A package
+dependency over \sc{Eigen} is marked on the <a
+href="https://doc.cgal.org/latest/Manual/packages.html">Package
+Overview</a> page. In order to use Eigen in \cgal programs, the
+provided CMake function `CGAL_target_use_Eigen(<target>)` should be
+used.
 
 The \sc{Eigen} web site is <A HREF="http://eigen.tuxfamily.org/index.php?title=Main_Page">`http://eigen.tuxfamily.org`</A>.
 
@@ -194,7 +198,9 @@ It can be downloaded from <A HREF="http://esbtl.sourceforge.net/">`http://esbtl.
 \sc{Tbb} (Threading Building Blocks) is a library developed by Intel Corporation for writing software
 programs that take advantage of multi-core processors.
 
-In \cgal, \sc{Tbb} is used by the packages that offer parallel code.
+In \cgal, \sc{Tbb} is used by the packages that offer parallel
+code. In order to use \sc{Tbb} in \cgal programs, the provided CMake
+function `CGAL_target_use_TBB(<target>)` should be used.
 
 The \sc{Tbb} web site is <A HREF="https://www.threadingbuildingblocks.org">`https://www.threadingbuildingblocks.org`</A>.
 
@@ -204,7 +210,9 @@ The \sc{Tbb} web site is <A HREF="https://www.threadingbuildingblocks.org">`http
 the LAS format (or the compressed LAZ format).
 
 In \cgal, \sc{LASlib} is used to provide input and output functions in
-the \ref PkgPointSetProcessing3 package.
+the \ref PkgPointSetProcessing3 package. In order to use \sc{LASlib} in
+\cgal programs, the provided CMake function
+`CGAL_target_use_LASLIB(<target>)` should be used.
 
 The \sc{LASlib} web site is <a
 href="https://rapidlasso.com/lastools/">`https://rapidlasso.com/lastools/`</a>. \sc{LASlib}
@@ -217,7 +225,9 @@ CMake based install procedure</a>.
 \sc{OpenCV} (Open Computer Vision) is a library designed for computer
 vision, computer graphics and machine learning.
 
-In \cgal, \sc{OpenCV} is used by the \ref PkgClassification package.
+In \cgal, \sc{OpenCV} is used by the \ref PkgClassification
+package. In order to use \sc{OpenCV} in \cgal programs, the provided
+CMake function `CGAL_target_use_OpenCV(<target>)` should be used.
 
 The \sc{OpenCV} web site is <A HREF="https://opencv.org/">`https://opencv.org/`</A>.
 
@@ -235,6 +245,9 @@ enable and compile the following targets:
 - `tensorflow_BUILD_PYTHON_BINDINGS`
 - `tensorflow_BUILD_SHARED_LIB`.
 
+In order to use \sc{TensorFlow} in \cgal programs, the provided CMake
+function `CGAL_target_use_TensorFlow(<target>)` should be used.
+
 The \sc{TensorFlow} web site is <A HREF="https://www.tensorflow.org/">`https://www.tensorflow.org/`</A>.
 
 \subsection thirdpartyMETIS METIS
@@ -274,7 +287,10 @@ for more information.
 
 \sc{GLPK} (GNU Linear Programming Kit) is a library for solving linear programming (LP), mixed integer programming (MIP), and other related problems.
 
-In \cgal, \sc{GLPK} provides an optional linear integer program solver in the \ref PkgPolygonalSurfaceReconstruction package.
+In \cgal, \sc{GLPK} provides an optional linear integer program solver
+in the \ref PkgPolygonalSurfaceReconstruction package. In order to use
+\sc{GLPK} in \cgal programs, the provided CMake function
+`CGAL_target_use_GLPK(<target>)` should be used.
 
 The \sc{GLPK} web site is <A HREF="https://www.gnu.org/software/glpk/">`https://www.gnu.org/software/glpk/`</A>.
 
@@ -282,7 +298,10 @@ The \sc{GLPK} web site is <A HREF="https://www.gnu.org/software/glpk/">`https://
 
 \sc{SCIP} (Solving Constraint Integer Programs) is currently one of the fastest open source solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP).
 
-In \cgal, \sc{SCIP} provides an optional linear integer program solver in the \ref PkgPolygonalSurfaceReconstruction package.
+In \cgal, \sc{SCIP} provides an optional linear integer program solver
+in the \ref PkgPolygonalSurfaceReconstruction package. In order to use
+\sc{SCIP} in \cgal programs, the provided CMake function
+`CGAL_target_use_SCIP(<target>)` should be used.
 
 The \sc{SCIP} web site is <A HREF="http://scip.zib.de/">`http://scip.zib.de/`</A>.
 
diff --git a/Documentation/doc/Documentation/Usage.txt b/Documentation/doc/Documentation/Usage.txt
index b1a21d4c121..38d2b257697 100644
--- a/Documentation/doc/Documentation/Usage.txt
+++ b/Documentation/doc/Documentation/Usage.txt
@@ -60,6 +60,12 @@ On most operating systems, package managers offer \cgal and its essential third
 On macOS, we recommend using of <a href="https://brew.sh/">Homebrew</a> in the following way:
 
     brew install cgal
+    brew install cgal-qt5   #(only for GUI)
+
+You should check that cgal and cgal-qt5 are correctly "linked", especially when upgrading from an old version. If not, run the following command:
+
+    brew link cgal
+    brew link cgal-qt5  #(if you installed it)
 
 On Linux distributions such as `Debian`/`Ubuntu`/`Mint`, use `apt-get` in the following way:
 
@@ -148,10 +154,14 @@ The variable `CGAL_DIR` is also generally found when \cgal has been obtained via
 In the rare event that it has not, the variable `CGAL_DIR` should be set manually to:
 
 <ul>
-<li>something like `/usr/local/Cellar/cgal/CGAL-\cgalReleaseNumber/lib/cmake/CGAL`, for Brew.</li>
+<li>something like `/usr/local/opt/cgal/lib/cmake/CGAL`, for Brew.</li>
 <li>something like `/usr/lib/x86_64-linux-gnu/cmake/CGAL`, for Linux distributions.</li>
 </ul>
 
+Note that you can also use `CMAKE_PREFIX_PATH` to point to a directory that contains all dependencies, like so:
+
+    cmake -DCMAKE_PREFIX_PATH=/my/custom/brew/installation/dir -DCMAKE_BUILD_TYPE=Release .
+
 If \cgal has been obtained via other means, `CGAL_DIR` must point to the root directory
 of the \cgal source code (either the root of the unpacked release tarball or the root
 of the Git working directory).
@@ -162,6 +172,13 @@ if no debugging is intended. Users should thus run:
     cd CGAL-\cgalReleaseNumber/examples/Triangulation_2
     cmake -DCGAL_DIR=$HOME/CGAL-\cgalReleaseNumber -DCMAKE_BUILD_TYPE=Release . # we are here using a release tarball
 
+Note that the package Qt on brew is "keg-only", which means it cannot be "linked" with brew.
+You will have to specify the Qt5_DIR by hand to cmake, using something like
+
+    -DQt5_DIR=/usr/local/opt/qt/lib/cmake/Qt5
+
+where '/usr/local/` is actually your current brew installation directory.
+
 \subsection usage_configuring_cmake_gui Specifying Missing Dependencies
 
 The configuration process launched above might fail if CMake fails to find
diff --git a/Documentation/doc/Documentation/advanced/Configuration_variables.txt b/Documentation/doc/Documentation/advanced/Configuration_variables.txt
index 1bebdc5ddd7..2a880f1e488 100644
--- a/Documentation/doc/Documentation/advanced/Configuration_variables.txt
+++ b/Documentation/doc/Documentation/advanced/Configuration_variables.txt
@@ -85,6 +85,7 @@ and will serverly limit performances.
 | Variable              | Description                                                           | Type        | %Default Value |
 | :-                    | :-                    | :-   |  :-            |
 | `CGAL_DIR`            | Full-path to the binary directory where \cgal was configured          |Either CMake or Environment | none |
+| `Qt5_DIR`             | Full-path to the Qt cmake directory  |CMake| platform-dependent|
 
 
 \subsection installation_variables_third_party Variables Providing Information About 3rd-Party Libraries
@@ -300,6 +301,20 @@ environment variable is sufficient.
 | `ESBTL_INC_DIR` | Directory containing the `ESBTL/default.h` file | Environment |
 | `ESBTL_INCLUDE_DIR` | Directory containing the `ESBTL/default.h` file | CMake |
 
+\subsection installation_metis METIS Library
+
+Some BGL examples require the \sc{Metis} library in order to partition \sc{Metis} meshes.
+
+If \sc{Metis} is not automatically found, setting the `METIS_INCLUDE_DIR` and `METIS_LIBRARY`
+cmake variables is necessary.
+
+
+| Variable             | Description           | Type        |
+| :-                   | :-                    | :-             |
+| `METIS_INCLUDE_DIR` | Directory of \sc{Metis} default installation | CMAKE |
+| `METIS_LIBRARY` | Directory containing the `libmetis.so or .lib` file | CMAKE |
+
+
 \subsection installation_tbb TBB Library
 
 If \sc{Tbb} is not automatically found, the user must set the `TBB_ROOT`
@@ -324,6 +339,44 @@ Note that the variables in the table below are being used.
 | `TBB_MALLOCPROXY_DEBUG_LIBRARY` | Full pathname of the compiled TBB debug malloc_proxy library (optional) | CMake |
 | `TBB_MALLOCPROXY_RELEASE_LIBRARY` | Full pathname of the compiled TBB release malloc_proxy library (optional) | CMake |
 
+\subsection installation_laslib LASlib library
+
+If LASLIB is not automatically found, the following variables must be set:
+
+| Variable             | Description           | Type        |
+| :-                   | :-                    | :-             |
+| `LASLIB_INCLUDE_DIR` | Directory containing the file `lasreader.hpp` | CMake |
+| `LASZIP_INCLUDE_DIR` | Directory containing the file `mydefs.hpp` | CMake |
+| `LASLIB_LIBRARIES` | Full pathname of the compiled LASLIB library | CMake |
+
+\subsection installation_OpenCV OpenCV library
+
+The environment variable `OPENCV_DIR` should be set to the directory
+containing the file `OpenCVConfig.cmake` provided by OpenCV.
+
+\subsection installation_TensorFlow TensorFlow library
+
+If TensorFlow is not automatically found, the following variables must be set:
+
+| Variable             | Description           | Type        |
+| :-                   | :-                    | :-             |
+| `TensorFlow_INCLUDE_DIR` | Directory containing the directories `tensorflow/core`, `tensorflow/cc`, etc. | CMake |
+| `TensorFlow_LIBRARY` | Full pathname of the compiled TensorFlow C++ library | CMake |
+
+\subsection installation_SCIP SCIP library
+
+The environment variable `SCIP_DIR` should be set to the directory
+containing the file `scip-config.cmake` provided by SCIP.
+
+\subsection installation_GLPK GLPK library
+
+If GLPK is not automatically found, the following variables must be set:
+
+| Variable             | Description           | Type        |
+| :-                   | :-                    | :-             |
+| `GLPK_INCLUDE_DIR` | Directory containing the file `glpk.h` | CMake |
+| `GLPK_LIBRARIES` | Full pathname of the compiled GLPK library | CMake |
+
 \section installation_compiler_workarounds Compiler Workarounds
 
 A number of boolean flags are used to workaround compiler bugs and
diff --git a/Documentation/doc/Documentation/windows.txt b/Documentation/doc/Documentation/windows.txt
index ca37e021001..c123b537496 100644
--- a/Documentation/doc/Documentation/windows.txt
+++ b/Documentation/doc/Documentation/windows.txt
@@ -37,8 +37,8 @@ The first step is to clone or download `vcpkg` from
 
 By default `vcpkg` installs for 32 bit binaries and will use the latest version of Visual C++
 installed on your machine.   If you develop 64 bit software you must
-set the Windows environment variable `VCPKG_DEFAULT_TRIPLE` to `x64-windows`
-or pass the option `--triplet x64-windows` whenever you install a package.
+set the Windows environment variable `VCPKG_DEFAULT_TRIPLET` to `x64-windows`
+or add the suffix `:x64-windows` to the package name you want to install (for example `cgal:x64-windows`).
 We refer to the
 <a href="https://github.com/microsoft/vcpkg/blob/master/docs/examples/installing-and-using-packages.md#step-2-use">official documentation</a>
 of `vcpkg` if you want to compile for an older version of a compiler.
diff --git a/Documentation/doc/resources/1.8.13/menu_version.js b/Documentation/doc/resources/1.8.13/menu_version.js
index 03ad8f3fbd0..36b298ee045 100644
--- a/Documentation/doc/resources/1.8.13/menu_version.js
+++ b/Documentation/doc/resources/1.8.13/menu_version.js
@@ -3,12 +3,12 @@
 
   var url_re =  /(cgal\.geometryfactory\.com\/CGAL\/doc\/|doc\.cgal\.org\/)(master|latest|(\d\.\d+|\d\.\d+\.\d+))\//;
   var url_local =  /.*\/doc_output\//;
-  var current_version_local = '5.0.1'
+  var current_version_local = '5.1-dev'
   var all_versions = [
       'master',
       'latest',
-      '5.0.1',
-      '4.14.2',
+      '5.0.2',
+      '4.14.3',
       '4.13.2',
       '4.12.2',
       '4.11.3',
diff --git a/Documentation/doc/resources/1.8.14/menu_version.js b/Documentation/doc/resources/1.8.14/menu_version.js
index 03ad8f3fbd0..36b298ee045 100644
--- a/Documentation/doc/resources/1.8.14/menu_version.js
+++ b/Documentation/doc/resources/1.8.14/menu_version.js
@@ -3,12 +3,12 @@
 
   var url_re =  /(cgal\.geometryfactory\.com\/CGAL\/doc\/|doc\.cgal\.org\/)(master|latest|(\d\.\d+|\d\.\d+\.\d+))\//;
   var url_local =  /.*\/doc_output\//;
-  var current_version_local = '5.0.1'
+  var current_version_local = '5.1-dev'
   var all_versions = [
       'master',
       'latest',
-      '5.0.1',
-      '4.14.2',
+      '5.0.2',
+      '4.14.3',
       '4.13.2',
       '4.12.2',
       '4.11.3',
diff --git a/Documentation/doc/resources/1.8.4/menu_version.js b/Documentation/doc/resources/1.8.4/menu_version.js
index 03ad8f3fbd0..36b298ee045 100644
--- a/Documentation/doc/resources/1.8.4/menu_version.js
+++ b/Documentation/doc/resources/1.8.4/menu_version.js
@@ -3,12 +3,12 @@
 
   var url_re =  /(cgal\.geometryfactory\.com\/CGAL\/doc\/|doc\.cgal\.org\/)(master|latest|(\d\.\d+|\d\.\d+\.\d+))\//;
   var url_local =  /.*\/doc_output\//;
-  var current_version_local = '5.0.1'
+  var current_version_local = '5.1-dev'
   var all_versions = [
       'master',
       'latest',
-      '5.0.1',
-      '4.14.2',
+      '5.0.2',
+      '4.14.3',
       '4.13.2',
       '4.12.2',
       '4.11.3',
diff --git a/Filtered_kernel/include/CGAL/Kernel_profiler.h b/Filtered_kernel/include/CGAL/Kernel_profiler.h
index 9a55a12ea13..d592de79fc9 100644
--- a/Filtered_kernel/include/CGAL/Kernel_profiler.h
+++ b/Filtered_kernel/include/CGAL/Kernel_profiler.h
@@ -34,77 +34,13 @@ struct Primitive_profiler
     Primitive_profiler(const P& p = P())
       : P(p) {}
 
-    template <class A1>
+    template <class ... A>
     result_type
-    operator()(const A1 &a1) const
+    operator()(A&& ... a) const
     {
 	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1);
+	return P::operator()(std::forward<A>(a)...);
     }
-
-    template <class A1, class A2>
-    result_type
-    operator()(const A1 &a1, const A2 &a2) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2);
-    }
-
-    template <class A1, class A2, class A3>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3);
-    }
-
-    template <class A1, class A2, class A3, class A4>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3, a4);
-    }
-
-    template <class A1, class A2, class A3, class A4, class A5>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	       const A5 &a5) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3, a4, a5);
-    }
-
-    template <class A1, class A2, class A3, class A4, class A5, class A6>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	       const A5 &a5, const A6 &a6) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3, a4, a5, a6);
-    }
-
-    template <class A1, class A2, class A3, class A4,
-              class A5, class A6, class A7>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	       const A5 &a5, const A6 &a6, const A7 &a7) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3, a4, a5, a6, a7);
-    }
-
-    template <class A1, class A2, class A3, class A4,
-              class A5, class A6, class A7, class A8>
-    result_type
-    operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	       const A5 &a5, const A6 &a6, const A7 &a7, const A8 &a8) const
-    {
-	CGAL_KERNEL_PROFILER;
-	return P::operator()(a1, a2, a3, a4, a5, a6, a7, a8);
-    }
-
-    // ...
 };
 
 // We inherit all geometric objects from K, and just replace the primitives.
diff --git a/Filtered_kernel/include/CGAL/Lazy.h b/Filtered_kernel/include/CGAL/Lazy.h
index 2a887d57b48..dd3616d4a7e 100644
--- a/Filtered_kernel/include/CGAL/Lazy.h
+++ b/Filtered_kernel/include/CGAL/Lazy.h
@@ -731,6 +731,9 @@ public :
     PTR = new Lazy_rep_0<AT,ET,E2A>(std::move(e));
   }
 
+  friend void swap(Lazy& a, Lazy& b) noexcept
+  { swap(static_cast<Handle&>(a), static_cast<Handle&>(b)); }
+
   const AT& approx() const
   { return ptr()->approx(); }
 
diff --git a/Generator/examples/Generator/CMakeLists.txt b/Generator/examples/Generator/CMakeLists.txt
index 8ef7883800d..0fa1a97db40 100644
--- a/Generator/examples/Generator/CMakeLists.txt
+++ b/Generator/examples/Generator/CMakeLists.txt
@@ -12,9 +12,6 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0 QUIET) #(3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
   
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
@@ -23,6 +20,10 @@ if ( CGAL_FOUND )
         OR NOT (${cppfile} STREQUAL "random_points_on_tetrahedral_mesh_3.cpp")
         OR EIGEN3_FOUND)
       create_single_source_cgal_program( "${cppfile}" )
+      if (EIGEN3_FOUND)
+        get_filename_component(target ${cppfile} NAME_WE)
+        CGAL_target_use_Eigen(${target})
+      endif()
     endif()
   endforeach()
 
diff --git a/Generator/test/Generator/CMakeLists.txt b/Generator/test/Generator/CMakeLists.txt
index 8842178b20b..0eb1657d2a9 100644
--- a/Generator/test/Generator/CMakeLists.txt
+++ b/Generator/test/Generator/CMakeLists.txt
@@ -12,15 +12,16 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0 QUIET) #(3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
 
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     if(NOT (${cppfile} STREQUAL "generic_random_test.cpp") OR EIGEN3_FOUND)
       create_single_source_cgal_program( "${cppfile}" )
+      if (EIGEN3_FOUND)
+        get_filename_component(target ${cppfile} NAME_WE)
+        CGAL_target_use_Eigen(${target})
+      endif()
     endif()
   endforeach()
 
diff --git a/GraphicsView/demo/Polygon/CMakeLists.txt b/GraphicsView/demo/Polygon/CMakeLists.txt
index 8d0df276e19..1a84a55e34a 100644
--- a/GraphicsView/demo/Polygon/CMakeLists.txt
+++ b/GraphicsView/demo/Polygon/CMakeLists.txt
@@ -16,9 +16,7 @@ endif()
 find_package(CGAL COMPONENTS Qt5 Core)
 
 find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-else()
+if (NOT EIGEN3_FOUND)
   message(STATUS "NOTICE: This project requires the Eigen library, and will not be compiled.")
   return()
 endif()
@@ -48,6 +46,7 @@ if ( CGAL_FOUND AND CGAL_Qt5_FOUND AND Qt5_FOUND )
 
   # The executable itself.
   add_executable  ( Polygon_2 Polygon_2.cpp  ${DT_UI_FILES} ${DT_RESOURCE_FILES} ${CGAL_Qt5_RESOURCE_FILES} ${CGAL_Qt5_MOC_FILES} )
+  CGAL_target_use_Eigen(Polygon_2)
 
   add_to_cached_list( CGAL_EXECUTABLE_TARGETS Polygon_2 )
 
diff --git a/GraphicsView/src/CGAL_Qt5/CMakeLists.txt b/GraphicsView/src/CGAL_Qt5/CMakeLists.txt
index 224de8bbe4b..c9ab3d99241 100644
--- a/GraphicsView/src/CGAL_Qt5/CMakeLists.txt
+++ b/GraphicsView/src/CGAL_Qt5/CMakeLists.txt
@@ -31,8 +31,8 @@ if(COMMAND add_config_flag)
   add_config_flag( CGAL_HAS_QT5 )
 endif()
 
+install(DIRECTORY "../../include/CGAL/Qt/" DESTINATION "${CGAL_INSTALL_INC_DIR}/CGAL/Qt" COMPONENT CGAL_Qt5)
 if (CGAL_HEADER_ONLY)
-  install(DIRECTORY "../../include/CGAL/Qt/" DESTINATION "${CGAL_INSTALL_INC_DIR}/CGAL/include/CGAL/Qt" COMPONENT CGAL_Qt5)
   install(DIRECTORY "../../demo/resources/" DESTINATION "${CGAL_INSTALL_CMAKE_DIR}/demo/resources" COMPONENT CGAL_Qt5)
   install(DIRECTORY "../../demo/icons/" DESTINATION "${CGAL_INSTALL_CMAKE_DIR}/demo/icons" COMPONENT CGAL_Qt5)
 endif()
diff --git a/Heat_method_3/examples/Heat_method_3/CMakeLists.txt b/Heat_method_3/examples/Heat_method_3/CMakeLists.txt
index ee40274e08e..f9703071b81 100644
--- a/Heat_method_3/examples/Heat_method_3/CMakeLists.txt
+++ b/Heat_method_3/examples/Heat_method_3/CMakeLists.txt
@@ -34,11 +34,8 @@ endif()
 
 find_package(Eigen3 3.3.0)
 
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-else()
+if (NOT EIGEN3_FOUND)
   message(STATUS "This project requires the Eigen library (3.3 or greater), and will not be compiled.")
-
   return()
 endif()
 
@@ -54,6 +51,10 @@ include_directories( BEFORE include )
 include( CGAL_CreateSingleSourceCGALProgram )
 
 create_single_source_cgal_program( "heat_method.cpp" )
+CGAL_target_use_Eigen(heat_method)
 create_single_source_cgal_program( "heat_method_polyhedron.cpp" )
+CGAL_target_use_Eigen(heat_method_polyhedron)
 create_single_source_cgal_program( "heat_method_surface_mesh.cpp" )
+CGAL_target_use_Eigen(heat_method_surface_mesh)
 create_single_source_cgal_program( "heat_method_surface_mesh_direct.cpp" )
+CGAL_target_use_Eigen(heat_method_surface_mesh_direct)
diff --git a/Heat_method_3/test/Heat_method_3/CMakeLists.txt b/Heat_method_3/test/Heat_method_3/CMakeLists.txt
index adb6cfa80c0..af4fd6eb470 100644
--- a/Heat_method_3/test/Heat_method_3/CMakeLists.txt
+++ b/Heat_method_3/test/Heat_method_3/CMakeLists.txt
@@ -34,11 +34,8 @@ endif()
 
 find_package(Eigen3 3.3.0)
 
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-else()  
+if (NOT EIGEN3_FOUND)
   message(STATUS "This project requires the  Eigen library (3.3 or greater), and will not be compiled.")
-
   return()
 endif()
 
@@ -52,5 +49,8 @@ include_directories( BEFORE include )
 include( CGAL_CreateSingleSourceCGALProgram )
 
 create_single_source_cgal_program( "heat_method_concept.cpp" )
+CGAL_target_use_Eigen(heat_method_concept)
 create_single_source_cgal_program( "heat_method_surface_mesh_test.cpp" )
+CGAL_target_use_Eigen(heat_method_surface_mesh_test)
 create_single_source_cgal_program( "heat_method_surface_mesh_direct_test.cpp" )
+CGAL_target_use_Eigen(heat_method_surface_mesh_direct_test)
diff --git a/INSTALL.md b/INSTALL.md
index c2c9526c05e..50f7a3d3e8c 100644
--- a/INSTALL.md
+++ b/INSTALL.md
@@ -8,7 +8,7 @@ git clone https://github.com/CGAL/cgal.git /path/to/cgal.git
 cd /path/to/cgal.git/Triangulation_2/examples/Triangulation_2
 mkdir -p build/debug
 cd build/debug
-cmake -DCMAKE_BUILD_TYPE=Debug -DCGAL_DIR=/path/to/cgal.git
+cmake -DCMAKE_BUILD_TYPE=Debug -DCGAL_DIR=/path/to/cgal.git ../..
 make
 ```
 
diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index 2e87bd47f28..642b1be4140 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -21,6 +21,10 @@ Release date: June 2020
 ### Intersecting Sequences of dD Iso-oriented Boxes 
  -   Added parallel versions of the functions `CGAL::box_intersection_d()` and `CGAL::box_self_intersection_d()`.
 
+### CGAL and the Boost Graph Library (BGL)
+ -   Introduced the function `set_triangulation_ids(Triangulation& tr)` which must be used to initialize vertex,
+     edge, and face indices of a triangulation meant to be used with BGL algorithms.
+
 ### Polygon Mesh Processing
 
 -   Introduced a new function, `CGAL::Polygon_mesh_processing::remove_connected_components_of_negligible_size()`, 
@@ -91,6 +95,11 @@ Release date: June 2020
 ### STL Extensions for CGAL
  -   Added a new concurrency tag: `CGAL::Parallel_if_available_tag`. This tag is a convenience typedef to `CGAL::Parallel_tag`
      if the third party library TBB has been found and linked with, and to `CGAL::Sequential_tag` otherwise.
+     
+
+### Convex_hull_3
+- A new overload for `convex_hull_3()` that takes a model of `VertexListGraph` has been added.
+
 
 [Release 5.0](https://github.com/CGAL/cgal/releases/tag/releases%2FCGAL-5.0)
 -----------
diff --git a/Installation/CMakeLists.txt b/Installation/CMakeLists.txt
index c96b2b9af03..4b5aaa2f173 100644
--- a/Installation/CMakeLists.txt
+++ b/Installation/CMakeLists.txt
@@ -882,11 +882,11 @@ endif()
 
 foreach (dir ${CGAL_CONFIGURED_PACKAGES})
   if (EXISTS ${dir}/include/CGAL) 
-    install(DIRECTORY ${dir}/include/CGAL              DESTINATION ${CGAL_INSTALL_INC_DIR} PATTERN ".svn" EXCLUDE)
+    install(DIRECTORY ${dir}/include/CGAL              DESTINATION ${CGAL_INSTALL_INC_DIR} PATTERN ".svn" EXCLUDE PATTERN "Qt" EXCLUDE)
   endif()
 endforeach()
 if(EXISTS ${CMAKE_BINARY_DIR}/include/CGAL)
-  install(DIRECTORY ${CMAKE_BINARY_DIR}/include/CGAL     DESTINATION ${CGAL_INSTALL_INC_DIR} PATTERN ".svn" EXCLUDE)
+  install(DIRECTORY ${CMAKE_BINARY_DIR}/include/CGAL     DESTINATION ${CGAL_INSTALL_INC_DIR} PATTERN ".svn" EXCLUDE PATTERN "Qt" EXCLUDE)
 endif()
 
 file(GLOB scripts "scripts/*")
diff --git a/Installation/cmake/modules/CGAL_Common.cmake b/Installation/cmake/modules/CGAL_Common.cmake
index 51967d5f6d5..4ba76b468b9 100644
--- a/Installation/cmake/modules/CGAL_Common.cmake
+++ b/Installation/cmake/modules/CGAL_Common.cmake
@@ -56,10 +56,13 @@ if( NOT CGAL_COMMON_FILE_INCLUDED )
     endif()
   endif()
 
-  # set minimal version of some optional libraries:
-  set( Eigen3_FIND_VERSION "3.1.0")
-  # set use-file for Eigen3 (needed to have default solvers)
-  set(EIGEN3_USE_FILE "UseEigen3")
-
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_Boost_IOStreams.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_Boost_Serialization.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_Eigen.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_GLPK.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_LASLIB.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_OpenCV.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_SCIP.cmake)
   include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_TBB.cmake)
+  include(${CMAKE_CURRENT_LIST_DIR}/CGAL_target_use_TensorFlow.cmake)
 endif()
diff --git a/Installation/cmake/modules/CGAL_SetupCGALDependencies.cmake b/Installation/cmake/modules/CGAL_SetupCGALDependencies.cmake
index f0a2f7c3ea3..9125a477c93 100644
--- a/Installation/cmake/modules/CGAL_SetupCGALDependencies.cmake
+++ b/Installation/cmake/modules/CGAL_SetupCGALDependencies.cmake
@@ -119,12 +119,23 @@ function(CGAL_setup_CGAL_dependencies target)
   # Now setup compilation flags
   if(MSVC)
     target_compile_options(${target} ${keyword}
-      "-D_SCL_SECURE_NO_DEPRECATE;-D_SCL_SECURE_NO_WARNINGS"
-      "/fp:strict"
-      "/fp:except-"
-      "/wd4503"  # Suppress warnings C4503 about "decorated name length exceeded"
-      "/bigobj"  # Use /bigobj by default
-      )
+      "-D_SCL_SECURE_NO_DEPRECATE;-D_SCL_SECURE_NO_WARNINGS")
+    if(CMAKE_VERSION VERSION_LESS 3.11)
+      target_compile_options(${target} ${keyword}
+        /fp:strict
+        /fp:except-
+        /wd4503  # Suppress warnings C4503 about "decorated name length exceeded"
+        /bigobj  # Use /bigobj by default
+        )
+    else()
+      # The MSVC generator supports `$<COMPILE_LANGUAGE: >` since CMake 3.11.
+      target_compile_options(${target} ${keyword}
+        $<$<COMPILE_LANGUAGE:CXX>:/fp:strict>
+        $<$<COMPILE_LANGUAGE:CXX>:/fp:except->
+        $<$<COMPILE_LANGUAGE:CXX>:/wd4503>  # Suppress warnings C4503 about "decorated name length exceeded"
+        $<$<COMPILE_LANGUAGE:CXX>:/bigobj>  # Use /bigobj by default
+        )
+    endif()
   elseif(CMAKE_CXX_COMPILER_ID MATCHES "Intel")
     message( STATUS "Using Intel Compiler. Adding -fp-model strict" )
     if(WIN32)
diff --git a/Installation/cmake/modules/CGAL_target_use_Boost_IOStreams.cmake b/Installation/cmake/modules/CGAL_target_use_Boost_IOStreams.cmake
new file mode 100644
index 00000000000..d57f785d54f
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_Boost_IOStreams.cmake
@@ -0,0 +1,39 @@
+if (CGAL_target_use_Boost_IOStreams_included)
+  return()
+endif()
+set(CGAL_target_use_Boost_IOStreams_included TRUE)
+
+function(CGAL_target_use_Boost_IOStreams target)
+
+  if( WIN32 )
+    # to avoid a warning with old cmake 
+    set(_Boost_BZIP2_HEADERS             "boost/iostreams/filter/bzip2.hpp")
+    set(_Boost_ZLIB_HEADERS              "boost/iostreams/filter/zlib.hpp")
+    find_package( Boost OPTIONAL_COMPONENTS bzip2 zlib)
+  else()
+    find_package(ZLIB QUIET)
+  endif()
+
+  if(TARGET Boost::iostreams)
+    target_link_libraries(${target} PUBLIC Boost::iostreams)
+  else()
+    target_link_libraries(${target} PUBLIC ${Boost_IOSTREAMS_LIBRARY})
+  endif()
+  
+  if( WIN32 )
+    if (Boost_ZLIB_FOUND AND Boost_BZIP2_FOUND)
+      target_link_libraries(${target} PUBLIC ${Boost_ZLIB_LIBRARY} ${Boost_BZIP2_LIBRARY})
+    else()
+      message(STATUS "NOTICE: This project requires Boost ZLIB and Boost BZIP2, and will not be compiled.")
+      return()
+    endif()
+  else()
+    if(ZLIB_FOUND)
+      target_link_libraries(${target} PUBLIC ZLIB::ZLIB)
+    else()
+      message(STATUS "NOTICE: This project requires ZLIB, and will not be compiled.")
+      return()
+    endif()
+  endif()
+
+endfunction()
diff --git a/Installation/cmake/modules/CGAL_target_use_Boost_Serialization.cmake b/Installation/cmake/modules/CGAL_target_use_Boost_Serialization.cmake
new file mode 100644
index 00000000000..d6ae805efd8
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_Boost_Serialization.cmake
@@ -0,0 +1,14 @@
+if (CGAL_target_use_Boost_Serialization_included)
+  return()
+endif()
+set(CGAL_target_use_Boost_Serialization_included TRUE)
+
+function(CGAL_target_use_Boost_Serialization target)
+
+  if(TARGET Boost::serialization)
+    target_link_libraries(${target} PUBLIC Boost::serialization)
+  else()
+    target_link_libraries(${target} PUBLIC ${Boost_SERIALIZATION_LIBRARY})
+  endif()
+
+endfunction()
diff --git a/Installation/cmake/modules/CGAL_target_use_Eigen.cmake b/Installation/cmake/modules/CGAL_target_use_Eigen.cmake
new file mode 100644
index 00000000000..84f9f3be721
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_Eigen.cmake
@@ -0,0 +1,13 @@
+if (CGAL_target_use_Eigen_included)
+  return()
+endif()
+set(CGAL_target_use_Eigen_included TRUE)
+
+set( Eigen3_FIND_VERSION "3.1.0")
+set(EIGEN3_USE_FILE "UseEigen3")
+
+function(CGAL_target_use_Eigen target)
+  target_include_directories(${target} PUBLIC ${EIGEN3_INCLUDE_DIR})
+  target_compile_options( ${target} PUBLIC -DCGAL_EIGEN3_ENABLED)
+endfunction()
+
diff --git a/Installation/cmake/modules/CGAL_target_use_GLPK.cmake b/Installation/cmake/modules/CGAL_target_use_GLPK.cmake
new file mode 100644
index 00000000000..f19bd315b16
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_GLPK.cmake
@@ -0,0 +1,11 @@
+if (CGAL_target_use_GLPK_included)
+  return()
+endif()
+set(CGAL_target_use_GLPK_included TRUE)
+
+function(CGAL_target_use_GLPK target)
+  target_include_directories(${target} PUBLIC ${GLPK_INCLUDE_DIR})
+  target_compile_options(${target} PUBLIC -DCGAL_USE_GLPK)
+  target_link_libraries(${target} PUBLIC ${GLPK_LIBRARIES})
+endfunction()
+
diff --git a/Installation/cmake/modules/CGAL_target_use_LASLIB.cmake b/Installation/cmake/modules/CGAL_target_use_LASLIB.cmake
new file mode 100644
index 00000000000..65ad9084e5a
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_LASLIB.cmake
@@ -0,0 +1,11 @@
+if (CGAL_target_use_LASLIB_included)
+  return()
+endif()
+set(CGAL_target_use_LASLIB_included TRUE)
+
+function(CGAL_target_use_LASLIB target)
+  target_include_directories(${target} PUBLIC ${LASLIB_INCLUDE_DIR})
+  target_include_directories(${target} PUBLIC ${LASZIP_INCLUDE_DIR})
+  target_compile_options( ${target} PUBLIC -DCGAL_LINKED_WITH_LASLIB)
+  target_link_libraries(${target} PUBLIC ${LASLIB_LIBRARIES})
+endfunction()
diff --git a/Installation/cmake/modules/CGAL_target_use_OpenCV.cmake b/Installation/cmake/modules/CGAL_target_use_OpenCV.cmake
new file mode 100644
index 00000000000..d378d50aead
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_OpenCV.cmake
@@ -0,0 +1,10 @@
+if (CGAL_target_use_OpenCV_included)
+  return()
+endif()
+set(CGAL_target_use_OpenCV_included TRUE)
+
+function(CGAL_target_use_OpenCV target)
+  target_include_directories(${target} PUBLIC ${OpenCV_INCLUDE_DIRS})
+  target_compile_options( ${target} PUBLIC -DCGAL_LINKED_WITH_OPENCV)
+  target_link_libraries(${target} PUBLIC ${OpenCV_LIBS})
+endfunction()
diff --git a/Installation/cmake/modules/CGAL_target_use_SCIP.cmake b/Installation/cmake/modules/CGAL_target_use_SCIP.cmake
new file mode 100644
index 00000000000..354216bb1f7
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_SCIP.cmake
@@ -0,0 +1,11 @@
+if (CGAL_target_use_SCIP_included)
+  return()
+endif()
+set(CGAL_target_use_SCIP_included TRUE)
+
+function(CGAL_target_use_SCIP target)
+  target_include_directories(${target} PUBLIC ${SCIP_INCLUDE_DIRS})
+  target_compile_options(${target} PUBLIC -DCGAL_USE_SCIP)
+  target_link_libraries(${target} PUBLIC ${SCIP_LIBRARIES})
+endfunction()
+
diff --git a/Installation/cmake/modules/CGAL_target_use_TensorFlow.cmake b/Installation/cmake/modules/CGAL_target_use_TensorFlow.cmake
new file mode 100644
index 00000000000..80bda689dab
--- /dev/null
+++ b/Installation/cmake/modules/CGAL_target_use_TensorFlow.cmake
@@ -0,0 +1,10 @@
+if (CGAL_target_use_TensorFlow_included)
+  return()
+endif()
+set(CGAL_target_use_TensorFlow_included TRUE)
+
+function(CGAL_target_use_TensorFlow target)
+  target_include_directories(${target} PUBLIC ${TensorFlow_INCLUDE_DIR})
+  target_compile_options( ${target} PUBLIC -DCGAL_LINKED_WITH_TENSORFLOW)
+  target_link_libraries(${target} PUBLIC ${TensorFlow_LIBRARU})
+endfunction()
diff --git a/Installation/cmake/modules/FindLibSSH.cmake b/Installation/cmake/modules/FindLibSSH.cmake
new file mode 100644
index 00000000000..e2c49ee2fce
--- /dev/null
+++ b/Installation/cmake/modules/FindLibSSH.cmake
@@ -0,0 +1,39 @@
+# - Try to find the LibSSH libraries
+# This module defines:
+#  LIBSSH_FOUND             - system has LibSSH lib
+#  LIBSSH_INCLUDE_DIR       - the LibSSH include directory
+#  LIBSSH_LIBRARIES_DIR     - directory where the LibSSH libraries are located
+#  LIBSSH_LIBRARIES         - Link these to use LibSSH
+
+
+include(FindPackageHandleStandardArgs)
+include(${CMAKE_CURRENT_LIST_DIR}/CGAL_GeneratorSpecificSettings.cmake)
+
+if(LIBSSH_INCLUDE_DIR)
+  set(LIBSSH_in_cache TRUE)
+else()
+  set(LIBSSH_in_cache FALSE)
+endif()
+if(NOT LIBSSH_LIBRARIES)
+  set(LIBSSH_in_cache FALSE)
+endif()
+
+# Is it already configured?
+if( NOT LIBSSH_in_cache )
+
+  find_path(LIBSSH_INCLUDE_DIR
+    NAMES "libssh/libssh.h"
+    )
+
+  find_library(LIBSSH_LIBRARIES NAMES ssh libssh
+    HINTS "/usr/lib"
+    "usr/lib/x86_64-linux-gnu"
+    PATH_SUFFIXES lib
+    DOC "Path to the LIBSSH library"
+    )
+endif()
+
+SET(LIBSSH_FOUND TRUE)
+if( NOT LIBSSH_LIBRARIES OR NOT LIBSSH_INCLUDE_DIR)
+  SET(LIBSSH_FOUND FALSE)
+endif()
diff --git a/Installation/cmake/modules/UseEigen3.cmake b/Installation/cmake/modules/UseEigen3.cmake
index e3ed18be243..850bb638392 100644
--- a/Installation/cmake/modules/UseEigen3.cmake
+++ b/Installation/cmake/modules/UseEigen3.cmake
@@ -7,3 +7,5 @@ include_directories( SYSTEM ${EIGEN3_INCLUDE_DIR} )
 add_definitions(-DCGAL_EIGEN3_ENABLED)
 
 set (EIGEN3_SETUP TRUE)
+
+message(DEPRECATION "This file UseEigen.cmake is deprecated, and the function `CGAL_target_use_Eigen` from CGAL_target_use_Eigen.cmake should be used instead.")
diff --git a/Installation/cmake/modules/UseLASLIB.cmake b/Installation/cmake/modules/UseLASLIB.cmake
index 9235230eb1f..99f3374a24f 100644
--- a/Installation/cmake/modules/UseLASLIB.cmake
+++ b/Installation/cmake/modules/UseLASLIB.cmake
@@ -2,3 +2,6 @@
 # It assumes that find_package(LASLIB) was already called.
 
 add_definitions(-DCGAL_LINKED_WITH_LASLIB)
+
+message(DEPRECATION "This file UseLASLIB.cmake is deprecated, and the function `CGAL_target_use_LASLIB` from CGAL_target_use_LASLIB.cmake should be used instead.")
+
diff --git a/Jet_fitting_3/examples/Jet_fitting_3/CMakeLists.txt b/Jet_fitting_3/examples/Jet_fitting_3/CMakeLists.txt
index 19a1b9d32bd..d53b00b46a6 100644
--- a/Jet_fitting_3/examples/Jet_fitting_3/CMakeLists.txt
+++ b/Jet_fitting_3/examples/Jet_fitting_3/CMakeLists.txt
@@ -14,7 +14,6 @@ if ( CGAL_FOUND )
   # use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     # Link with Boost.ProgramOptions (optional)
     find_package(Boost QUIET COMPONENTS program_options)
     if(Boost_PROGRAM_OPTIONS_FOUND)
@@ -30,9 +29,11 @@ if ( CGAL_FOUND )
       list(APPEND CGAL_3RD_PARTY_LIBRARIES ${Boost_PROGRAM_OPTIONS_LIBRARY})
    endif()
 
-    create_single_source_cgal_program( "Mesh_estimation.cpp" )
-    create_single_source_cgal_program( "Single_estimation.cpp" )
-    
+   create_single_source_cgal_program( "Mesh_estimation.cpp" )
+   CGAL_target_use_Eigen(Mesh_estimation)
+   create_single_source_cgal_program( "Single_estimation.cpp" )
+   CGAL_target_use_Eigen(Single_estimation)
+   
   else()
     message(STATUS "NOTICE: This program requires Eigen 3.1 (or greater) and will not be compiled.")
   endif()
diff --git a/Jet_fitting_3/test/Jet_fitting_3/CMakeLists.txt b/Jet_fitting_3/test/Jet_fitting_3/CMakeLists.txt
index c1cbc58150d..feff5e7bb7a 100644
--- a/Jet_fitting_3/test/Jet_fitting_3/CMakeLists.txt
+++ b/Jet_fitting_3/test/Jet_fitting_3/CMakeLists.txt
@@ -14,8 +14,8 @@ if ( CGAL_FOUND )
   # use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "blind_1pt.cpp" )
+    CGAL_target_use_Eigen(blind_1pt)
   else()
     message(STATUS "NOTICE: This program requires Eigen 3.1 (or greater) and will not be compiled.")
   endif()
diff --git a/Kernel_23/doc/Kernel_23/CGAL/Filtered_predicate.h b/Kernel_23/doc/Kernel_23/CGAL/Filtered_predicate.h
index 4d0ba6880ec..b08e4274f56 100644
--- a/Kernel_23/doc/Kernel_23/CGAL/Filtered_predicate.h
+++ b/Kernel_23/doc/Kernel_23/CGAL/Filtered_predicate.h
@@ -59,19 +59,13 @@ Filtered_predicate<EP, FP, C2E, C2F>();
 /// @} 
 
 /// \name Operations 
-/// Similar function operators are defined for up to 7 arguments.
 /// @{
 
 /*!
-The unary function operator for unary predicates. 
+The function operator for predicates. 
 */ 
-template <class A1> result_type operator()(A1 a1); 
+template <class ... A> result_type operator()(A a...); 
 
-/*!
-The binary function operator for binary predicates. 
-*/ 
-template <class A1, class A2> 
-result_type operator()(A1 a1, A2 a2); 
 
 /// @}
 
diff --git a/Kernel_23/include/CGAL/Kernel/interface_macros.h b/Kernel_23/include/CGAL/Kernel/interface_macros.h
index 18d35b53366..908a6dd277c 100644
--- a/Kernel_23/include/CGAL/Kernel/interface_macros.h
+++ b/Kernel_23/include/CGAL/Kernel/interface_macros.h
@@ -110,8 +110,8 @@ CGAL_Kernel_pred(Compare_dihedral_angle_3,
 		 compare_dihedral_angle_3_object)
 CGAL_Kernel_pred(Compare_distance_2,
 		 compare_distance_2_object)
-CGAL_Kernel_pred_RT(Compare_distance_3,
-                    compare_distance_3_object)
+CGAL_Kernel_pred(Compare_distance_3,
+                 compare_distance_3_object)
 CGAL_Kernel_pred_RT(Compare_power_distance_2,
                     compare_power_distance_2_object)
 CGAL_Kernel_pred_RT(Compare_power_distance_3,
diff --git a/Kernel_23/include/CGAL/Kernel_checker.h b/Kernel_23/include/CGAL/Kernel_checker.h
index a4ee19def63..483ab5b645d 100644
--- a/Kernel_23/include/CGAL/Kernel_checker.h
+++ b/Kernel_23/include/CGAL/Kernel_checker.h
@@ -79,164 +79,21 @@ public:
     : p1(pp1), p2(pp2), cmp(c)
   { }
 
-  template <class A1>
-  typename Pairify<typename CGAL::cpp11::result_of<P1(const A1&)>::type,
-                   typename CGAL::cpp11::result_of<P2(const A1&)>::type>::result_type
-  operator()(const A1 &a1) const
+  template <class ... A>
+  typename Pairify<typename CGAL::cpp11::result_of<P1(const A&...)>::type,
+                   typename CGAL::cpp11::result_of<P2(const A&...)>::type>::result_type
+  operator()(const A&... a) const
   {
-    typedef typename CGAL::cpp11::result_of<P1(const A1&)>::type result_type_1;
-    typedef typename CGAL::cpp11::result_of<P2(const A1&)>::type result_type_2;
-    result_type_1 res1 = p1(a1.first);
-    result_type_2 res2 = p2(a1.second);
+    typedef typename CGAL::cpp11::result_of<P1(const A&...)>::type result_type_1;
+    typedef typename CGAL::cpp11::result_of<P2(const A&...)>::type result_type_2;
+    result_type_1 res1 = p1(a.first...);
+    result_type_2 res2 = p2(a.second...);
     if (! cmp(res1, res2))
     {
-      std::cerr << "Kernel_checker error : " << res1 << " != " << res2
-                << " for the inputs : " << std::endl;
-      std::cerr << a1.first << std::endl;
-      std::cerr << a1.second << std::endl;
-      std::cerr << "functor first kernel : "
-                << typeid(p1).name() << std::endl;
-      std::cerr << "functor second kernel: "
-                << typeid(p2).name() << std::endl;
-      std::cerr << CGAL_PRETTY_FUNCTION << std::endl;
       CGAL_kernel_assertion(false);
     }
     return Pairify<result_type_1, result_type_2>()(res1, res2);
   }
-
-  template <class A1, class A2>
-  typename Pairify<typename CGAL::cpp11::result_of<P1(const A1&, const A2&)>::type,
-                   typename CGAL::cpp11::result_of<P2(const A1&, const A2&)>::type>::result_type
-  operator()(const A1 &a1, const A2 &a2) const
-  {
-    typedef typename CGAL::cpp11::result_of<P1(const A1&, const A2&)>::type result_type_1;
-    typedef typename CGAL::cpp11::result_of<P2(const A1&, const A2&)>::type result_type_2;
-    result_type_1 res1 = p1(a1.first, a2.first);
-    result_type_2 res2 = p2(a1.second, a2.second);
-    if (! cmp(res1, res2))
-    {
-      std::cerr << "Kernel_checker error : " << res1 << " != " << res2
-                << " for the inputs : " << std::endl;
-      std::cerr << a1.first << std::endl;
-      std::cerr << a1.second << std::endl;
-      std::cerr << a2.first << std::endl;
-      std::cerr << a2.second << std::endl;
-      std::cerr << "functor first kernel : "
-                << typeid(p1).name() << std::endl;
-      std::cerr << "functor second kernel: "
-                << typeid(p2).name() << std::endl;
-      std::cerr << CGAL_PRETTY_FUNCTION << std::endl;
-      CGAL_kernel_assertion(false);
-    }
-    return Pairify<result_type_1, result_type_2>()(res1, res2);
-  }
-
-  template <class A1, class A2, class A3>
-  typename Pairify<typename CGAL::cpp11::result_of<P1(
-                     const A1&, const A2&, const A3&)>::type,
-                   typename CGAL::cpp11::result_of<P2(
-                     const A1&, const A2&, const A3&)>::type>::result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3) const
-  {
-    typedef typename CGAL::cpp11::result_of<P1(const A1&, const A2&, const A3&)>::type result_type_1;
-    typedef typename CGAL::cpp11::result_of<P2(const A1&, const A2&, const A3&)>::type result_type_2;
-    result_type_1 res1 = p1(a1.first, a2.first, a3.first);
-    result_type_2 res2 = p2(a1.second, a2.second, a3.second);
-    if (! cmp(res1, res2))
-    {
-      std::cerr << "Kernel_checker error : " << res1 << " != " << res2
-                << " for the inputs : " << std::endl;
-      std::cerr << a1.first << std::endl;
-      std::cerr << a1.second << std::endl;
-      std::cerr << a2.first << std::endl;
-      std::cerr << a2.second << std::endl;
-      std::cerr << a3.first << std::endl;
-      std::cerr << a3.second << std::endl;
-      std::cerr << "functor first kernel : "
-                << typeid(p1).name() << std::endl;
-      std::cerr << "functor second kernel: "
-                << typeid(p2).name() << std::endl;
-      std::cerr << CGAL_PRETTY_FUNCTION << std::endl;
-      CGAL_kernel_assertion(false);
-    }
-    return Pairify<result_type_1, result_type_2>()(res1, res2);
-  }
-
-  template <class A1, class A2, class A3, class A4>
-  typename Pairify<typename CGAL::cpp11::result_of<P1(
-                     const A1&, const A2&, const A3&, const A4&)>::type,
-                   typename CGAL::cpp11::result_of<P2(
-                     const A1&, const A2&, const A3&, const A4&)>::type>::result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4) const
-  {
-    typedef typename CGAL::cpp11::result_of<P1(
-                       const A1&, const A2&, const A3&, const A4&)>::type result_type_1;
-    typedef typename CGAL::cpp11::result_of<P2(
-                       const A1&, const A2&, const A3&, const A4&)>::type result_type_2;
-
-    result_type_1 res1 = p1(a1.first, a2.first, a3.first, a4.first);
-    result_type_2 res2 = p2(a1.second, a2.second, a3.second, a4.second);
-    if (! cmp(res1, res2))
-    {
-      std::cerr << "Kernel_checker error : " << res1 << " != " << res2
-                << " for the inputs : " << std::endl;
-      std::cerr << a1.first << std::endl;
-      std::cerr << a1.second << std::endl;
-      std::cerr << a2.first << std::endl;
-      std::cerr << a2.second << std::endl;
-      std::cerr << a3.first << std::endl;
-      std::cerr << a3.second << std::endl;
-      std::cerr << a4.first << std::endl;
-      std::cerr << a4.second << std::endl;
-      std::cerr << "functor first kernel : "
-                << typeid(p1).name() << std::endl;
-      std::cerr << "functor second kernel: "
-                << typeid(p2).name() << std::endl;
-      std::cerr << CGAL_PRETTY_FUNCTION << std::endl;
-      CGAL_kernel_assertion(false);
-    }
-    return Pairify<result_type_1, result_type_2>()(res1, res2);
-  }
-
-  template <class A1, class A2, class A3, class A4, class A5>
-  typename Pairify<typename CGAL::cpp11::result_of<P1(
-                     const A1&, const A2&, const A3&, const A4&, const A5&)>::type,
-                   typename CGAL::cpp11::result_of<P2(
-                     const A1&, const A2&, const A3&, const A4&, const A5&)>::type>::result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4, const A5 &a5) const
-  {
-    typedef typename CGAL::cpp11::result_of<P1(
-      const A1&, const A2&, const A3&, const A4&, const A5&)>::type result_type_1;
-    typedef typename CGAL::cpp11::result_of<P2(
-      const A1&, const A2&, const A3&, const A4&, const A5&)>::type result_type_2;
-
-    result_type_1 res1 = p1(a1.first, a2.first, a3.first, a4.first, a5.first);
-    result_type_2 res2 = p2(a1.second, a2.second, a3.second, a4.second, a5.second);
-    if (! cmp(res1, res2))
-    {
-      std::cerr << "Kernel_checker error : " << res1 << " != " << res2
-                << " for the inputs : " << std::endl;
-      std::cerr << a1.first << std::endl;
-      std::cerr << a1.second << std::endl;
-      std::cerr << a2.first << std::endl;
-      std::cerr << a2.second << std::endl;
-      std::cerr << a3.first << std::endl;
-      std::cerr << a3.second << std::endl;
-      std::cerr << a4.first << std::endl;
-      std::cerr << a4.second << std::endl;
-      std::cerr << a5.first << std::endl;
-      std::cerr << a5.second << std::endl;
-      std::cerr << "functor first kernel : "
-                << typeid(p1).name() << std::endl;
-      std::cerr << "functor second kernel: "
-                << typeid(p2).name() << std::endl;
-      std::cerr << CGAL_PRETTY_FUNCTION << std::endl;
-      CGAL_kernel_assertion(false);
-    }
-    return Pairify<result_type_1, result_type_2>()(res1, res2);
-  }
-
-  // Same thing with more arguments...
 };
 
 struct dont_check_equal {
diff --git a/Kernel_23/include/CGAL/Point_2.h b/Kernel_23/include/CGAL/Point_2.h
index a5b00bb1eb9..7358d0dc46b 100644
--- a/Kernel_23/include/CGAL/Point_2.h
+++ b/Kernel_23/include/CGAL/Point_2.h
@@ -48,12 +48,12 @@ public:
   typedef RPoint_2 Rep;
   typedef typename R_::Cartesian_const_iterator_2 Cartesian_const_iterator;
 
-  const Rep& rep() const
+  const Rep& rep() const noexcept
   {
     return *this;
   }
 
-  Rep& rep()
+  Rep& rep() noexcept
   {
     return *this;
   }
@@ -84,6 +84,15 @@ public:
     : RPoint_2(typename R::Construct_point_2()(Return_base_tag(), hx, hy, hw))
   {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Rep>)
+#endif
+  {
+    using std::swap;
+    swap(a.rep(), b.rep());
+  }
+
   typename cpp11::result_of<typename R::Compute_x_2(Point_2)>::type
   x() const
   {
diff --git a/Kernel_23/include/CGAL/Point_3.h b/Kernel_23/include/CGAL/Point_3.h
index bf3952fb0dc..01b07bd3e0e 100644
--- a/Kernel_23/include/CGAL/Point_3.h
+++ b/Kernel_23/include/CGAL/Point_3.h
@@ -46,12 +46,12 @@ public:
   typedef typename R_::Kernel_base::Point_3  Rep;
   typedef typename R_::Cartesian_const_iterator_3 Cartesian_const_iterator;
 
-  const Rep& rep() const
+  const Rep& rep() const noexcept
   {
     return *this;
   }
 
-  Rep& rep()
+  Rep& rep() noexcept
   {
     return *this;
   }
@@ -81,6 +81,15 @@ public:
     : Rep(typename R::Construct_point_3()(Return_base_tag(), hx, hy, hz, hw))
   {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Rep>)
+#endif
+  {
+    using std::swap;
+    swap(a.rep(), b.rep());
+  }
+
   typename cpp11::result_of<typename R::Compute_x_3( Point_3)>::type
   x() const
   {
diff --git a/Kernel_23/include/CGAL/Vector_2.h b/Kernel_23/include/CGAL/Vector_2.h
index 4f570ed6b02..67f07e5e3e6 100644
--- a/Kernel_23/include/CGAL/Vector_2.h
+++ b/Kernel_23/include/CGAL/Vector_2.h
@@ -54,12 +54,12 @@ public:
   typedef RVector_2 Rep;
   typedef typename R_::Cartesian_const_iterator_2 Cartesian_const_iterator;
 
-  const Rep& rep() const
+  const Rep& rep() const noexcept
   {
     return *this;
   }
 
-  Rep& rep()
+  Rep& rep() noexcept
   {
     return *this;
   }
@@ -93,6 +93,15 @@ public:
   Vector_2(const RT &x, const RT &y, const RT &w)
       : RVector_2(typename R::Construct_vector_2()(Return_base_tag(), x,y,w)) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Rep>)
+#endif
+  {
+    using std::swap;
+    swap(a.rep(), b.rep());
+  }
+
 
   typename cpp11::result_of<typename R::Compute_x_2(Vector_2)>::type
   x() const
diff --git a/Kernel_23/include/CGAL/Vector_3.h b/Kernel_23/include/CGAL/Vector_3.h
index c3c7c0bc953..077da5d649d 100644
--- a/Kernel_23/include/CGAL/Vector_3.h
+++ b/Kernel_23/include/CGAL/Vector_3.h
@@ -93,6 +93,15 @@ public:
   Vector_3(const RT& x, const RT& y, const RT& z, const RT& w)
     : Rep(typename R::Construct_vector_3()(Return_base_tag(), x, y, z, w)) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Rep>)
+#endif
+  {
+    using std::swap;
+    swap(a.rep(), b.rep());
+  }
+
   Direction_3 direction() const
   {
     return R().construct_direction_3_object()(*this);
diff --git a/Kernel_d/include/CGAL/Kernel_d/function_objects.h b/Kernel_d/include/CGAL/Kernel_d/function_objects.h
index 725167722a7..25d8c84628f 100644
--- a/Kernel_d/include/CGAL/Kernel_d/function_objects.h
+++ b/Kernel_d/include/CGAL/Kernel_d/function_objects.h
@@ -32,81 +32,10 @@ class Construct
   public:
     typedef ToBeConstructed  result_type;
 
+    template <class ... A>
     ToBeConstructed
-    operator()() const
-    { return ToBeConstructed(); }
-
-    template <class A1> 
-    ToBeConstructed
-    operator()( const A1& a1) const
-    { return ToBeConstructed(a1); }
-
-    template <class A1, class A2> 
-    ToBeConstructed
-    operator()( const A1& a1, const A2& a2) const
-    { return ToBeConstructed(a1,a2); }
-
-    template <class A1, class A2, class A3> 
-    ToBeConstructed
-    operator()( const A1& a1, const A2& a2, const A3& a3) const
-    { return ToBeConstructed(a1,a2,a3); }
-
-    template <class A1, class A2, class A3, class A4> 
-    ToBeConstructed
-    operator()( const A1& a1, const A2& a2, const A3& a3, const A4& a4) const
-    { return ToBeConstructed(a1,a2,a3,a4); }
-
-    template <class A1, class A2, class A3, class A4, class A5> 
-    ToBeConstructed
-    operator()( const A1& a1, const A2& a2, const A3& a3, const A4& a4,
-	    const A5& a5) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6 ) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6,
-                const A& a7 ) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6,a7); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6,
-                const A& a7, const A& a8, const A& a9) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6,a7,a8,a9); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6,
-                const A& a7, const A& a8, const A& a9,
-                const A& a10) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6,
-                const A& a7, const A& a8, const A& a9,
-                const A& a10,const A& a11,const A& a12) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12); }
-
-    template <class A> 
-    ToBeConstructed
-    operator()( const A& a1, const A& a2, const A& a3,
-                const A& a4, const A& a5, const A& a6,
-                const A& a7, const A& a8, const A& a9,
-                const A& a10,const A& a11,const A& a12,
-                const A& a13) const
-    { return ToBeConstructed(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13); }
-
+    operator()( A&& ... a) const
+    { return ToBeConstructed(std::forward<A>(a)...); }
 };
 
 class Call_has_on_positive_side
diff --git a/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h b/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
index 6799463d399..5c6c15505e6 100644
--- a/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
+++ b/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
@@ -25,11 +25,11 @@ namespace CGAL {
   class Point_for_cell
   {
   public:
-    /// Contructor without parameter.
+    /// Constructor without parameter.
     Point_for_cell()
     {}
 
-    /// Contructor with a point in parameter.
+    /// Constructor with a point in parameter.
     Point_for_cell(const Point& apoint) : mpoint(apoint)
     {}
 
@@ -87,15 +87,15 @@ namespace CGAL {
     { return !operator==(other); }
 
   protected:
-    /// Default contructor.
+    /// Default constructor.
     Cell_attribute_with_point()
     {}
 
-    /// Contructor with a point in parameter.
+    /// Constructor with a point in parameter.
     Cell_attribute_with_point(const Point& apoint) : Base2(apoint)
     {}
 
-    /// Contructor with a point and an attribute in parameters.
+    /// Constructor with a point and an attribute in parameters.
     Cell_attribute_with_point(const Point& apoint, const Info& ainfo) :
       Base1(ainfo),
       Base2(apoint)
@@ -144,11 +144,11 @@ namespace CGAL {
     { return false; }
 
   protected:
-    /// Default contructor.
+    /// Default constructor.
     Cell_attribute_with_point()
     {}
 
-    /// Contructor with a point in parameter.
+    /// Constructor with a point in parameter.
     Cell_attribute_with_point(const Point& apoint) : Base2(apoint)
     {}
   };
diff --git a/Maintenance/infrastructure/cgal.geometryfactory.com/crontab b/Maintenance/infrastructure/cgal.geometryfactory.com/crontab
index 6912301cc49..d98d42b770d 100644
--- a/Maintenance/infrastructure/cgal.geometryfactory.com/crontab
+++ b/Maintenance/infrastructure/cgal.geometryfactory.com/crontab
@@ -25,11 +25,11 @@ LC_CTYPE=en_US.UTF-8
 # "master" alone
 0 21  *  *  Sun                      cd $HOME/CGAL/create_internal_release && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/master.git --do-it || echo ERROR
 # "integration"
-0 21  *  *  Mon,Tue,Wed,Thu      cd $HOME/CGAL/create_internal_release && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/integration.git $HOME/CGAL/branches/empty-dir --do-it --public || echo ERROR
+0 21  *  *  Mon,Tue,Wed,Thu,Fri      cd $HOME/CGAL/create_internal_release && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/integration.git $HOME/CGAL/branches/empty-dir --do-it --public || echo ERROR
 # from branch 5.0
-0 21  *  *  Fri                      cd $HOME/CGAL/create_internal_release-5.0-branch && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/CGAL-5.0-branch.git --public --do-it || echo ERROR
+0 21  *  *  Sat                      cd $HOME/CGAL/create_internal_release-5.0-branch && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/CGAL-5.0-branch.git --public --do-it || echo ERROR
 # from branch 4.14
-0 21  *  *  Sat                      cd $HOME/CGAL/create_internal_release-4.14-branch && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/CGAL-4.14-branch.git --public --do-it || echo ERROR
+#0 21  *  *  Sat                      cd $HOME/CGAL/create_internal_release-4.14-branch && /usr/bin/time scl enable rh-git29 -- $HOME/bin/create_release $HOME/CGAL/branches/CGAL-4.14-branch.git --public --do-it || echo ERROR
 
 ## Older stuff
 # from branch 4.13
diff --git a/Mesh_2/include/CGAL/Delaunay_mesh_size_criteria_2.h b/Mesh_2/include/CGAL/Delaunay_mesh_size_criteria_2.h
index 86b17c1030b..62de1a1e3de 100644
--- a/Mesh_2/include/CGAL/Delaunay_mesh_size_criteria_2.h
+++ b/Mesh_2/include/CGAL/Delaunay_mesh_size_criteria_2.h
@@ -111,10 +111,8 @@ public:
       typedef typename Geom_traits::Compute_squared_distance_2
 	Compute_squared_distance_2;
 
-      Geom_traits traits; /** @warning traits with data!! */
-
       Compute_squared_distance_2 squared_distance = 
-	traits.compute_squared_distance_2_object();
+	this->traits.compute_squared_distance_2_object();
 
       const Point_2& pa = fh->vertex(0)->point();
       const Point_2& pb = fh->vertex(1)->point();
@@ -165,7 +163,7 @@ public:
 	    }
 	}
 
-      Compute_area_2 area_2 = traits.compute_area_2_object();
+      Compute_area_2 area_2 = this->traits.compute_area_2_object();
 
       double area = 2*CGAL::to_double(area_2(pa, pb, pc));
 
diff --git a/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp b/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp
new file mode 100644
index 00000000000..030471c0295
--- /dev/null
+++ b/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp
@@ -0,0 +1,43 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Delaunay_mesher_2.h>
+#include <CGAL/Delaunay_mesh_face_base_2.h>
+#include <CGAL/Delaunay_mesh_size_criteria_2.h>
+#include <CGAL/Triangulation_2_projection_traits_3.h>
+
+#include <iostream>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K1;
+typedef CGAL::Triangulation_2_projection_traits_3<K1> K;
+typedef CGAL::Triangulation_vertex_base_2<K> Vb;
+typedef CGAL::Delaunay_mesh_face_base_2<K> Fb;
+typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds> CDT;
+typedef CGAL::Delaunay_mesh_size_criteria_2<CDT> Criteria;
+
+typedef CDT::Vertex_handle Vertex_handle;
+typedef CDT::Point Point;
+
+int main()
+{
+  K gt{ { 0, 0, 1} };
+  CDT cdt(gt);
+
+  Vertex_handle va = cdt.insert(Point(-4,0,0));
+  Vertex_handle vb = cdt.insert(Point(0,-1,0));
+  Vertex_handle vc = cdt.insert(Point(4,0,0));
+  Vertex_handle vd = cdt.insert(Point(0,1,0));
+  cdt.insert(Point(2, 0.6, 0));
+
+  cdt.insert_constraint(va, vb);
+  cdt.insert_constraint(vb, vc);
+  cdt.insert_constraint(vc, vd);
+  cdt.insert_constraint(vd, va);
+
+  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
+
+  std::cout << "Meshing the triangulation..." << std::endl;
+  CGAL::refine_Delaunay_mesh_2(cdt, Criteria(0.125, 0.5, gt));
+
+  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
+}
diff --git a/Mesh_3/examples/Mesh_3/CMakeLists.txt b/Mesh_3/examples/Mesh_3/CMakeLists.txt
index dcaedc3629a..a6f7848d200 100644
--- a/Mesh_3/examples/Mesh_3/CMakeLists.txt
+++ b/Mesh_3/examples/Mesh_3/CMakeLists.txt
@@ -48,8 +48,6 @@ if ( CGAL_FOUND )
   if (NOT EIGEN3_FOUND)
     message(STATUS "This project requires the Eigen library, and will not be compiled.")
     return()
-  else()
-    include( ${EIGEN3_USE_FILE} )
   endif()
   
   find_package(VTK QUIET COMPONENTS vtkImagingGeneral vtkIOImage NO_MODULE)
@@ -72,49 +70,99 @@ if ( CGAL_FOUND )
 
     # Compilable examples
     create_single_source_cgal_program( "mesh_hybrid_mesh_domain.cpp" )
+    CGAL_target_use_Eigen(mesh_hybrid_mesh_domain)
+    
     create_single_source_cgal_program( "mesh_implicit_sphere.cpp" )
+    CGAL_target_use_Eigen(mesh_implicit_sphere)
+    
     create_single_source_cgal_program( "mesh_implicit_sphere_variable_size.cpp" )
+    CGAL_target_use_Eigen(mesh_implicit_sphere_variable_size)
+    
     create_single_source_cgal_program( "mesh_two_implicit_spheres_with_balls.cpp" )
+    CGAL_target_use_Eigen(mesh_two_implicit_spheres_with_balls)
+    
     create_single_source_cgal_program( "mesh_implicit_domains_2.cpp" "implicit_functions.cpp" )
+    CGAL_target_use_Eigen(mesh_implicit_domains_2)
+    
     create_single_source_cgal_program( "mesh_cubes_intersection.cpp" )
+    CGAL_target_use_Eigen(mesh_cubes_intersection)
+    
     create_single_source_cgal_program( "mesh_cubes_intersection_with_features.cpp" )
+    CGAL_target_use_Eigen(mesh_cubes_intersection_with_features)
+    
     create_single_source_cgal_program( "mesh_implicit_domains.cpp" "implicit_functions.cpp" )
+    CGAL_target_use_Eigen(mesh_implicit_domains)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain_sm.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain_sm)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain_with_surface_inside.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain_with_surface_inside)
+    
     create_single_source_cgal_program( "remesh_polyhedral_surface.cpp" )
+    CGAL_target_use_Eigen(remesh_polyhedral_surface)
+    
     create_single_source_cgal_program( "remesh_polyhedral_surface_sm.cpp" )
+    CGAL_target_use_Eigen(remesh_polyhedral_surface_sm)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain_with_features.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain_with_features)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain_with_features_sm.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain_with_features_sm)
+    
     create_single_source_cgal_program( "mesh_polyhedral_domain_with_lipschitz_sizing.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_domain_with_lipschitz_sizing)
+    
     create_single_source_cgal_program( "mesh_polyhedral_complex.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_complex)
+    
     create_single_source_cgal_program( "mesh_polyhedral_complex_sm.cpp" )
+    CGAL_target_use_Eigen(mesh_polyhedral_complex_sm)
+    
     if( WITH_CGAL_ImageIO )
       if( VTK_FOUND AND ("${VTK_VERSION_MAJOR}" GREATER "5" OR VTK_VERSION VERSION_GREATER 5) )
         add_executable ( mesh_3D_gray_vtk_image mesh_3D_gray_vtk_image.cpp )
+        CGAL_target_use_Eigen(mesh_3D_gray_vtk_image)
         target_link_libraries(  mesh_3D_gray_vtk_image ${CGAL_LIBRARIES} ${CGAL_3RD_PARTY_LIBRARIES} ${VTK_LIBRARIES})
         cgal_add_test( mesh_3D_gray_vtk_image )
         add_to_cached_list( CGAL_EXECUTABLE_TARGETS mesh_3D_gray_vtk_image )
       endif()
  
       create_single_source_cgal_program( "mesh_3D_gray_image.cpp" )
+      CGAL_target_use_Eigen(mesh_3D_gray_image)
+      
       create_single_source_cgal_program( "mesh_3D_gray_image_multiple_values.cpp" )
+      CGAL_target_use_Eigen(mesh_3D_gray_image_multiple_values)
+      
       create_single_source_cgal_program( "mesh_3D_image_with_features.cpp" )
+      CGAL_target_use_Eigen(mesh_3D_image_with_features)
+      
       if( CGAL_ImageIO_USE_ZLIB )
         create_single_source_cgal_program( "mesh_optimization_example.cpp" )
+        CGAL_target_use_Eigen(mesh_optimization_example)
 
         create_single_source_cgal_program( "mesh_optimization_lloyd_example.cpp" )
+        CGAL_target_use_Eigen(mesh_optimization_lloyd_example)
 
         create_single_source_cgal_program( "mesh_3D_image.cpp" )
+        CGAL_target_use_Eigen(mesh_3D_image)
+        
         create_single_source_cgal_program( "mesh_3D_image_with_custom_initialization.cpp" )
+        CGAL_target_use_Eigen(mesh_3D_image_with_custom_initialization)
 
         create_single_source_cgal_program( "mesh_3D_image_variable_size.cpp" )
+        CGAL_target_use_Eigen(mesh_3D_image_variable_size)
       else()
         message( STATUS "NOTICE: The examples mesh_3D_image.cpp, mesh_3D_image_variable_size.cpp, mesh_optimization_example.cpp and mesh_optimization_lloyd_example.cpp need CGAL_ImageIO to be configured with ZLIB support, and will not be compiled." )
       endif()
     else()
       message( STATUS "NOTICE: Some examples need the CGAL_ImageIO library, and will not be compiled." )
     endif()
+    
 #    create_single_source_cgal_program( "mesh_polyhedral_implicit_function.cpp" )
 #    create_single_source_cgal_program( "mesh_polyhedral_surface_tolerance_region.cpp" )
 #    create_single_source_cgal_program( "mesh_polyhedral_edge_tolerance_region.cpp" )
diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index e00ea7ade01..a35de5e6c50 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -824,7 +824,7 @@ protected:
                                                       false>           Wrapper;
     return Wrapper(image,
                    transform_fct,
-                   transform_fct(value_outside));
+                   value_outside) ;
   }
 
   template <typename FT, typename FT2, typename Functor>
diff --git a/Mesh_3/include/CGAL/Polyhedral_complex_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_complex_mesh_domain_3.h
index ae6413ca009..9421e883a45 100644
--- a/Mesh_3/include/CGAL/Polyhedral_complex_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_complex_mesh_domain_3.h
@@ -750,8 +750,7 @@ detect_features(FT angle_in_degree,
   for(Polyhedron_type& p : poly)
   {
     initialize_ts(p);
-    using Mesh_3::internal::Get_face_index_pmap;
-    Get_face_index_pmap<Polyhedron_type> get_face_index_pmap(p);
+
 #ifdef CGAL_MESH_3_VERBOSE
     std::size_t poly_id = &p-&poly[0];
     std::cerr << "Polyhedron #" << poly_id << " :\n";
@@ -768,9 +767,9 @@ detect_features(FT angle_in_degree,
       , eif
       , pid_map
       , PMP::parameters::first_index(nb_of_patch_plus_one)
-      .face_index_map(get_face_index_pmap(p))
-      .vertex_incident_patches_map(vip_map)
-      .vertex_feature_degree_map(vertex_feature_degree_map));
+                        .face_index_map(get_initialized_face_index_map(p))
+                        .vertex_incident_patches_map(vip_map)
+                        .vertex_feature_degree_map(vertex_feature_degree_map));
 
     Mesh_3::internal::Is_featured_edge<Polyhedron_type> is_featured_edge(p);
 
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
index f9a7a0d5cf4..42abf9d1256 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
@@ -105,47 +105,6 @@ struct IGT_generator<Gt,CGAL::Tag_false>
 }  // end namespace details
 }  // end namespace Mesh_3
 
-namespace Mesh_3 {
-namespace internal {
-
-template <typename Polyhedron_type,
-          bool = CGAL::graph_has_property<Polyhedron_type,
-                                           CGAL::face_index_t>::value>
-class Get_face_index_pmap {
-public:
-  typedef typename boost::property_map<Polyhedron_type,
-                                       CGAL::face_index_t>::const_type Pmap;
-  Get_face_index_pmap(const Polyhedron_type&) {}
-  Pmap operator()(const Polyhedron_type& polyhedron) {
-    return get(CGAL::face_index, polyhedron);
-  }
-};
-
-template <typename Polyhedron_type>
-class Get_face_index_pmap<Polyhedron_type, false> {
-  typedef typename boost::graph_traits<Polyhedron_type>::face_descriptor
-                                                              face_descriptor;
-  typedef std::map<face_descriptor, int> Map;
-public:
-  Get_face_index_pmap(const Polyhedron_type& polyhedron) {
-    int id = 0;
-    for(face_descriptor f : faces(polyhedron))
-    {
-      face_ids[f] = id++;
-    }
-  }
-  typedef boost::associative_property_map<Map> Pmap;
-
-  Pmap operator()(const Polyhedron_type&) {
-    return Pmap(face_ids);
-  }
-private:
-  Map face_ids;
-};
-
-} // end namespace internal
-} // end namespace Mesh_3
-
 /**
  * @class Polyhedral_mesh_domain_3
  *
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
index d5f9979bc9b..ea92e1341ea 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
@@ -348,9 +348,6 @@ detect_features(FT angle_in_degree, std::vector<Polyhedron>& poly)
     typedef typename boost::property_map<Polyhedron,CGAL::vertex_incident_patches_t<P_id> >::type VIPMap;
     typedef typename boost::property_map<Polyhedron, CGAL::edge_is_feature_t>::type EIFMap;
 
-    using Mesh_3::internal::Get_face_index_pmap;
-    Get_face_index_pmap<Polyhedron> get_face_index_pmap(p);
-
     PIDMap pid_map = get(face_patch_id_t<Tag_>(), p);
     VIPMap vip_map = get(vertex_incident_patches_t<P_id>(), p);
     EIFMap eif_map = get(CGAL::edge_is_feature, p);
@@ -360,8 +357,8 @@ detect_features(FT angle_in_degree, std::vector<Polyhedron>& poly)
       , eif_map
       , pid_map
       , PMP::parameters::first_index(nb_of_patch_plus_one)
-      .face_index_map(get_face_index_pmap(p))
-      .vertex_incident_patches_map(vip_map));
+                        .face_index_map(get_initialized_face_index_map(p))
+                        .vertex_incident_patches_map(vip_map));
 
     Mesh_3::internal::Is_featured_edge<Polyhedron> is_featured_edge(p);
 
diff --git a/Mesh_3/test/Mesh_3/CMakeLists.txt b/Mesh_3/test/Mesh_3/CMakeLists.txt
index 525573cbeb4..bd6221a9aa6 100644
--- a/Mesh_3/test/Mesh_3/CMakeLists.txt
+++ b/Mesh_3/test/Mesh_3/CMakeLists.txt
@@ -22,8 +22,6 @@ if ( CGAL_FOUND )
   if (NOT EIGEN3_FOUND)
     message(STATUS "This project requires the Eigen library, and will not be compiled.")
     return()
-  else()
-    include( ${EIGEN3_USE_FILE} )
   endif()
   
   create_single_source_cgal_program( "test_boost_has_xxx.cpp" )
@@ -61,6 +59,42 @@ if ( CGAL_FOUND )
   create_single_source_cgal_program( "test_mesh_polyhedral_domain_with_features_deprecated.cpp" )
   create_single_source_cgal_program( "test_meshing_with_one_step.cpp" )
 
+  foreach(target
+      test_boost_has_xxx
+      test_c3t3
+      test_mesh_capsule_var_distance_bound
+      test_implicit_multi_domain_to_labeling_function_wrapper
+      test_c3t3_io
+      test_c3t3_with_features
+      test_criteria
+      test_domain_with_polyline_features
+      test_labeled_mesh_domain_3
+      test_mesh_criteria_creation
+      test_c3t3_into_facegraph
+      test_without_detect_features
+      test_meshing_3D_image
+      test_meshing_3D_image_deprecated
+      test_meshing_3D_gray_image
+      test_meshing_3D_gray_image_deprecated
+      test_meshing_implicit_function
+      test_meshing_implicit_function_deprecated
+      test_meshing_polyhedral_complex
+      test_meshing_polyhedron
+      test_meshing_polylines_only
+      test_meshing_polyhedron_with_features
+      test_meshing_verbose
+      test_meshing_unit_tetrahedron
+      test_meshing_with_default_edge_size
+      test_meshing_determinism
+      test_c3t3_extract_subdomains_boundaries
+      test_mesh_3_issue_1554
+      test_mesh_polyhedral_domain_with_features_deprecated
+      test_meshing_with_one_step.cpp)
+    if(TARGET ${target})
+      CGAL_target_use_Eigen(${target})
+    endif()
+  endforeach()
+  
   foreach(target
       test_meshing_verbose
       test_meshing_polyhedron_with_features
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/Lazy_cartesian.h b/NewKernel_d/include/CGAL/NewKernel_d/Lazy_cartesian.h
index 5e0e24254fe..7c3c8e01878 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/Lazy_cartesian.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/Lazy_cartesian.h
@@ -109,6 +109,12 @@ template<typename AT, typename ET, typename AC, typename EC, typename E2A, typen
 class Lazy_rep_XXX :
   public Lazy_rep< AT, ET, E2A >, private EC
 {
+  // `default_construct<T>()` is the same as `T{}`. But, this is a
+  // workaround to a MSVC-2015 bug (fixed in MSVC-2017): its parser
+  // seemed confused by `T{}` somewhere below.
+  template <typename T>
+  static T default_construct() { return T(); }
+
   // Lazy_rep_0 does not inherit from EC or take a parameter AC. It has different constructors.
   static_assert(sizeof...(L)>0, "Use Lazy_rep_0 instead");
   template <class Ei, class Ai, class E2Ai, class Ki> friend class Lazy_kernel_base;
@@ -138,7 +144,7 @@ class Lazy_rep_XXX :
   // Currently we construct the vectors, then move them into the tuple. It would be nicer to construct them in their final destination, because eventually we will also have arrays instead of vectors.
   template<class...T,class LLL,class...LL>
   Lazy_rep_XXX(Lazy_internal::typelist<T...>, const AC& ac, const EC& ec, LLL const&lll, LL const&...ll) :
-    Lazy_rep<AT, ET, E2A>(ac(CGAL::approx(ll)...)), EC(ec), l(Lazy_internal::do_extract(T{},lll)...)
+    Lazy_rep<AT, ET, E2A>(ac(CGAL::approx(ll)...)), EC(ec), l(Lazy_internal::do_extract(default_construct<T>(),lll)...)
   {
     //this->set_depth(std::max({ -1, (int)CGAL::depth(ll)...}) + 1);
     this->set_depth(1); // FIXME: now that we have ranges, we could actually compute the depth if we cared...
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/Wrapper/Point_d.h b/NewKernel_d/include/CGAL/NewKernel_d/Wrapper/Point_d.h
index 404eca88bf3..5c0dce2db1f 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/Wrapper/Point_d.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/Wrapper/Point_d.h
@@ -51,12 +51,12 @@ public:
   typedef typename Get_type<Kbase, Point_tag>::type      Rep;
   //typedef typename CGAL::decay<typename boost::result_of<CPI(Rep,Begin_tag)>::type>::type Cartesian_const_iterator;
 
-  const Rep& rep() const
+  const Rep& rep() const noexcept
   {
     return *this;
   }
 
-  Rep& rep()
+  Rep& rep() noexcept
   {
     return *this;
   }
@@ -101,6 +101,14 @@ public:
   Point_d(Origin&& v)
     : Rep(CPBase()(std::move(v))) {}
 
+  friend void swap(Self& a, Self& b)
+#ifdef __cpp_lib_is_swappable
+    noexcept(std::is_nothrow_swappable_v<Rep>)
+#endif
+    {
+      using std::swap;
+      swap(a.rep(), b.rep());
+    }
 
   decltype(auto) cartesian(int i)const{
 	  return CCBase()(rep(),i);
diff --git a/NewKernel_d/test/NewKernel_d/CMakeLists.txt b/NewKernel_d/test/NewKernel_d/CMakeLists.txt
index 9cbe76d8204..8f7ee2b990c 100644
--- a/NewKernel_d/test/NewKernel_d/CMakeLists.txt
+++ b/NewKernel_d/test/NewKernel_d/CMakeLists.txt
@@ -18,10 +18,8 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "Epick_d.cpp" )
-
+    CGAL_target_use_Eigen(Epick_d)
   else()
 
     message(STATUS "NOTICE: This program requires the Eigen3 library, and will not be compiled.")
diff --git a/Number_types/include/CGAL/FPU.h b/Number_types/include/CGAL/FPU.h
index 1ed1d728d34..1d290381603 100644
--- a/Number_types/include/CGAL/FPU.h
+++ b/Number_types/include/CGAL/FPU.h
@@ -408,7 +408,7 @@ typedef unsigned int FPU_CW_t;
 
 #elif defined __mips__
 #define CGAL_IA_SETFPCW(CW) asm volatile ("ctc1 %0,$31" : :"r" (CW))
-#define CGAL_IA_GETFPCW(CW) asm volatile ("cfc1 %0,$31" : "=r" (CW))
+#define CGAL_IA_GETFPCW(CW) asm volatile ("cfc1 %0,$31" : "=r" (CW)); CW &= 3
 typedef unsigned int FPU_CW_t;
 #define CGAL_FE_TONEAREST    (0x0)
 #define CGAL_FE_TOWARDZERO   (0x1)
diff --git a/Number_types/include/CGAL/GMP/Gmpq_type.h b/Number_types/include/CGAL/GMP/Gmpq_type.h
index 8fa397492d5..e339590b8d1 100644
--- a/Number_types/include/CGAL/GMP/Gmpq_type.h
+++ b/Number_types/include/CGAL/GMP/Gmpq_type.h
@@ -222,20 +222,23 @@ public:
   Gmpq& operator*=(const Gmpq &q);
   Gmpq& operator/=(const Gmpq &q);
 
-  bool operator==(const Gmpq &q) const { return mpq_equal(this->mpq(), q.mpq()) != 0;}
-  bool operator< (const Gmpq &q) const { return mpq_cmp(this->mpq(), q.mpq()) < 0; }
+  bool operator==(const Gmpq &q) const noexcept { return mpq_equal(this->mpq(), q.mpq()) != 0;}
+  bool operator< (const Gmpq &q) const noexcept { return mpq_cmp(this->mpq(), q.mpq()) < 0; }
 
-  double to_double() const;
-  Sign sign() const;
+  double to_double() const noexcept;
+  Sign sign() const noexcept;
 
-  const mpq_t & mpq() const { return Ptr()->mpQ; }
-  mpq_t & mpq() { return ptr()->mpQ; }
+  const mpq_t & mpq() const noexcept { return Ptr()->mpQ; }
+  mpq_t & mpq() noexcept { return ptr()->mpQ; }
 
+  friend void swap(Gmpq &x, Gmpq &y) noexcept { x.Base::swap(y); }
+#ifdef CGAL_PROFILE
   ~Gmpq()
   {
      CGAL_HISTOGRAM_PROFILER("[Gmpq sizes in log2 scale]",
                              (unsigned) ( ::log(double(size())) / ::log(double(2)) )  );
   }
+#endif
 
   // Interoperability with int
   Gmpq& operator+=(int z){return (*this)+= Gmpq(z);}
@@ -446,12 +449,12 @@ Gmpq& Gmpq::operator/=(const Gmpz &z){
 
 inline
 double
-Gmpq::to_double() const
+Gmpq::to_double() const noexcept
 { return mpq_get_d(mpq()); }
 
 inline
 Sign
-Gmpq::sign() const
+Gmpq::sign() const noexcept
 { return static_cast<Sign>(mpq_sgn(mpq())); }
 
 inline
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index 471096f37ba..41e2c597981 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -383,6 +383,9 @@ public :
   typename boost::disable_if<is_implicit_convertible<ET1,ET>,int>::type=0)
     : Base(new Lazy_lazy_exact_Cst<ET, ET1>(x)){}
 
+  friend void swap(Lazy_exact_nt& a, Lazy_exact_nt& b) noexcept
+  { swap(static_cast<Base&>(a), static_cast<Base&>(b)); }
+
   Self operator+ () const
   { return *this; }
 
diff --git a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
index b51e888839a..dc934692689 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
@@ -19,13 +19,6 @@ namespace Eigen {
   template <class NT,class ROOT, class ACDE_TAG, class FP_TAG>
   struct NumTraits<CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> >
   {
-    typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
-    typedef Real NonInteger;
-    typedef Real Nested;
-    typedef Real Literal;
-
-    static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
-
     enum {
       IsInteger = 0,
       IsSigned = 1,
@@ -35,6 +28,19 @@ namespace Eigen {
       AddCost = 2*NumTraits<NT>::AddCost+NumTraits<ROOT>::ReadCost,
       MulCost = 5*NumTraits<NT>::MulCost+2*NumTraits<NT>::AddCost
     };
+    
+    typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
+    typedef Real NonInteger;
+    typedef Real Nested;
+    typedef Real Literal;
+
+    static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
+    static inline int digits10() { return NumTraits<NT>::digits10(); }
+    static inline Real dummy_precision() { return NumTraits<NT>::dummy_precision(); }
+    static inline Real highest() { return NumTraits<NT>::highest(); }
+    static inline Real lowest() { return NumTraits<NT>::lowest(); }
+    static inline Real infinity() { return NumTraits<NT>::infinity(); }
+    static inline Real quiet_NaN() { return NumTraits<NT>::quiet_NaN(); }
   };
 }
 
diff --git a/Number_types/test/Number_types/CMakeLists.txt b/Number_types/test/Number_types/CMakeLists.txt
index 6a74945aea9..0bb60b63e1d 100644
--- a/Number_types/test/Number_types/CMakeLists.txt
+++ b/Number_types/test/Number_types/CMakeLists.txt
@@ -26,7 +26,6 @@ if ( CGAL_FOUND )
   create_single_source_cgal_program( "Counted_number.cpp" )
   create_single_source_cgal_program( "double.cpp" )
   create_single_source_cgal_program( "doubletst.cpp" )
-  create_single_source_cgal_program( "eigen.cpp" )
   create_single_source_cgal_program( "float.cpp" )
   create_single_source_cgal_program( "floattst.cpp" )
   create_single_source_cgal_program( "Gmpfr.cpp" )
@@ -80,7 +79,13 @@ if ( CGAL_FOUND )
   create_single_source_cgal_program( "Gmpfr_bug.cpp" )
   create_single_source_cgal_program( "Quotient_new.cpp" )
   create_single_source_cgal_program( "test_nt_Coercion_traits.cpp" )
-
+  
+  create_single_source_cgal_program( "eigen.cpp" )
+  find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
+  if (EIGEN3_FOUND)
+    cgal_target_use_Eigen(eigen)
+  endif()
+  
 else( CGAL_FOUND )
 
   message(STATUS
diff --git a/Number_types/test/Number_types/eigen.cpp b/Number_types/test/Number_types/eigen.cpp
index 91f620b0b3b..8e0dd9bf194 100644
--- a/Number_types/test/Number_types/eigen.cpp
+++ b/Number_types/test/Number_types/eigen.cpp
@@ -34,7 +34,7 @@ void check_(){
   v << 1, 2, 3;
   NT t=v.dot(v);
   v+=d*m*(t*v);
-  int si=v.size();
+  std::ptrdiff_t si=v.size();
   CGAL_USE(si);
 }
 template <class NT>
@@ -59,7 +59,7 @@ int main(){
   //check<CGAL::Lazy_exact_nt<CGAL::Quotient<CGAL::MP_Float> > >();
   check<CGAL::Sqrt_extension<double,double> >();
 #ifdef CGAL_USE_GMP
-  check<CGAL::Gmpz>();
+//  check<CGAL::Gmpz>();
   check<CGAL::Gmpq>();
   check<CGAL::Gmpfr>();
   check<CGAL::Quotient<CGAL::Gmpz> >();
@@ -69,7 +69,7 @@ int main(){
   check<CGAL::Gmpfi>();
 #endif
 #ifdef CGAL_USE_CORE
-  check<CORE::BigInt>();
+//  check<CORE::BigInt>();
   check<CORE::BigRat>();
   check<CORE::BigFloat>();
   check<CORE::Expr>();
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/CMakeLists.txt b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/CMakeLists.txt
index b18274683b9..8b1fb98c95f 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/CMakeLists.txt
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/CMakeLists.txt
@@ -26,8 +26,6 @@ find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
 if (NOT EIGEN3_FOUND)
   message(STATUS "This project requires the Eigen library, and will not be compiled.")
   return()
-else()
-  include( ${EIGEN3_USE_FILE} )
 endif()
 
 # Boost and its components
@@ -46,3 +44,13 @@ create_single_source_cgal_program( "mesh_implicit_multi_domain.cpp" )
 create_single_source_cgal_program( "mesh_implicit_shape_with_subdomains.cpp" )
 create_single_source_cgal_program( "mesh_implicit_shape_with_optimizers.cpp" )
 create_single_source_cgal_program( "mesh_implicit_shape_with_features.cpp" )
+
+
+foreach(target
+    mesh_implicit_shape
+    mesh_implicit_multi_domain
+    mesh_implicit_shape_with_subdomains
+    mesh_implicit_shape_with_optimizers
+    mesh_implicit_shape_with_features)
+  CGAL_target_use_Eigen(${target})
+endforeach()
diff --git a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/CMakeLists.txt b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/CMakeLists.txt
index dddf3a8f260..d1929fd2bbb 100644
--- a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/CMakeLists.txt
+++ b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/CMakeLists.txt
@@ -19,14 +19,15 @@ if ( CGAL_FOUND )
   if (NOT EIGEN3_FOUND)
     message(STATUS "This project requires the Eigen library, and will not be compiled.")
     return()
-  else()
-    include( ${EIGEN3_USE_FILE} )
   endif()
 
   create_single_source_cgal_program( "test_implicit_shapes_bunch.cpp" )
+  CGAL_target_use_Eigen(test_implicit_shapes_bunch)
   create_single_source_cgal_program( "test_implicit_shapes_with_features.cpp" )
+  CGAL_target_use_Eigen(test_implicit_shapes_with_features)
   create_single_source_cgal_program( "test_triply_periodic_minimal_surfaces.cpp" )
-
+  CGAL_target_use_Eigen(test_triply_periodic_minimal_surfaces)
+  
 else()
 
   message(STATUS "This program requires the CGAL library, and will not be compiled.")
diff --git a/Point_set_3/examples/Point_set_3/CMakeLists.txt b/Point_set_3/examples/Point_set_3/CMakeLists.txt
index 45172ef603d..21055796731 100644
--- a/Point_set_3/examples/Point_set_3/CMakeLists.txt
+++ b/Point_set_3/examples/Point_set_3/CMakeLists.txt
@@ -44,14 +44,9 @@ set(needed_cxx_features cxx_rvalue_references cxx_variadic_templates)
 create_single_source_cgal_program( "point_set_read_ply.cpp" CXX_FEATURES ${needed_cxx_features} )
 
 find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if (NOT EIGEN3_FOUND)
-  find_package(LAPACK)
-  if(LAPACK_FOUND)
-    include( ${LAPACK_USE_FILE} )
-  endif(LAPACK_FOUND)
-else()
-  include( ${EIGEN3_USE_FILE} )
+if (EIGEN3_FOUND)
   create_single_source_cgal_program( "point_set_algo.cpp" )
+  CGAL_target_use_Eigen(point_set_algo)
 endif()
 
 create_single_source_cgal_program("draw_point_set_3.cpp" )
diff --git a/Point_set_processing_3/examples/Point_set_processing_3/CMakeLists.txt b/Point_set_processing_3/examples/Point_set_processing_3/CMakeLists.txt
index c2da826d49b..34cff04d333 100644
--- a/Point_set_processing_3/examples/Point_set_processing_3/CMakeLists.txt
+++ b/Point_set_processing_3/examples/Point_set_processing_3/CMakeLists.txt
@@ -3,8 +3,6 @@
 cmake_minimum_required(VERSION 3.1...3.15)
 project( Point_set_processing_3_Examples )
 
-
-
 # Find CGAL
 find_package(CGAL QUIET)
 
@@ -42,30 +40,21 @@ if ( CGAL_FOUND )
   create_single_source_cgal_program( "bilateral_smooth_point_set_example.cpp" )
   create_single_source_cgal_program( "grid_simplification_example.cpp" )
   create_single_source_cgal_program( "grid_simplify_indices.cpp" )
-  create_single_source_cgal_program( "hierarchy_simplification_example.cpp" )
-  create_single_source_cgal_program( "normals_example.cpp" )
   create_single_source_cgal_program( "property_map.cpp" )
   create_single_source_cgal_program( "random_simplification_example.cpp" )
   create_single_source_cgal_program( "read_write_xyz_point_set_example.cpp" )
   create_single_source_cgal_program( "remove_outliers_example.cpp" )
-  create_single_source_cgal_program( "scale_estimation_example.cpp" )
-  create_single_source_cgal_program( "scale_estimation_2d_example.cpp" )
   create_single_source_cgal_program( "wlop_simplify_and_regularize_point_set_example.cpp" )
   create_single_source_cgal_program( "edge_aware_upsample_point_set_example.cpp" )
   create_single_source_cgal_program( "structuring_example.cpp" )
-  create_single_source_cgal_program( "callback_example.cpp" )
 
-  set(needed_cxx_features cxx_rvalue_references cxx_variadic_templates)    
-  create_single_source_cgal_program( "read_ply_points_with_colors_example.cpp" CXX_FEATURES ${needed_cxx_features} )
-  create_single_source_cgal_program( "write_ply_points_example.cpp" CXX_FEATURES ${needed_cxx_features} )
+  create_single_source_cgal_program( "read_ply_points_with_colors_example.cpp" )
+  create_single_source_cgal_program( "write_ply_points_example.cpp" )
     
   find_package(LASLIB)
   if (LASLIB_FOUND)
-    include(${LASLIB_USE_FILE})
-    include_directories(${LASLIB_INCLUDE_DIR})
-    include_directories(${LASZIP_INCLUDE_DIR})
-    create_single_source_cgal_program( "read_las_example.cpp" CXX_FEATURES ${needed_cxx_features} )
-    target_link_libraries(read_las_example PRIVATE ${LASLIB_LIBRARIES})
+    create_single_source_cgal_program( "read_las_example.cpp" )
+    CGAL_target_use_LASLIB(read_las_example)
   else()
     message(STATUS "NOTICE : the LAS reader test requires LASlib and will not be compiled.")
   endif()
@@ -73,30 +62,51 @@ if ( CGAL_FOUND )
   # Use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     # Executables that require Eigen
     create_single_source_cgal_program( "jet_smoothing_example.cpp" )
+    CGAL_target_use_Eigen(jet_smoothing_example)
+    
     create_single_source_cgal_program( "normal_estimation.cpp" )
+    CGAL_target_use_Eigen(normal_estimation)
+    
     create_single_source_cgal_program( "edges_example.cpp" )
-  else()
+    CGAL_target_use_Eigen(edges_example)
+    
+    create_single_source_cgal_program( "callback_example.cpp" )
+    CGAL_target_use_Eigen(callback_example)
+    
+    create_single_source_cgal_program( "scale_estimation_example.cpp" )
+    CGAL_target_use_Eigen(scale_estimation_example)
+    
+    create_single_source_cgal_program( "scale_estimation_2d_example.cpp" )
+    CGAL_target_use_Eigen(scale_estimation_2d_example)
 
+    create_single_source_cgal_program( "hierarchy_simplification_example.cpp" )
+    CGAL_target_use_Eigen(hierarchy_simplification_example)
+
+    create_single_source_cgal_program( "normals_example.cpp" )
+    CGAL_target_use_Eigen(normals_example)
+
+  else()
     message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
   endif()
 
-  foreach(target
-      scale_estimation_example
-      wlop_simplify_and_regularize_point_set_example
-      bilateral_smooth_point_set_example
-      edge_aware_upsample_point_set_example
-      average_spacing_example
-      normals_example
-      jet_smoothing_example
-      normal_estimation
-      callback_example)
-    if(TBB_FOUND AND TARGET ${target})
-      CGAL_target_use_TBB(${target})
-    endif()
-  endforeach()
+  if (TBB_FOUND)
+    foreach(target
+        scale_estimation_example
+        wlop_simplify_and_regularize_point_set_example
+        bilateral_smooth_point_set_example
+        edge_aware_upsample_point_set_example
+        average_spacing_example
+        normals_example
+        jet_smoothing_example
+        normal_estimation
+        callback_example)
+      if(TARGET ${target})
+        CGAL_target_use_TBB(${target})
+      endif()
+    endforeach()
+  endif()
 
 else()
     message(STATUS "NOTICE: This program requires the CGAL library, and will not be compiled.")
diff --git a/Point_set_processing_3/test/Point_set_processing_3/CMakeLists.txt b/Point_set_processing_3/test/Point_set_processing_3/CMakeLists.txt
index 264c713ef55..1b5e1a80746 100644
--- a/Point_set_processing_3/test/Point_set_processing_3/CMakeLists.txt
+++ b/Point_set_processing_3/test/Point_set_processing_3/CMakeLists.txt
@@ -41,29 +41,41 @@ if ( CGAL_FOUND )
   # Use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     # Executables that require Eigen
     create_single_source_cgal_program( "normal_estimation_test.cpp" )
+    CGAL_target_use_Eigen(normal_estimation_test)
+    
     create_single_source_cgal_program( "hierarchy_simplification_test.cpp" )
+    CGAL_target_use_Eigen(hierarchy_simplification_test)
+    
     create_single_source_cgal_program( "smoothing_test.cpp" )
+    CGAL_target_use_Eigen(smoothing_test)
+
     create_single_source_cgal_program( "vcm_plane_test.cpp" )
+    CGAL_target_use_Eigen(vcm_plane_test)
+    
     create_single_source_cgal_program( "vcm_all_test.cpp" )
+    CGAL_target_use_Eigen(vcm_all_test)
+    
     create_single_source_cgal_program( "jet_pointer_as_property_map.cpp" )
+    CGAL_target_use_Eigen(jet_pointer_as_property_map)
   else()
     message(STATUS "NOTICE: This program requires Eigen 3.1 (or greater) and will not be compiled.")
   endif()
 
-  foreach(target
-      analysis_test
-      smoothing_test
-      bilateral_smoothing_test
-      wlop_simplify_and_regularize_test
-      edge_aware_upsample_test
-      normal_estimation_test)
-    if(TBB_FOUND AND TARGET ${target})
-      CGAL_target_use_TBB(${target})
-    endif()
-  endforeach()
+  if (TBB_FOUND)
+    foreach(target
+        analysis_test
+        smoothing_test
+        bilateral_smoothing_test
+        wlop_simplify_and_regularize_test
+        edge_aware_upsample_test
+        normal_estimation_test)
+      if(TARGET ${target})
+        CGAL_target_use_TBB(${target})
+      endif()
+    endforeach()
+  endif()
 
 else()
 
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/CMakeLists.txt b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/CMakeLists.txt
index ae0215158da..0b65cf899cf 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/CMakeLists.txt
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/CMakeLists.txt
@@ -23,15 +23,14 @@ if ( CGAL_FOUND )
 
   # Find Eigen3 (requires 3.1.0 or greater)
   find_package(Eigen3 3.1.0)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
-  
   if (EIGEN3_FOUND)
     # Executables that require Eigen 3
     create_single_source_cgal_program( "poisson_reconstruction_example.cpp" )
+    CGAL_target_use_Eigen(poisson_reconstruction_example)
     create_single_source_cgal_program( "poisson_reconstruction.cpp" )
+    CGAL_target_use_Eigen(poisson_reconstruction)
     create_single_source_cgal_program( "poisson_reconstruction_function.cpp" )
+    CGAL_target_use_Eigen(poisson_reconstruction_function)
   else()
     message(STATUS "NOTICE: The examples need Eigen 3.1 (or greater) will not be compiled.")
   endif()
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
index e1d9326840b..1c518a1267b 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
@@ -25,11 +25,9 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if(EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     # Executables that require Eigen 3.1
     create_single_source_cgal_program( "poisson_reconstruction_test.cpp" )
-
+    CGAL_target_use_Eigen(poisson_reconstruction_test)
   else()
 
     message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
diff --git a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
index 45799830a42..7db73683150 100644
--- a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
+++ b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
@@ -29,10 +29,6 @@ endif()
 
 # include for local package
 find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
-if (EIGEN3_FOUND)
-  # Executables that require Eigen 3.2
-  include( ${EIGEN3_USE_FILE} )
-endif(EIGEN3_FOUND)
 
 # Creating entries for all .cpp/.C files with "main" routine
 # ##########################################################
@@ -41,4 +37,8 @@ create_single_source_cgal_program( "polygon_mesh_slicer.cpp" )
 
 create_single_source_cgal_program( "hole_filling.cpp" )
 
+if (EIGEN3_FOUND)
+  CGAL_target_use_Eigen(polygon_mesh_slicer)
+  CGAL_target_use_Eigen(hole_filling)
+endif()
 
diff --git a/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt b/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
index 20cea4f136f..b95f8671c34 100644
--- a/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
+++ b/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
@@ -32,20 +32,27 @@ is the property map with the points associated to the vertices of the polygon me
 \cgalNPEnd
 
 \cgalNPBegin{vertex_index_map} \anchor PMP_vertex_index_map
-is the property map containing the index of each vertex of the input polygon mesh.\n
+is the property map associating a unique index to each vertex of a polygon mesh,
+between `0` and `num_vertices(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a vertex index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and the value type
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::vertex_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::vertex_index, pmesh)\endcode
+<b>Default:</b> an initialized vertex index property map
 \cgalNPEnd
 
 \cgalNPBegin{face_index_map} \anchor PMP_face_index_map
-is the property map containing the index of each face of the input polygon mesh.\n
+is the property map associating a unique index to each face of a polygon mesh,
+between `0` and `num_faces(g)-1`.
+If this parameter is not passed, internal machinery will create and initialize a face index
+property map, either using the internal property map if it exists or using an external map. The latter
+might result in  - slightly - worsened performance in case of non-constant complexity for index access.\n
 <b>Type:</b> a class model of `ReadablePropertyMap` with
 `boost::graph_traits<PolygonMesh>::%face_descriptor` as key type and the value type:
 \code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::face_index_t>::type>::value_type \endcode
-<b>Default:</b> \code boost::get(CGAL::face_index, pmesh)\endcode
-If this internal property map exists, its values must be initialized.
+<b>Default:</b> an initialized face index property map
 \cgalNPEnd
 
 \cgalNPBegin{edge_is_constrained_map} \anchor PMP_edge_is_constrained_map
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/CMakeLists.txt b/Polygon_mesh_processing/examples/Polygon_mesh_processing/CMakeLists.txt
index eff0d48d229..ec36a4b70f0 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/CMakeLists.txt
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/CMakeLists.txt
@@ -46,14 +46,16 @@ find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
 create_single_source_cgal_program( "hausdorff_distance_remeshing_example.cpp")
 
 if (EIGEN3_FOUND)
-  # Executables that require Eigen 3.2
-  include( ${EIGEN3_USE_FILE} )
-
   create_single_source_cgal_program( "hole_filling_example.cpp" )
+  CGAL_target_use_Eigen(hole_filling_example)
   create_single_source_cgal_program( "hole_filling_example_SM.cpp" )
+  CGAL_target_use_Eigen(hole_filling_example_SM)
   create_single_source_cgal_program( "refine_fair_example.cpp")
+  CGAL_target_use_Eigen(refine_fair_example)
   create_single_source_cgal_program( "shape_smoothing_example.cpp")
-
+  CGAL_target_use_Eigen(shape_smoothing_example)
+  create_single_source_cgal_program( "hole_filling_example_LCC.cpp" )
+  CGAL_target_use_Eigen(hole_filling_example_LCC)
 endif(EIGEN3_FOUND)
 
 create_single_source_cgal_program( "self_intersections_example.cpp" )
@@ -80,19 +82,24 @@ create_single_source_cgal_program( "corefinement_mesh_union_with_attributes.cpp"
 create_single_source_cgal_program( "corefinement_polyhedron_union.cpp" )
 create_single_source_cgal_program( "random_perturbation_SM_example.cpp" )
 create_single_source_cgal_program( "corefinement_LCC.cpp")
-create_single_source_cgal_program( "hole_filling_example_LCC.cpp" )
 create_single_source_cgal_program( "detect_features_example.cpp" )
 create_single_source_cgal_program( "manifoldness_repair_example.cpp" )
 create_single_source_cgal_program( "repair_polygon_soup_example.cpp" )
 create_single_source_cgal_program( "mesh_smoothing_example.cpp")
 create_single_source_cgal_program( "locate_example.cpp")
+#create_single_source_cgal_program( "self_snapping_example.cpp")
+#create_single_source_cgal_program( "snapping_example.cpp")
 
 if(OpenMesh_FOUND)
+
 create_single_source_cgal_program( "compute_normals_example_OM.cpp" )
 target_link_libraries( compute_normals_example_OM PRIVATE ${OPENMESH_LIBRARIES} )
 
-create_single_source_cgal_program( "hole_filling_example_OM.cpp" )
-target_link_libraries( hole_filling_example_OM PRIVATE ${OPENMESH_LIBRARIES} )
+if (EIGEN3_FOUND)
+  create_single_source_cgal_program( "hole_filling_example_OM.cpp" )
+  target_link_libraries( hole_filling_example_OM PRIVATE ${OPENMESH_LIBRARIES} )
+  CGAL_target_use_Eigen( hole_filling_example_OM )
+endif()
 
 create_single_source_cgal_program( "point_inside_example_OM.cpp")
 target_link_libraries( point_inside_example_OM PRIVATE ${OPENMESH_LIBRARIES} )
@@ -109,6 +116,8 @@ endif(OpenMesh_FOUND)
 
 find_package( TBB )
 if( TBB_FOUND )
+#  CGAL_target_use_TBB(self_snapping_example)
+#  CGAL_target_use_TBB(snapping_example)
   CGAL_target_use_TBB(self_intersections_example)
   CGAL_target_use_TBB(hausdorff_distance_remeshing_example)
 else()
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/self_snapping_example.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/self_snapping_example.cpp
new file mode 100644
index 00000000000..c20c59a2172
--- /dev/null
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/self_snapping_example.cpp
@@ -0,0 +1,75 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/snap.h>
+#include <CGAL/Polygon_mesh_processing/stitch_borders.h>
+
+#include <iostream>
+#include <fstream>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel           Kernel;
+
+typedef Kernel::FT                                                    FT;
+typedef Kernel::Point_3                                               Point_3;
+typedef Kernel::Vector_3                                              Vector_3;
+typedef CGAL::Surface_mesh<Point_3>                                   Surface_mesh;
+
+typedef boost::graph_traits<Surface_mesh>::vertex_descriptor          vertex_descriptor;
+
+namespace PMP = CGAL::Polygon_mesh_processing;
+
+int main(int argc, char** argv)
+{
+  std::cout.precision(17);
+
+  if(argc != 3)
+  {
+    std::cerr << "Usage: " << argv[0] << " input_mesh tolerance" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  Surface_mesh sm;
+  std::ifstream in(argv[1]);
+  if(!in || in >> sm)
+  {
+    std::cerr << "Problem loading the input data" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  Surface_mesh::Property_map<vertex_descriptor, double> tolerance_map;
+  tolerance_map = sm.add_property_map<vertex_descriptor, double>("v:t").first;
+  for(vertex_descriptor v : vertices(sm))
+    put(tolerance_map, v, std::atof(argv[3]));
+
+  std::chrono::steady_clock::time_point start_time = std::chrono::steady_clock::now();
+
+  // Snap
+  std::size_t nb_snapped = PMP::experimental::snap_borders<CGAL::Parallel_tag>(sm, tolerance_map);
+  std::cout << "#snapped: " << nb_snapped << std::endl;
+
+  std::chrono::steady_clock::time_point snap_time = std::chrono::steady_clock::now();
+  std::cout << "Time elapsed (snap): "
+            << std::chrono::duration_cast<std::chrono::milliseconds>(snap_time - start_time).count()
+            << "ms" << std::endl;
+
+  // Stitch
+  std::cout << "Stitch, #ne: " << edges(sm).size() << std::endl;
+  PMP::stitch_borders(sm);
+
+  std::chrono::steady_clock::time_point stitch_time = std::chrono::steady_clock::now();
+  std::cout << "Time elapsed (stitch): "
+            << std::chrono::duration_cast<std::chrono::milliseconds>(stitch_time - snap_time).count()
+            << "ms" << std::endl;
+
+  std::chrono::steady_clock::time_point end_time = std::chrono::steady_clock::now();
+  std::cout << "Total time elapsed: "
+            << std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time).count()
+            << "ms" << std::endl;
+
+  std::cout << "#border: " << PMP::number_of_borders(sm) << std::endl;
+  std::cout << "Done!" << std::endl;
+
+  std::ofstream("snapped.off") << std::setprecision(17) << sm;
+
+  return EXIT_SUCCESS;
+}
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/snapping_example.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/snapping_example.cpp
new file mode 100644
index 00000000000..b5bb4d913ed
--- /dev/null
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/snapping_example.cpp
@@ -0,0 +1,78 @@
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/snap.h>
+
+#include <iostream>
+#include <fstream>
+
+typedef CGAL::Simple_cartesian<double>                          Kernel;
+typedef Kernel::Point_3                                         Point_3;
+typedef CGAL::Surface_mesh<Point_3>                             Surface_mesh;
+
+typedef boost::graph_traits<Surface_mesh>::vertex_descriptor    vertex_descriptor;
+
+namespace PMP = CGAL::Polygon_mesh_processing;
+
+int main(int argc, char** argv)
+{
+  if(argc != 4)
+  {
+    std::cerr << "Usage: " << argv[0] << " movable_mesh fixed_mesh tolerance" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  Surface_mesh movable_mesh, fixed_mesh;
+
+  std::ifstream in_m(argv[1]);
+  if(!in_m || in_m >> movable_mesh)
+  {
+    std::cerr << "Problem loading the input data" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::ifstream in_f(argv[2]);
+  if(!in_f || in_f >> fixed_mesh)
+  {
+    std::cerr << "Problem loading the input data" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::cout << "Movable mesh: " << num_vertices(movable_mesh) << std::endl;
+  std::cout << "Fixed mesh: " << num_vertices(fixed_mesh) << std::endl;
+
+  const double tolerance = std::atof(argv[3]);
+
+  Surface_mesh::Property_map<vertex_descriptor, double> movable_tolerance_map;
+  movable_tolerance_map = movable_mesh.add_property_map<vertex_descriptor, double>("v:t").first;
+  for(vertex_descriptor v : vertices(movable_mesh))
+    put(movable_tolerance_map, v, tolerance);
+
+  Surface_mesh::Property_map<vertex_descriptor, double> fixed_tolerance_map;
+  fixed_tolerance_map = fixed_mesh.add_property_map<vertex_descriptor, double>("v:t").first;
+  for(vertex_descriptor v : vertices(fixed_mesh))
+    put(fixed_tolerance_map, v, tolerance);
+
+  std::chrono::steady_clock::time_point start_time = std::chrono::steady_clock::now();
+
+  // Choice of named parameters indicates that:
+  // - We want to simplify the boundary of the first mesh
+  // - The geometry of the second mesh cannot change
+  std::size_t nb_snapped = PMP::experimental::snap_borders(movable_mesh, movable_tolerance_map,
+                                                           fixed_mesh, fixed_tolerance_map,
+                                                           CGAL::parameters::do_simplify_border(true),
+                                                           CGAL::parameters::do_lock_mesh(true));
+
+  std::chrono::steady_clock::time_point end_time = std::chrono::steady_clock::now();
+
+  std::cout << "Time elapsed: "
+            << std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time).count()
+            << "ms" << std::endl;
+
+  std::cout << "#Snapped: " << nb_snapped << std::endl;
+
+  std::ofstream("snapped_movable.off") << std::setprecision(17) << movable_mesh;
+  std::ofstream("snapped_fixed.off") << std::setprecision(17) << fixed_mesh;
+
+  return EXIT_SUCCESS;
+}
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/border.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/border.h
index 54a520908e0..c52695b90cf 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/border.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/border.h
@@ -17,6 +17,7 @@
 
 #include <CGAL/algorithm.h>
 #include <CGAL/boost/graph/iterator.h>
+#include <CGAL/boost/graph/helpers.h>
 #include <CGAL/Polygon_mesh_processing/internal/named_function_params.h>
 #include <CGAL/Polygon_mesh_processing/internal/named_params_helper.h>
 
@@ -28,13 +29,31 @@
 
 namespace CGAL{
 namespace Polygon_mesh_processing {
+namespace internal {
 
-  namespace internal
+template<typename PolygonMesh>
+std::size_t border_size(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor h,
+                        const PolygonMesh& pmesh)
+{
+  // if you want to use it on a non-border halfedge, just use `degree(face, mesh)`
+  CGAL_precondition(is_border(h, pmesh));
+
+  std::size_t res = 0;
+  typename boost::graph_traits<PolygonMesh>::halfedge_descriptor done = h;
+  do
   {
+    ++res;
+    h = next(h, pmesh);
+  }
+  while(h != done);
+
+  return res;
+}
+
     template<typename PM
            , typename FaceRange
            , typename HalfedgeOutputIterator>
-    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& faces
+    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& face_range
                                                , HalfedgeOutputIterator out
                                                , const PM& pmesh)
     {
@@ -45,7 +64,7 @@ namespace Polygon_mesh_processing {
       // the bool is true if the halfedge stored is the one of the face,
       // false if it is its opposite
       std::map<halfedge_descriptor, bool> border;
-      for(face_descriptor f : faces)
+      for(face_descriptor f : face_range)
       {
         for(halfedge_descriptor h :
           halfedges_around_face(halfedge(f, pmesh), pmesh))
@@ -75,13 +94,13 @@ namespace Polygon_mesh_processing {
            , typename FaceRange
            , typename HalfedgeOutputIterator
            , typename NamedParameters>
-    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& faces
+    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& face_range
                                                , typename boost::cgal_no_property::type
                                                , HalfedgeOutputIterator out
                                                , const PM& pmesh
                                                , const NamedParameters& /* np */)
     {
-      return border_halfedges_impl(faces, out, pmesh);
+      return border_halfedges_impl(face_range, out, pmesh);
     }
 
     template<typename PM
@@ -89,7 +108,7 @@ namespace Polygon_mesh_processing {
            , typename FaceIndexMap
            , typename HalfedgeOutputIterator
            , typename NamedParameters>
-    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& faces
+    HalfedgeOutputIterator border_halfedges_impl(const FaceRange& face_range
                                                , const FaceIndexMap& fmap
                                                , HalfedgeOutputIterator out
                                                , const PM& pmesh
@@ -98,25 +117,13 @@ namespace Polygon_mesh_processing {
       typedef typename boost::graph_traits<PM>::halfedge_descriptor halfedge_descriptor;
       typedef typename boost::graph_traits<PM>::face_descriptor     face_descriptor;
 
-      //make a minimal check that it's properly initialized :
-      //if the 2 first faces have the same id, we know the property map is not initialized
-      if (boost::is_same<typename GetFaceIndexMap<PM, NamedParameters>::Is_internal_map,
-                         boost::true_type>::value)
-      {
-        typename boost::range_iterator<const FaceRange>::type it = boost::const_begin(faces);
-        if (get(fmap, *it) == get(fmap, *std::next(it)))
-        {
-          std::cerr << "WARNING : the internal property map for CGAL::face_index_t" << std::endl
-                    << "          is not properly initialized." << std::endl
-                    << "          Initialize it before calling border_halfedges()" << std::endl;
-        }
-      }
+      CGAL_assertion(BGL::internal::is_index_map_valid(fmap, num_faces(pmesh), faces(pmesh)));
 
       std::vector<bool> present(num_faces(pmesh), false);
-      for(face_descriptor fd : faces)
+      for(face_descriptor fd : face_range)
         present[get(fmap, fd)] = true;
 
-      for(face_descriptor fd : faces)
+      for(face_descriptor fd : face_range)
         for(halfedge_descriptor hd :
                       halfedges_around_face(halfedge(fd, pmesh), pmesh))
        {
@@ -142,21 +149,16 @@ namespace Polygon_mesh_processing {
   * For each returned halfedge `h`, `opposite(h, pmesh)` belongs to a face of the patch,
   * but `face(h, pmesh)` does not belong to the patch.
   *
-  * @tparam PolygonMesh model of `HalfedgeGraph`. If `PolygonMesh`
-  *  has an internal property map
-  *  for `CGAL::face_index_t` and no `face_index_map` is given
-  *  as a named parameter, then the internal one must be initialized
-  * @tparam FaceRange range of
-       `boost::graph_traits<PolygonMesh>::%face_descriptor`, model of `Range`.
-        Its iterator type is `InputIterator`.
+  * @tparam PolygonMesh model of `HalfedgeGraph`
+  * @tparam FaceRange a model of `Range` with value type `boost::graph_traits<PolygonMesh>::%face_descriptor`.
   * @tparam HalfedgeOutputIterator model of `OutputIterator`
      holding `boost::graph_traits<PolygonMesh>::%halfedge_descriptor`
      for patch border
   * @tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
   *
-  * @param pmesh the polygon mesh to which `faces` belong
-  * @param faces the range of faces defining the patch whose border halfedges
-  *              are collected
+  * @param pmesh the polygon mesh to which the faces in `face_range` belong
+  * @param face_range the range of faces defining the patch whose border halfedges
+  *                   are collected
   * @param out the output iterator that collects the border halfedges of the patch,
   *            seen from outside.
   * @param np optional sequence of \ref pmp_namedparameters "Named Parameters" among the ones listed below
@@ -171,29 +173,18 @@ namespace Polygon_mesh_processing {
          , typename FaceRange
          , typename HalfedgeOutputIterator
          , typename NamedParameters>
-  HalfedgeOutputIterator border_halfedges(const FaceRange& faces
+  HalfedgeOutputIterator border_halfedges(const FaceRange& face_range
                                   , const PolygonMesh& pmesh
                                   , HalfedgeOutputIterator out
                                   , const NamedParameters& np)
   {
-    if (faces.empty()) return out;
+    if (face_range.empty())
+      return out;
 
-    typedef PolygonMesh PM;
-    typedef typename GetFaceIndexMap<PM, NamedParameters>::const_type     FIMap;
-    typedef typename boost::property_map<typename internal::Dummy_PM,
-                                              CGAL::face_index_t>::type   Unset_FIMap;
+    typedef typename CGAL::GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::const_type FIMap;
+    FIMap fim = CGAL::get_initialized_face_index_map(pmesh, np);
 
-    if (boost::is_same<FIMap, Unset_FIMap>::value || faces.size() == 1)
-    {
-      //face index map is not given in named parameters, nor as an internal property map
-      return internal::border_halfedges_impl(faces, out, pmesh);
-    }
-
-    //face index map given as a named parameter, or as an internal property map
-    FIMap fim = parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                                             get_const_property_map(CGAL::face_index, pmesh));
-
-    return internal::border_halfedges_impl(faces, fim, out, pmesh, np);
+    return internal::border_halfedges_impl(face_range, fim, out, pmesh, np);
   }
 
   template<typename PolygonMesh
@@ -212,11 +203,11 @@ namespace Polygon_mesh_processing {
   template<typename PolygonMesh
          , typename FaceRange
          , typename HalfedgeOutputIterator>
-  HalfedgeOutputIterator border_halfedges(const FaceRange& faces
+  HalfedgeOutputIterator border_halfedges(const FaceRange& face_range
                                         , const PolygonMesh& pmesh
                                         , HalfedgeOutputIterator out)
   {
-    return border_halfedges(faces, pmesh, out,
+    return border_halfedges(face_range, pmesh, out,
       CGAL::Polygon_mesh_processing::parameters::all_default());
   }
 
@@ -225,7 +216,7 @@ namespace Polygon_mesh_processing {
   //
   // @tparam PolygonMesh model of `HalfedgeGraph`.
   //
-  // @param pmesh the polygon mesh to which `faces` belong
+  // @param pmesh the polygon mesh to which `face_range` belong
   //
   template<typename PolygonMesh>
   unsigned int number_of_borders(const PolygonMesh& pmesh)
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
index a75689c127f..5b31be90cff 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
@@ -416,9 +416,6 @@ void split_along_edges(TriangleMesh& tm,
   * \pre \link CGAL::Polygon_mesh_processing::does_bound_a_volume() `CGAL::Polygon_mesh_processing::does_bound_a_volume(clipper)` \endlink
   *
   * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
-  *                      If `TriangleMesh` has an internal property map for `CGAL::face_index_t`,
-  *                      as a named parameter, then it must be initialized.
-  *
   * @tparam NamedParameters1 a sequence of \ref pmp_namedparameters "Named Parameters"
   * @tparam NamedParameters2 a sequence of \ref pmp_namedparameters "Named Parameters"
   *
@@ -434,8 +431,8 @@ void split_along_edges(TriangleMesh& tm,
   *     `CGAL::vertex_point_t` must be available in `TriangleMesh`
   *   \cgalParamEnd
   *   \cgalParamBegin{face_index_map} a property map containing the index of each face of `tm` (`clipper`).
-  *     Note that if the property map is writable, the indices of the faces
-  *     of `tm` and `clipper` will be set after refining `tm` with the intersection with `clipper`.
+  *     This property map must be either writable, or be automatically updated
+  *     when new faces are added and removed in the mesh.
   *   \cgalParamEnd
   *   \cgalParamBegin{visitor} a class model of `PMPCorefinementVisitor`
   *                            that is used to track the creation of new faces.
@@ -443,14 +440,14 @@ void split_along_edges(TriangleMesh& tm,
   *   \cgalParamBegin{throw_on_self_intersection} if `true`,
   *      the set of triangles closed to the intersection of `tm` and `clipper` will be
   *      checked for self-intersections and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
-  *      will be thrown if at least one is found.
+  *      will be thrown if at least one is found.  Default value is `false`.
   *   \cgalParamEnd
   *   \cgalParamBegin{clip_volume} if `true` and `tm` is closed, the clipping will be done on
   *      the volume \link coref_def_subsec bounded \endlink by `tm` rather than on its surface
-  *      (i.e., `tm` will be kept closed).
+  *      (i.e., `tm` will be kept closed). Default value is `false`.
   *   \cgalParamEnd
-  *   \cgalParamBegin{use_compact_clipper} if `false` and `clip_volume` is `false` and `tm` is open, the parts of `tm` coplanar with `clipper`
-  *                                        will not be part of the output.
+  *   \cgalParamBegin{use_compact_clipper} if `false`, the parts of `tm` coplanar with `clipper`
+  *      will not be part of the output. Default value is `true`.
   *   \cgalParamEnd
   * \cgalNamedParamsEnd
   *
@@ -476,26 +473,6 @@ clip(      TriangleMesh& tm,
                                            np_c);
 }
 
-namespace internal{
-template <class TriangleMesh, class NamedParameters>
-bool dispatch_clip_call(TriangleMesh& tm, TriangleMesh& clipper,
-                        const NamedParameters& np, Tag_false)
-{
-  return clip(tm, clipper,
-              np.face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm)),
-              parameters::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), clipper)));
-}
-
-template <class TriangleMesh, class NamedParameters>
-bool dispatch_clip_call(TriangleMesh& tm, TriangleMesh& clipper,
-                        const NamedParameters& np, Tag_true)
-{
-  return clip(tm, clipper,
-              np.face_index_map(get(face_index, tm)),
-              parameters::face_index_map(get(face_index, clipper)));
-}
-}
-
 /**
   * \ingroup PMP_corefinement_grp
   * clips `tm` by keeping the part that is on the negative side of `plane` (side opposite to its normal vector).
@@ -507,8 +484,6 @@ bool dispatch_clip_call(TriangleMesh& tm, TriangleMesh& clipper,
   * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
   *
   * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
-  *                      If `TriangleMesh` has an internal property map for `CGAL::face_index_t`,
-  *                      as a named parameter, then it must be initialized.
   *                      An internal property map for `CGAL::vertex_point_t` must be available.
   *
   * @tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
@@ -525,14 +500,14 @@ bool dispatch_clip_call(TriangleMesh& tm, TriangleMesh& clipper,
   *   \cgalParamBegin{throw_on_self_intersection} if `true`,
   *      the set of triangles closed to the intersection of `tm` and `plane` will be
   *      checked for self-intersections and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
-  *      will be thrown if at least one is found.
+  *      will be thrown if at least one is found. Default value is `false`.
   *   \cgalParamEnd
   *   \cgalParamBegin{clip_volume} if `true` and `tm` is closed, the clipping will be done on
   *      the volume \link coref_def_subsec bounded \endlink by `tm` rather than on its surface
-  *      (i.e., `tm` will be kept closed).
+  *      (i.e., `tm` will be kept closed). Default value is `false`.
   *   \cgalParamEnd
-  *   \cgalParamBegin{use_compact_clipper} if `false` and `clip_volume` is `false` and `tm` is open, the parts of `tm` coplanar with `plane`
-  *                                        will not be part of the output.
+  *   \cgalParamBegin{use_compact_clipper} if `false` the parts of `tm` coplanar with `plane`
+  *      will not be part of the output. Default value is `true`.
   * \cgalNamedParamsEnd
   *
   * @return `true` if the output surface mesh is manifold.
@@ -570,9 +545,8 @@ bool clip(      TriangleMesh& tm,
     default:
       break;
   }
-  // dispatch is needed because face index map for tm and clipper have to be of the same time
-  return internal::dispatch_clip_call(tm, clipper,
-                                      np, CGAL::graph_has_property<TriangleMesh, CGAL::face_index_t>());
+
+  return clip(tm, clipper, np, parameters::all_default());
 }
 
 
@@ -727,8 +701,6 @@ void split(      TriangleMesh& tm,
   * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
   *
   * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
-  *                      If `TriangleMesh` has an internal property map for `CGAL::face_index_t`,
-  *                      as a named parameter, then it must be initialized.
   *                      An internal property map for `CGAL::vertex_point_t` must be available.
   *
   * @tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
@@ -775,9 +747,7 @@ bool clip(      TriangleMesh& tm,
                   clipper);
   triangulate_faces(clipper);
 
-  // dispatch is needed because face index map for tm and clipper have to be of the same time
-  return internal::dispatch_clip_call(tm, clipper,
-                                      np, CGAL::graph_has_property<TriangleMesh, CGAL::face_index_t>());
+  return clip(tm, clipper, np, parameters::all_default());
 }
 
 /// \cond SKIP_IN_MANUAL
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
index 9932d96fdc5..a1b1013ae35 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
@@ -151,7 +151,7 @@ connected_component(typename boost::graph_traits<PolygonMesh>::face_descriptor s
       if (!already_processed.insert(seed_face).second) continue;
       *out++=seed_face;
       for(halfedge_descriptor hd :
-                    CGAL::halfedges_around_face(halfedge(seed_face, pmesh), pmesh) )
+                    halfedges_around_face(halfedge(seed_face, pmesh), pmesh) )
       {
         if(! get(ecmap, edge(hd, pmesh))){
           face_descriptor neighbor = face( opposite(hd, pmesh), pmesh );
@@ -177,9 +177,6 @@ connected_component(typename boost::graph_traits<PolygonMesh>::face_descriptor s
  * \ingroup keep_connected_components_grp
  *  computes for each face the index of the corresponding connected component.
  *
- *  A property map for `CGAL::face_index_t` must be either available as an internal property map
- *  to `pmesh` or provided as one of the \ref pmp_namedparameters "Named Parameters".
- *
  *  \tparam PolygonMesh a model of `FaceListGraph`
  *  \tparam FaceComponentMap a model of `WritablePropertyMap` with
         `boost::graph_traits<PolygonMesh>::%face_descriptor` as key type and
@@ -219,13 +216,13 @@ connected_components(const PolygonMesh& pmesh,
     NamedParameters,
     internal::No_constraint<PolygonMesh>//default
   > ::type                                               EdgeConstraintMap;
+  
   EdgeConstraintMap ecmap
     = choose_parameter(get_parameter(np, internal_np::edge_is_constrained),
                    internal::No_constraint<PolygonMesh>());
 
-  typedef typename GetFaceIndexMap<PolygonMesh, NamedParameters>::const_type  FaceIndexMap;
-  FaceIndexMap fimap = choose_parameter(get_parameter(np, internal_np::face_index),
-                                        get_const_property_map(boost::face_index, pmesh));
+  typedef typename GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::const_type FaceIndexMap;
+  FaceIndexMap fimap = get_initialized_face_index_map(pmesh, np);
 
   typename boost::property_traits<FaceComponentMap>::value_type i=0;
   std::vector<bool> handled(num_faces(pmesh), false);
@@ -329,10 +326,6 @@ std::size_t number_of_connected_components(const PolygonMesh& pmesh)
  * By default, the size of a face is `1` (and thus the size of a connected component is the number
  * of faces it contains), but it is also possible to pass custom sizes, such as the area of the face.
  *
- * Property maps for `CGAL::face_index_t` and `CGAL::vertex_index_t`
- * must be either available as internal property maps
- * to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
- *
  * \tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
  * \tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
  *
@@ -374,10 +367,8 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
   using parameters::choose_parameter;
   using parameters::get_parameter;
 
-  // FaceIndexMap
-  typedef typename GetFaceIndexMap<PM, NamedParameters>::type            FaceIndexMap;
-  FaceIndexMap fimap = choose_parameter(get_parameter(np, internal_np::face_index),
-                                        get_property_map(boost::face_index, pmesh));
+  typedef typename CGAL::GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::type FaceIndexMap;
+  FaceIndexMap fimap = CGAL::get_initialized_face_index_map(pmesh, np);
 
   // FaceSizeMap
   typedef typename internal_np::Lookup_named_param_def<internal_np::face_size_map_t,
@@ -462,10 +453,6 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
  * the size of a connected component is the number of faces it contains), but it is also possible
  * to pass custom sizes, such as the area of the face.
  *
- * Property maps for `CGAL::face_index_t` and `CGAL::vertex_index_t`
- * must be either available as internal property maps
- * to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
- *
  * \tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
  * \tparam ThresholdValueType the type of the threshold value
  * \tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
@@ -511,15 +498,13 @@ std::size_t keep_large_connected_components(PolygonMesh& pmesh,
   using parameters::choose_parameter;
   using parameters::get_parameter;
 
-  // FaceIndexMap
-  typedef typename GetFaceIndexMap<PM, NamedParameters>::type             FaceIndexMap;
-  FaceIndexMap fim = choose_parameter(get_parameter(np, internal_np::face_index),
-                                      get_property_map(boost::face_index, pmesh));
+  typedef typename CGAL::GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::type FaceIndexMap;
+  FaceIndexMap fim = CGAL::get_initialized_face_index_map(pmesh, np);
 
   typedef typename internal_np::Lookup_named_param_def<internal_np::face_size_map_t,
-                                                 NamedParameters,
-                                                 Constant_property_map<face_descriptor, std::size_t> // default
-                                                >::type                   FaceSizeMap;
+                                                       NamedParameters,
+                                                       Constant_property_map<face_descriptor, std::size_t> // default
+                                                      >::type             FaceSizeMap;
   typedef typename boost::property_traits<FaceSizeMap>::value_type        Face_size;
 
   CGAL_static_assertion((std::is_convertible<ThresholdValueType, Face_size>::value));
@@ -593,7 +578,6 @@ void keep_or_remove_connected_components(PolygonMesh& pmesh
                                         , bool  keep
                                         , const NamedParameters& np)
 {
-  typedef PolygonMesh PM;
   using parameters::choose_parameter;
   using parameters::get_parameter;
 
@@ -605,10 +589,8 @@ void keep_or_remove_connected_components(PolygonMesh& pmesh
   typedef typename boost::graph_traits<PolygonMesh>::edge_descriptor   edge_descriptor;
   typedef typename boost::graph_traits<PolygonMesh>::edge_iterator     edge_iterator;
 
-  //VertexIndexMap
-  typedef typename GetVertexIndexMap<PM, NamedParameters>::type VertexIndexMap;
-  VertexIndexMap vim = choose_parameter(get_parameter(np, internal_np::vertex_index),
-                                    get_const_property_map(boost::vertex_index, pmesh));
+  typedef typename GetInitializedVertexIndexMap<PolygonMesh, NamedParameters>::type VertexIndexMap;
+  VertexIndexMap vim = get_initialized_vertex_index_map(pmesh, np);
 
   std::set<std::size_t> cc_to_keep;
   for(std::size_t i : components_to_keep)
@@ -727,10 +709,6 @@ void keep_or_remove_connected_components(PolygonMesh& pmesh
 * \note If the removal of the connected components makes `pmesh` a non-manifold surface,
 * then the behavior of this function is undefined.
 *
-* Property maps for `CGAL::vertex_index_t`
-* must be either available as internal property map
-* to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
-*
 * \tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
 * \tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
 * \tparam ComponentRange a range of ids convertible to `std::size`
@@ -770,11 +748,6 @@ void keep_connected_components(PolygonMesh& pmesh
 * \note If the removal of the connected components makes `pmesh` a non-manifold surface,
 * then the behavior of this function is undefined.
 *
-* Property maps for `CGAL::vertex_index_t`
-* must be either available as internal property map
-* to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
-*
-*
 * \tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
 * \tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
 * \tparam ComponentRange a range of ids convertible to `std::size`
@@ -811,10 +784,6 @@ void remove_connected_components(PolygonMesh& pmesh
 *  keeps the connected components not designated by the faces in `components_to_remove`,
 *  and removes the other connected components and all isolated vertices.
 *
-* Property maps for `CGAL::face_index_t` and `CGAL::vertex_index_t`
-* must be either available as internal property maps
-* to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
-*
 * \note If the removal of the connected components makes `pmesh` a non-manifold surface,
 * then the behavior of this function is undefined.
 *
@@ -841,20 +810,19 @@ void remove_connected_components(PolygonMesh& pmesh
                                 , const FaceRange& components_to_remove
                                 , const CGAL_PMP_NP_CLASS& np)
 {
-  if (components_to_remove.empty()) return;
-  typedef PolygonMesh PM;
-  typedef typename boost::graph_traits<PM>::face_descriptor face_descriptor;
   using parameters::choose_parameter;
   using parameters::get_parameter;
 
-  //FaceIndexMap
-  typedef typename GetFaceIndexMap<PM, CGAL_PMP_NP_CLASS>::type FaceIndexMap;
-  FaceIndexMap fim = choose_parameter(get_parameter(np, internal_np::face_index),
-                                  get_property_map(boost::face_index, pmesh));
+  if (components_to_remove.empty())
+    return;
+
+  typedef PolygonMesh PM;
+  typedef typename boost::graph_traits<PM>::face_descriptor face_descriptor;
+
+  typedef typename CGAL::GetInitializedFaceIndexMap<PolygonMesh, CGAL_PMP_NP_CLASS>::type FaceIndexMap;
+  FaceIndexMap fim = CGAL::get_initialized_face_index_map(pmesh, np);
 
-  //vector_property_map
   boost::vector_property_map<std::size_t, FaceIndexMap> face_cc(fim);
-
   connected_components(pmesh, face_cc, np);
 
   std::vector<std::size_t> cc_to_remove;
@@ -869,10 +837,6 @@ void remove_connected_components(PolygonMesh& pmesh
 *  keeps the connected components designated by the faces in `components_to_keep`,
 *  and removes the other connected components and all isolated vertices.
 *
-* Property maps for `CGAL::face_index_t` and `CGAL::vertex_index_t`
-* must be either available as internal property maps
-* to `pmesh` or provided as \ref pmp_namedparameters "Named Parameters".
-*
 * \note If the removal of the connected components makes `pmesh` a non-manifold surface,
 * then the behavior of this function is undefined.
 *
@@ -905,14 +869,10 @@ void keep_connected_components(PolygonMesh& pmesh
   using parameters::choose_parameter;
   using parameters::get_parameter;
 
-  //FaceIndexMap
-  typedef typename GetFaceIndexMap<PM, CGAL_PMP_NP_CLASS>::type FaceIndexMap;
-  FaceIndexMap fim = choose_parameter(get_parameter(np, internal_np::face_index),
-                                  get_property_map(boost::face_index, pmesh));
+  typedef typename CGAL::GetInitializedFaceIndexMap<PolygonMesh, CGAL_PMP_NP_CLASS>::type FaceIndexMap;
+  FaceIndexMap fim = CGAL::get_initialized_face_index_map(pmesh, np);
 
-  //vector_property_map
   boost::vector_property_map<std::size_t, FaceIndexMap> face_cc(fim);
-
   connected_components(pmesh, face_cc, np);
 
   std::vector<std::size_t> cc_to_keep;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
index a6f2f052434..3c4f77b9bbe 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
@@ -17,11 +17,12 @@
 
 #include <CGAL/disable_warnings.h>
 
+#include <CGAL/boost/graph/copy_face_graph.h>
+#include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/Polygon_mesh_processing/intersection.h>
 #include <CGAL/Polygon_mesh_processing/internal/Corefinement/Visitor.h>
 #include <CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h>
 #include <CGAL/Polygon_mesh_processing/internal/Corefinement/Output_builder_for_autorefinement.h>
-#include <CGAL/boost/graph/copy_face_graph.h>
 #include <CGAL/iterator.h>
 
 namespace CGAL {
@@ -39,16 +40,17 @@ namespace internal {
 template <class Kernel, class TriangleMesh, class VD, class Fid_map, class Vpm>
 bool recursive_does_bound_a_volume(const TriangleMesh& tm,
                                          Vpm& vpm,
-                                         Fid_map& fid_map,
+                                         Fid_map fid_map,
                                          const std::vector<VD>& xtrm_vertices,
                                          boost::dynamic_bitset<>& cc_handled,
                                          const std::vector<std::size_t>& face_cc,
                                          std::size_t xtrm_cc_id,
                                          bool is_parent_outward_oriented)
 {
-  typedef boost::graph_traits<TriangleMesh> GT;
-  typedef typename GT::face_descriptor face_descriptor;
-  typedef Side_of_triangle_mesh<TriangleMesh, Kernel, Vpm> Side_of_tm;
+  typedef boost::graph_traits<TriangleMesh>                 Graph_traits;
+  typedef typename Graph_traits::face_descriptor            face_descriptor;
+  typedef Side_of_triangle_mesh<TriangleMesh, Kernel, Vpm>  Side_of_tm;
+
 // first check that the orientation of the current cc is consistant with its
 // parent cc containing it
   bool new_is_parent_outward_oriented = internal::is_outward_oriented(
@@ -170,25 +172,23 @@ enum Boolean_operation_type {UNION = 0, INTERSECTION=1,
  * \see `CGAL::Polygon_mesh_processing::orient_to_bound_a_volume()`
  */
 template <class TriangleMesh, class NamedParameters>
-bool does_bound_a_volume(const TriangleMesh& tm, const NamedParameters& np)
+bool does_bound_a_volume(const TriangleMesh& tm,
+                         const NamedParameters& np)
 {
-  typedef boost::graph_traits<TriangleMesh> GT;
-  typedef typename GT::vertex_descriptor vertex_descriptor;
-  typedef typename GetVertexPointMap<TriangleMesh,
-                                     NamedParameters>::const_type Vpm;
-  typedef typename GetFaceIndexMap<TriangleMesh,
-                                   NamedParameters>::const_type Fid_map;
-  typedef typename Kernel_traits<
-    typename boost::property_traits<Vpm>::value_type >::Kernel Kernel;
+  typedef boost::graph_traits<TriangleMesh>                                     Graph_traits;
+  typedef typename Graph_traits::vertex_descriptor                              vertex_descriptor;
+  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::const_type Vpm;
+  typedef typename boost::property_traits<Vpm>::value_type                      Point;
+  typedef typename Kernel_traits<Point>::Kernel                                 Kernel;
 
   if (!is_closed(tm)) return false;
   if (!is_triangle_mesh(tm)) return false;
 
   Vpm vpm = parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_point),
-                                get_const_property_map(boost::vertex_point, tm));
+                                         get_const_property_map(boost::vertex_point, tm));
 
-  Fid_map fid_map = parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                                        get_const_property_map(boost::face_index, tm));
+  typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::const_type Fid_map;
+  Fid_map fid_map = get_initialized_face_index_map(tm, np);
 
   std::vector<std::size_t> face_cc(num_faces(tm), std::size_t(-1));
 
@@ -203,11 +203,11 @@ bool does_bound_a_volume(const TriangleMesh& tm, const NamedParameters& np)
   boost::dynamic_bitset<> cc_handled(nb_cc, 0);
 
   // extract a vertex with max z coordinate for each connected component
-  std::vector<vertex_descriptor> xtrm_vertices(nb_cc, GT::null_vertex());
+  std::vector<vertex_descriptor> xtrm_vertices(nb_cc, Graph_traits::null_vertex());
   for(vertex_descriptor vd : vertices(tm))
   {
     std::size_t cc_id = face_cc[get(fid_map, face(halfedge(vd, tm), tm))];
-    if (xtrm_vertices[cc_id]==GT::null_vertex())
+    if (xtrm_vertices[cc_id] == Graph_traits::null_vertex())
       xtrm_vertices[cc_id]=vd;
     else
       if (get(vpm, vd).z()>get(vpm,xtrm_vertices[cc_id]).z())
@@ -514,21 +514,14 @@ corefine_and_compute_boolean_operations(
   typedef std::tuple<Ecm_out_0, Ecm_out_1, Ecm_out_2, Ecm_out_3>
                                                             Edge_mark_map_tuple;
 
-// Face index point maps
-  typedef typename GetFaceIndexMap<TriangleMesh,
-                                   NamedParameters1>::type Fid_map;
-  typedef typename GetFaceIndexMap<TriangleMesh,
-                                   NamedParameters2>::type Fid_map2;
-  CGAL_USE_TYPE(Fid_map2);
-  CGAL_assertion_code(
-    static const bool same_fidmap = (boost::is_same<Fid_map,Fid_map2>::value);)
-  CGAL_static_assertion(same_fidmap);
+  // Face index point maps
+  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters1>::type FaceIndexMap1;
+  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters2>::type FaceIndexMap2;
 
-  Fid_map fid_map1 = parameters::choose_parameter(parameters::get_parameter(np1, internal_np::face_index),
-                                        get_property_map(boost::face_index, tm1));
-  Fid_map fid_map2 = parameters::choose_parameter(parameters::get_parameter(np2, internal_np::face_index),
-                                         get_property_map(boost::face_index, tm2));
-// User visitor
+  FaceIndexMap1 fid_map1 = get_initialized_face_index_map(tm1, np1);
+  FaceIndexMap2 fid_map2 = get_initialized_face_index_map(tm2, np2);
+
+  // User visitor
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::graph_visitor_t,
     NamedParameters1,
@@ -541,7 +534,8 @@ corefine_and_compute_boolean_operations(
   typedef Corefinement::Face_graph_output_builder<TriangleMesh,
                                                   Vpm,
                                                   Vpm_out_tuple,
-                                                  Fid_map,
+                                                  FaceIndexMap1,
+                                                  FaceIndexMap2,
                                                   Default,
                                                   Ecm_in,
                                                   Edge_mark_map_tuple,
@@ -551,8 +545,7 @@ corefine_and_compute_boolean_operations(
     TriangleMesh, Vpm, Ob, Ecm_in, User_visitor> Algo_visitor;
   Ecm_in ecm_in(tm1,tm2,ecm1,ecm2);
   Edge_mark_map_tuple ecms_out(ecm_out_0, ecm_out_1, ecm_out_2, ecm_out_3);
-  Ob ob(tm1, tm2, vpm1, vpm2, fid_map1, fid_map2, ecm_in,
-        vpm_out_tuple, ecms_out, uv, output);
+  Ob ob(tm1, tm2, vpm1, vpm2, fid_map1, fid_map2, ecm_in, vpm_out_tuple, ecms_out, uv, output);
 
   // special case used for clipping open meshes
   if (  parameters::choose_parameter( parameters::get_parameter(np1, internal_np::use_bool_op_to_clip_surface),
@@ -933,8 +926,7 @@ namespace experimental {
             const NamedParameters& np)
 {
 // Vertex point maps
-  typedef typename GetVertexPointMap<TriangleMesh,
-                                     NamedParameters>::type Vpm;
+  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::type Vpm;
 
   Vpm vpm = parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_point),
                                 get_property_map(boost::vertex_point, tm));
@@ -1014,10 +1006,9 @@ namespace experimental {
   Vpm vpm = parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_point),
                                 get_property_map(boost::vertex_point, tm));
 // Face index map
-  typedef typename GetFaceIndexMap<TriangleMesh,
-                                   NamedParameters>::type Fid_map;
-  Fid_map fid_map = parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                                        get_property_map(boost::face_index, tm));
+  typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::type Fid_map;
+  Fid_map fid_map = get_initialized_face_index_map(tm, np);
+
 // Edge is-constrained maps
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::edge_is_constrained_t,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/detect_features.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/detect_features.h
index ffbb806305a..55b007d16b3 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/detect_features.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/detect_features.h
@@ -138,11 +138,6 @@ detect_surface_patches(PolygonMesh& p,
                        EdgeIsFeatureMap eif,
                        const NamedParameters& np)
 {
-  //extract types from NPs
-  typename GetFaceIndexMap<PolygonMesh, NamedParameters>::const_type
-          fimap = parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                                      get_const_property_map(boost::face_index, p));
-
   int offset = static_cast<int>(
           parameters::choose_parameter(parameters::get_parameter(np, internal_np::first_index),
           1));
@@ -150,11 +145,12 @@ detect_surface_patches(PolygonMesh& p,
   internal::PatchIdMapWrapper<PatchIdMap,
                               typename boost::property_traits<PatchIdMap>::value_type>
           wrapmap(patch_id_map, offset);
+
   return connected_components(p, wrapmap,
                               parameters::edge_is_constrained_map(eif)
-                             .face_index_map(fimap));
-
+                                         .face_index_map(CGAL::get_initialized_face_index_map(p, np)));
 }
+
 template <typename PolygonMesh, typename EdgeIsFeatureMap, typename PatchIdMap>
 typename boost::graph_traits<PolygonMesh>::faces_size_type
 detect_surface_patches(PolygonMesh& p,
@@ -373,8 +369,6 @@ namespace internal
  * computing a
  * surface patch id for each face.
  *
- * A property map for `CGAL::face_index_t` must be either available
- * as an internal property map to `pmesh` or provided as one of the Named Parameters.
  *
  * \tparam PolygonMesh a model of `FaceGraph`
  * \tparam FT a number type. It is
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
index 2f93d176784..602ae2a2fde 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
@@ -60,7 +60,8 @@ namespace params=PMP::parameters;
 template <class TriangleMesh,
           class VertexPointMap,
           class VpmOutTuple,
-          class FaceIdMap,
+          class FaceIdMap1,
+          class FaceIdMap2,
           class Kernel_=Default,
           class EdgeMarkMapBind_  = Default,
           class EdgeMarkMapTuple_ = Default,
@@ -110,8 +111,10 @@ class Face_graph_output_builder
 //Data members
   TriangleMesh &tm1, &tm2;
   // property maps of input meshes
-  const VertexPointMap &vpm1, &vpm2;
-  const FaceIdMap &fids1, &fids2;
+  const VertexPointMap vpm1;
+  const VertexPointMap vpm2;
+  FaceIdMap1 fids1;
+  FaceIdMap2 fids2;
   EdgeMarkMapBind& marks_on_input_edges;
   // property maps of output meshes
   const VpmOutTuple& output_vpms;
@@ -215,7 +218,7 @@ class Face_graph_output_builder
   // detect if a polyline is incident to two patches that won't be imported
   // for the current operation (polylines skipt are always incident to a
   // coplanar patch)
-  template <class TM, class FIM>
+  template <class TM, class FIM1, class FIM2>
   static
   void fill_polylines_to_skip(
     Intersection_polylines& polylines,
@@ -223,8 +226,8 @@ class Face_graph_output_builder
     const std::vector<std::size_t>& tm2_patch_ids,
     const boost::dynamic_bitset<>& patches_of_tm1_used,
     const boost::dynamic_bitset<>& patches_of_tm2_used,
-    const FIM& fids1,
-    const FIM& fids2,
+    const FIM1 fids1,
+    const FIM2 fids2,
     const TM& tm1,
     const TM& tm2)
   {
@@ -341,18 +344,17 @@ class Face_graph_output_builder
 
 public:
 
-  Face_graph_output_builder(      TriangleMesh& tm1,
-                                  TriangleMesh& tm2,
-                            const VertexPointMap &vpm1,
-                            const VertexPointMap &vpm2,
-                            const FaceIdMap& fids1,
-                            const FaceIdMap& fids2,
-                                  EdgeMarkMapBind& marks_on_input_edges,
+  Face_graph_output_builder(TriangleMesh& tm1,
+                            TriangleMesh& tm2,
+                            const VertexPointMap vpm1,
+                            const VertexPointMap vpm2,
+                            FaceIdMap1 fids1,
+                            FaceIdMap2 fids2,
+                            EdgeMarkMapBind& marks_on_input_edges,
                             const VpmOutTuple& output_vpms,
-                                  EdgeMarkMapTuple& out_edge_mark_maps,
-                                  UserVisitor& user_visitor,
-                            const std::array<
-                              boost::optional<TriangleMesh*>, 4 >& requested_output)
+                            EdgeMarkMapTuple& out_edge_mark_maps,
+                            UserVisitor& user_visitor,
+                            const std::array<boost::optional<TriangleMesh*>, 4 >& requested_output)
     : tm1(tm1), tm2(tm2)
     , vpm1(vpm1), vpm2(vpm2)
     , fids1(fids1), fids2(fids2)
@@ -460,9 +462,12 @@ public:
     Intersection_edge_map& intersection_edges1 = mesh_to_intersection_edges[&tm1];
     Intersection_edge_map& intersection_edges2 = mesh_to_intersection_edges[&tm2];
 
-    // this will initialize face indices if the face index map is writable.
-    helpers::init_face_indices(tm1, fids1);
-    helpers::init_face_indices(tm2, fids2);
+    // The property map must be either writable or well-initialized
+    if(!BGL::internal::is_index_map_valid(fids1, num_faces(tm1), faces(tm1)))
+      BGL::internal::initialize_face_index_map(fids1, tm1);
+
+    if(!BGL::internal::is_index_map_valid(fids2, num_faces(tm2), faces(tm2)))
+      BGL::internal::initialize_face_index_map(fids2, tm2);
 
     // bitset to identify coplanar faces
     boost::dynamic_bitset<> tm1_coplanar_faces(num_faces(tm1), 0);
@@ -620,9 +625,8 @@ public:
     std::size_t nb_patches_tm1 =
       PMP::connected_components(tm1,
                                 bind_property_maps(fids1,make_property_map(&tm1_patch_ids[0])),
-                                params::edge_is_constrained_map(
-                                    is_marked_1)
-                                .face_index_map(fids1));
+                                params::edge_is_constrained_map(is_marked_1)
+                                       .face_index_map(fids1));
 
     std::vector <std::size_t> tm1_patch_sizes(nb_patches_tm1, 0);
     for(std::size_t i : tm1_patch_ids)
@@ -634,9 +638,8 @@ public:
     std::size_t nb_patches_tm2 =
       PMP::connected_components(tm2,
                                 bind_property_maps(fids2,make_property_map(&tm2_patch_ids[0])),
-                                params::edge_is_constrained_map(
-                                    is_marked_2)
-                                .face_index_map(fids2));
+                                params::edge_is_constrained_map(is_marked_2)
+                                       .face_index_map(fids2));
 
     std::vector <std::size_t> tm2_patch_sizes(nb_patches_tm2, 0);
     for(Node_id i : tm2_patch_ids)
@@ -1245,9 +1248,8 @@ public:
       polyline_lengths.push_back(polyline_info.second+1);
     }
 
-    typedef Patch_container<TriangleMesh,
-                            FaceIdMap,
-                            Intersection_edge_map> Patches;
+    typedef Patch_container<TriangleMesh, FaceIdMap1, Intersection_edge_map> Patches1;
+    typedef Patch_container<TriangleMesh, FaceIdMap2, Intersection_edge_map> Patches2;
 
     boost::unordered_set<vertex_descriptor> border_nm_vertices; // only used if used_to_clip_a_surface == true
     if (used_to_clip_a_surface)
@@ -1279,8 +1281,8 @@ public:
     }
 
     //store the patch description in a container to avoid recomputing it several times
-    Patches patches_of_tm1( tm1, tm1_patch_ids, fids1, intersection_edges1, nb_patches_tm1),
-            patches_of_tm2( tm2, tm2_patch_ids, fids2, intersection_edges2, nb_patches_tm2);
+    Patches1 patches_of_tm1(tm1, tm1_patch_ids, fids1, intersection_edges1, nb_patches_tm1);
+    Patches2 patches_of_tm2(tm2, tm2_patch_ids, fids2, intersection_edges2, nb_patches_tm2);
 
     // for each boolean operation, define two bitsets of patches contributing
     // to the result
@@ -1460,11 +1462,12 @@ public:
 
         // operation in tm1 with removal (and optionally inside-out) delayed
         // First backup the border edges of patches to be used
-        Patches tmp_patches_of_tm1(tm1,
-          patches_of_tm1.patch_ids,
-          patches_of_tm1.fids,
-          patches_of_tm1.is_intersection_edge,
-          patches_of_tm1.patches.size());
+        Patches1 tmp_patches_of_tm1(tm1,
+                                    patches_of_tm1.patch_ids,
+                                    patches_of_tm1.fids,
+                                    patches_of_tm1.is_intersection_edge,
+                                    patches_of_tm1.patches.size());
+
         boost::dynamic_bitset<> patches_of_tm1_removed =
             ~patches_of_tm1_used[inplace_operation_tm1];
         for (std::size_t i = patches_of_tm1_removed.find_first();
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Output_builder_for_autorefinement.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Output_builder_for_autorefinement.h
index 3656f46aea3..031d23a1c36 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Output_builder_for_autorefinement.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Output_builder_for_autorefinement.h
@@ -214,9 +214,6 @@ public:
     const boost::dynamic_bitset<>& is_node_of_degree_one,
     const Mesh_to_map_node&)
   {
-    // this will initialize face indices if the face index map is writable.
-    helpers::init_face_indices(tm, fids);
-
     // first build an unordered_map mapping a vertex to its node id + a set
     // of all intersection edges
     typedef boost::unordered_set<edge_descriptor> Intersection_edge_map;
@@ -239,8 +236,9 @@ public:
       intersection_edges.insert(edge(p.second.h2, tm));
     }
 
-    // this will initialize face indices if the face index map is writable.
-    helpers::init_face_indices(tm, fids);
+    // The property map must be either writable or well-initialized
+    if(!BGL::internal::is_index_map_valid(fids, num_faces(tm), faces(tm)))
+      BGL::internal::initialize_face_index_map(fids, tm);
 
     // bitset to identify coplanar faces
     boost::dynamic_bitset<> tm_coplanar_faces(num_faces(tm), 0);
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/face_graph_utils.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/face_graph_utils.h
index 3e9b5499feb..c188231238c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/face_graph_utils.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/face_graph_utils.h
@@ -424,7 +424,7 @@ template <class PolygonMesh, class FaceIndexMap, class IsIntersectionEdge>
 void extract_patch_simplices(
   std::size_t patch_id,
   PolygonMesh& pm,
-  const FaceIndexMap& fids,
+  const FaceIndexMap fids,
   const std::vector<std::size_t>& patch_ids,
   std::vector<typename boost::graph_traits<PolygonMesh>::face_descriptor>& patch_faces,
   std::set<typename boost::graph_traits<PolygonMesh>::vertex_descriptor>& interior_vertices,
@@ -480,13 +480,13 @@ struct Patch_container{
 // external data members
   PolygonMesh& pm;
   const std::vector<std::size_t>& patch_ids;
-  const FaceIndexMap& fids;
+  const FaceIndexMap fids;
   const IsIntersectionEdge& is_intersection_edge;
 // constructor
   Patch_container(
     PolygonMesh& pm,
     const std::vector<std::size_t>& patch_ids,
-    const FaceIndexMap& fids,
+    const FaceIndexMap fids,
     const IsIntersectionEdge& is_intersection_edge,
     std::size_t nb_patches
   ) : patches(nb_patches)
@@ -1010,14 +1010,15 @@ template < class TriangleMesh,
            class EdgeMarkMap2,
            class EdgeMarkMapOut,
            class IntersectionPolylines,
-           class PatchContainer,
+           class PatchContainer1,
+           class PatchContainer2,
            class UserVisitor>
 void fill_new_triangle_mesh(
   TriangleMesh& output,
   const boost::dynamic_bitset<>& patches_of_tm1_to_import,
   const boost::dynamic_bitset<>& patches_of_tm2_to_import,
-  PatchContainer& patches_of_tm1,
-  PatchContainer& patches_of_tm2,
+  PatchContainer1& patches_of_tm1,
+  PatchContainer2& patches_of_tm2,
   bool reverse_orientation_of_patches_from_tm1,
   bool reverse_orientation_of_patches_from_tm2,
   const IntersectionPolylines& polylines,
@@ -1256,7 +1257,8 @@ void disconnect_patches(
 }
 
 template <class TriangleMesh,
-          class PatchContainer,
+          class PatchContainer1,
+          class PatchContainer2,
           class IntersectionPolylines,
           class EdgeMap,
           class VertexPointMap,
@@ -1269,8 +1271,8 @@ void compute_inplace_operation_delay_removal_and_insideout(
   TriangleMesh& tm2,
   const boost::dynamic_bitset<>& patches_of_tm1_to_keep,
   const boost::dynamic_bitset<>& patches_of_tm2_to_import,
-  PatchContainer& patches_of_tm1,
-  PatchContainer& patches_of_tm2,
+  PatchContainer1& patches_of_tm1,
+  PatchContainer2& patches_of_tm2,
   bool reverse_patch_orientation_tm2,
   const IntersectionPolylines& polylines,
   const VertexPointMap& vpm1,
@@ -1416,7 +1418,8 @@ remove_patches(TriangleMesh& tm,
 }
 
 template <class TriangleMesh,
-          class PatchContainer,
+          class PatchContainer1,
+          class PatchContainer2,
           class VertexPointMap,
           class EdgeMarkMapIn1,
           class EdgeMarkMapIn2,
@@ -1427,8 +1430,8 @@ void compute_inplace_operation(
   const TriangleMesh& /*tm2*/,
   const boost::dynamic_bitset<>& patches_of_tm1_to_keep,
   const boost::dynamic_bitset<>& patches_of_tm2_to_import,
-  PatchContainer& patches_of_tm1,
-  PatchContainer& patches_of_tm2,
+  PatchContainer1& patches_of_tm1,
+  PatchContainer2& patches_of_tm2,
   bool reverse_patch_orientation_tm1,
   bool reverse_patch_orientation_tm2,
   const VertexPointMap& vpm1,
@@ -1485,14 +1488,15 @@ void compute_inplace_operation(
 
 template <class TriangleMesh,
           class IntersectionPolylines,
-          class PatchContainer,
+          class PatchContainer1,
+          class PatchContainer2,
           class EdgeMap>
 void compute_border_edge_map(
   const TriangleMesh& tm1,
   const TriangleMesh& tm2,
   const IntersectionPolylines& polylines,
-  PatchContainer& patches_of_tm1,
-  PatchContainer& patches_of_tm2,
+  PatchContainer1& patches_of_tm1,
+  PatchContainer2& patches_of_tm2,
   EdgeMap& tm2_edge_to_tm1_edge)
 {
   typedef boost::graph_traits<TriangleMesh> GT;
@@ -1520,7 +1524,8 @@ void compute_border_edge_map(
 
 
 template <class TriangleMesh,
-          class PatchContainer,
+          class PatchContainer1,
+          class PatchContainer2,
           class IntersectionPolylines,
           class VertexPointMap,
           class EdgeMarkMapIn1,
@@ -1532,8 +1537,8 @@ void compute_inplace_operation(
   const TriangleMesh& tm2,
   const boost::dynamic_bitset<>& patches_of_tm1_to_keep,
   const boost::dynamic_bitset<>& patches_of_tm2_to_import,
-  PatchContainer& patches_of_tm1,
-  PatchContainer& patches_of_tm2,
+  PatchContainer1& patches_of_tm1,
+  PatchContainer2& patches_of_tm2,
   bool reverse_patch_orientation_tm1,
   bool reverse_patch_orientation_tm2,
   const VertexPointMap& vpm1,
@@ -1631,9 +1636,22 @@ void remove_unused_polylines(
     halfedge_descriptor h = halfedge(v, tm), start=GT::null_halfedge();
 
     do{
+
+      halfedge_descriptor tmp_start = h;
       while ( !is_border(h, tm) || is_border(opposite(h, tm), tm) )
+      {
         h = opposite(next(h, tm), tm);
+        if (tmp_start==h) break;
+      }
+      if( !is_border(h, tm) )
+      {
+        // nothing to do: the vertex has already been updated and is now in the middle of a patch kept.
+        // This function can be called after the stitching of the patches kept, the vertex halfedge
+        // can have been updated and no border halfedge might be found
+        break;
+      }
       halfedge_descriptor in = h;
+
       if (start==GT::null_halfedge())
         start=in;
       else
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
index e5ddeadf013..f5cdff44e23 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Isotropic_remeshing/remesh_impl.h
@@ -1513,7 +1513,9 @@ private:
       // tag patch border halfedges
       for(halfedge_descriptor h : halfedges(mesh_))
       {
-        if (status(h)==PATCH && status(opposite(h, mesh_))!=PATCH)
+        if (status(h) == PATCH
+          && (   status(opposite(h, mesh_)) != PATCH
+              || get_patch_id(face(h, mesh_)) != get_patch_id(face(opposite(h, mesh_), mesh_))))
         {
           set_status(h, PATCH_BORDER);
           has_border_ = true;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/helper.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/helper.h
new file mode 100644
index 00000000000..e43e37bebdf
--- /dev/null
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/helper.h
@@ -0,0 +1,136 @@
+// Copyright (c) 2018, 2019 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Mael Rouxel-Labbé
+
+#ifndef CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAPPING_HELPER_H
+#define CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAPPING_HELPER_H
+
+#include <CGAL/license/Polygon_mesh_processing/repair.h>
+
+#include <CGAL/boost/graph/iterator.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/Polygon_mesh_processing/internal/named_function_params.h>
+#include <CGAL/Polygon_mesh_processing/internal/named_params_helper.h>
+
+namespace CGAL {
+namespace Polygon_mesh_processing {
+namespace internal {
+
+template <typename VertexRange,
+          typename HalfedgeOutputIterator,
+          typename PolygonMesh>
+void vertices_as_halfedges(const VertexRange& vertex_range,
+                           const PolygonMesh& pmesh,
+                           HalfedgeOutputIterator out)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor                vertex_descriptor;
+
+  for(vertex_descriptor v : vertex_range)
+    *out++ = halfedge(v, pmesh);
+}
+
+// Assigns at each vertex the 'tolerance' value as tolerance, but bounded by a percentage of the length of its shortest incident edge
+template <typename HalfedgeRange,
+          typename ToleranceMap,
+          typename PolygonMesh,
+          typename NamedParameters>
+void assign_tolerance_with_local_edge_length_bound(const HalfedgeRange& halfedge_range,
+                                                   ToleranceMap& tolerance_map,
+                                                   const typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT tolerance,
+                                                   PolygonMesh& mesh,
+                                                   const NamedParameters& np)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor                vertex_descriptor;
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor              halfedge_descriptor;
+
+  typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type              VPM;
+  typedef typename GetGeomTraits<PolygonMesh, NamedParameters>::type                  GT;
+  typedef typename GT::FT                                                             FT;
+
+  using parameters::get_parameter;
+  using parameters::choose_parameter;
+
+  GT gt = choose_parameter(get_parameter(np, internal_np::geom_traits), GT());
+  VPM vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
+                             get_property_map(vertex_point, mesh));
+
+  for(halfedge_descriptor hd : halfedge_range)
+  {
+    const vertex_descriptor vd = target(hd, mesh);
+    CGAL::Halfedge_around_target_iterator<PolygonMesh> hit, hend;
+    boost::tie(hit, hend) = CGAL::halfedges_around_target(vd, mesh);
+    CGAL_assertion(hit != hend);
+
+    FT sq_length = gt.compute_squared_distance_3_object()(get(vpm, source(*hit, mesh)),
+                                                          get(vpm, target(*hit, mesh)));
+    FT min_sq_dist = sq_length;
+    ++hit;
+
+    for(; hit!=hend; ++hit)
+    {
+      sq_length = gt.compute_squared_distance_3_object()(get(vpm, source(*hit, mesh)),
+                                                         get(vpm, target(*hit, mesh)));
+
+      if(sq_length < min_sq_dist)
+        min_sq_dist = sq_length;
+    }
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "tolerance at vd: " << vd << " [" << get(vpm, vd) << "]: min of "
+              << 0.9 * CGAL::approximate_sqrt(min_sq_dist) << " AND " << tolerance << std::endl;
+#endif
+    put(tolerance_map, vd, CGAL::min<FT>(0.9 * CGAL::approximate_sqrt(min_sq_dist), tolerance));
+  }
+}
+
+template <typename HalfedgeRange,
+          typename ToleranceMap,
+          typename PolygonMesh>
+void assign_tolerance_with_local_edge_length_bound(const HalfedgeRange& halfedge_range,
+                                                   ToleranceMap& tolerance_map,
+                                                   const typename GetGeomTraits<PolygonMesh>::type::FT tolerance,
+                                                   PolygonMesh& mesh)
+{
+  return assign_tolerance_with_local_edge_length_bound(halfedge_range, tolerance_map, tolerance, mesh, CGAL::parameters::all_default());
+}
+
+template <typename GeomTraits>
+bool is_collinear_with_tolerance(const typename GeomTraits::Point_3& p, // va == vb
+                                 const typename GeomTraits::Point_3& pa,
+                                 const typename GeomTraits::Point_3& pb,
+                                 const GeomTraits& gt)
+{
+  typedef typename GeomTraits::FT                                                     FT;
+  typedef typename GeomTraits::Vector_3                                               Vector_3;
+
+  const Vector_3 va = gt.construct_vector_3_object()(p, pa);
+  const Vector_3 vb = gt.construct_vector_3_object()(p, pb);
+  const FT sp = gt.compute_scalar_product_3_object()(va, vb);
+
+  // To avoid junctions like:
+  //  ----va vb-----  from being locked since it could be needed in ------------- later
+  //       | |                                                      ----va  vb---
+  //                                                                    |   |
+  if(sp < FT(0))
+    return false;
+
+  const FT sq_va_l = gt.compute_squared_distance_3_object()(p, pa);
+  const FT sq_vb_l = gt.compute_squared_distance_3_object()(p, pb);
+  const FT sq_cos = 0.99999228397046306; // CGAL::square(std::cos(1°));
+
+  return (CGAL::square(sp) >= sq_va_l * sq_vb_l * sq_cos);
+}
+
+} // namespace internal
+} // namespace Polygon_mesh_processing
+} // namespace CGAL
+
+#endif // CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAPPING_HELPER_H
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
index 02a0422d5d6..0a1892d486d 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap.h
@@ -8,38 +8,49 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Sebastien Loriot
-//                 Mael Rouxel-Labbé
+// Author(s)     : Mael Rouxel-Labbé
+//                 Sebastien Loriot
 
-#ifndef CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAP_H
-#define CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAP_H
+#ifndef CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_H
+#define CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_H
 
 #include <CGAL/license/Polygon_mesh_processing/repair.h>
 
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+ #ifndef CGAL_PMP_SNAP_DEBUG
+  #define CGAL_PMP_SNAP_DEBUG
+ #endif
+#endif
+
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/helper.h>
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/snap_vertices.h>
+
 #include <CGAL/Polygon_mesh_processing/internal/named_function_params.h>
 #include <CGAL/Polygon_mesh_processing/internal/named_params_helper.h>
 #include <CGAL/Polygon_mesh_processing/border.h>
+#include <CGAL/Polygon_mesh_processing/compute_normal.h>
 
 #include <CGAL/AABB_tree.h>
 #include <CGAL/AABB_traits.h>
 #include <CGAL/AABB_halfedge_graph_segment_primitive.h>
 #include <CGAL/assertions.h>
-#include <CGAL/Bbox_3.h>
 #include <CGAL/boost/graph/helpers.h>
 #include <CGAL/boost/graph/iterator.h>
-#include <CGAL/box_intersection_d.h>
+#include <CGAL/boost/graph/selection.h>
 #include <CGAL/circulator.h>
 #include <CGAL/Dynamic_property_map.h>
 #include <CGAL/Kernel/global_functions.h>
 #include <CGAL/number_utils.h>
+#include <CGAL/Real_timer.h>
+#include <CGAL/utility.h>
 
-#include <boost/multi_index_container.hpp>
-#include <boost/multi_index/ordered_index.hpp>
-#include <boost/multi_index/member.hpp>
+#ifdef CGAL_EIGEN3_ENABLED
+#include <Eigen/Dense>
+#endif
 
 #ifdef CGAL_LINKED_WITH_TBB
-# include <tbb/concurrent_vector.h>
-# include <tbb/parallel_for.h>
+#include <tbb/concurrent_vector.h>
+#include <tbb/parallel_for.h>
 #endif
 
 #include <functional>
@@ -48,912 +59,635 @@
 #include <limits>
 #include <map>
 #include <type_traits>
-#include <utility>
 #include <unordered_set>
+#include <utility>
 #include <vector>
 
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+#include <fstream>
+#endif
+
 namespace CGAL {
 namespace Polygon_mesh_processing {
 namespace internal {
 
-// Assigns at each vertex the 'tolerance' value as tolerance, but bounded by a percentage of the length of its shortest incident edge
-template <typename HalfedgeRange,
-          typename ToleranceMap,
-          typename PolygonMesh,
-          typename SourceNamedParameters>
-void assign_tolerance_with_local_edge_length_bound(const HalfedgeRange& hrange,
-                                                   ToleranceMap& tol_pmap,
-                                                   const typename GetGeomTraits<PolygonMesh, SourceNamedParameters>::type::FT tolerance,
-                                                   PolygonMesh& mesh,
-                                                   const SourceNamedParameters& snp)
+template <typename HalfedgeRange, typename TriangleMesh,
+          typename ToleranceMap, typename NamedParameters>
+void simplify_range(HalfedgeRange& halfedge_range,
+                    TriangleMesh& tm,
+                    ToleranceMap tolerance_map,
+                    const NamedParameters& np)
 {
+  // @todo the simplification below is too naive and will fail to treat complicated zigzaging
+  // with long edges.
+  // A real simplification would create a fuzzy area around the border (say the dilation
+  // of the border polyline by a sphere of radius that continuously interpolates the tolerance
+  // at each vertex). The border is then simplified to use the least amount of edges possible
+  // in that fuzzy zone. Need to look into cartography papers, probably.
+
+  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor           vertex_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor         halfedge_descriptor;
+
+  typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type             GT;
+  typedef typename GT::FT                                                         FT;
+
+  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::type         VPM;
+  typedef typename boost::property_traits<VPM>::reference                         Point_ref;
+
   using parameters::get_parameter;
   using parameters::choose_parameter;
 
-  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor                vertex_descriptor;
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor              halfedge_descriptor;
+  const GT gt = choose_parameter(get_parameter(np, internal_np::geom_traits), GT());
+  VPM vpm = choose_parameter(get_parameter(np, internal_np::vertex_point), get_property_map(vertex_point, tm));
 
-  typedef typename GetVertexPointMap<PolygonMesh, SourceNamedParameters>::type        SVPM;
-  typedef typename GetGeomTraits<PolygonMesh, SourceNamedParameters>::type            GT;
-  typedef typename GT::FT                                                             FT;
+  typedef CGAL::dynamic_halfedge_property_t<bool>                                 Halfedge_bool_tag;
+  typedef typename boost::property_map<TriangleMesh, Halfedge_bool_tag>::type     Range_halfedges;
 
-  GT gt = choose_parameter(get_parameter(snp, internal_np::geom_traits), GT());
-  SVPM svpm = choose_parameter(get_parameter(snp, internal_np::vertex_point),
-                               get_property_map(vertex_point, mesh));
+  Range_halfedges range_halfedges = get(Halfedge_bool_tag(), tm);
+  for(halfedge_descriptor h : halfedge_range)
+    put(range_halfedges, h, true);
 
-  for(halfedge_descriptor hd : hrange)
+  CGAL_postcondition_code(const std::size_t initial_n = halfedge_range.size();)
+
+  std::set<halfedge_descriptor> edges_to_test(halfedge_range.begin(), halfedge_range.end());
+
+  int collapsed_n = 0;
+  while(!edges_to_test.empty())
   {
-    const vertex_descriptor vd = target(hd, mesh);
-    CGAL::Halfedge_around_target_iterator<PolygonMesh> hit, hend;
-    boost::tie(hit, hend) = CGAL::halfedges_around_target(vd, mesh);
-    CGAL_assertion(hit != hend);
+    const halfedge_descriptor h = *(edges_to_test.begin());
+    edges_to_test.erase(edges_to_test.begin());
 
-    FT sq_length = gt.compute_squared_distance_3_object()(get(svpm, source(*hit, mesh)),
-                                                          get(svpm, target(*hit, mesh)));
-    FT min_sq_dist = sq_length;
-    ++hit;
+    const vertex_descriptor vs = source(h, tm);
+    const vertex_descriptor vt = target(h, tm);
+    const Point_ref ps = get(vpm, vs);
+    const Point_ref pt = get(vpm, vt);
 
-    for(; hit!=hend; ++hit)
+    // @fixme what if the source vertex is not to be snapped? Tolerance cannot be obtained...
+    // and where should the post-collapse vertex be since we can't move the source vertex...
+    // --> simply don't collapse?
+    const FT min_tol = (std::min)(get(tolerance_map, vs), get(tolerance_map, vt));
+    const FT max_tol = (std::max)(get(tolerance_map, vs), get(tolerance_map, vt));
+
+    if(gt.compare_squared_distance_3_object()(ps,pt,CGAL::square(max_tol))==SMALLER)
     {
-      sq_length = gt.compute_squared_distance_3_object()(get(svpm, source(*hit, mesh)),
-                                                         get(svpm, target(*hit, mesh)));
+      const halfedge_descriptor prev_h = prev(h, tm);
+      const halfedge_descriptor next_h = next(h, tm);
 
-      if(sq_length < min_sq_dist)
-        min_sq_dist = sq_length;
+      // check that the border has at least 4 edges not to create degenerate volumes
+      if(border_size(h, tm) >= 4)
+      {
+        const FT h_sq_length = gt.compute_squared_distance_3_object()(ps, pt);
+        vertex_descriptor v = Euler::collapse_edge(edge(h, tm), tm);
+
+        put(vpm, v, gt.construct_midpoint_3_object()(ps, pt));
+        put(tolerance_map, v, min_tol + 0.5 * CGAL::approximate_sqrt(h_sq_length));
+
+        if(get(range_halfedges, prev_h))
+          edges_to_test.insert(prev_h);
+        if(get(range_halfedges, next_h))
+          edges_to_test.insert(next_h);
+
+        ++collapsed_n;
+      }
     }
+  }
 
 #ifdef CGAL_PMP_SNAP_DEBUG
-    std::cout << "tolerance at vd: " /*<< vd */ << " [" << get(svpm, vd) << "]: min of "
-              << 0.9 * CGAL::approximate_sqrt(min_sq_dist) << " AND " << tolerance << std::endl;
-#endif
-    put(tol_pmap, vd, CGAL::min<FT>(0.9 * CGAL::approximate_sqrt(min_sq_dist), tolerance));
-  }
-}
-
-template <typename HalfedgeRange,
-          typename ToleranceMap,
-          typename PolygonMesh>
-void assign_tolerance_with_local_edge_length_bound(const HalfedgeRange& hrange,
-                                                   ToleranceMap& tol_pmap,
-                                                   const typename GetGeomTraits<PolygonMesh>::type::FT tolerance,
-                                                   PolygonMesh& mesh)
-{
-  return assign_tolerance_with_local_edge_length_bound(hrange, tol_pmap, tolerance, mesh, CGAL::parameters::all_default());
-}
-
-template <typename PolygonMesh, typename GeomTraits>
-struct Snapping_pair
-{
-  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor       vertex_descriptor;
-  typedef typename GeomTraits::FT                                            FT;
-
-  Snapping_pair(const vertex_descriptor vs_, const vertex_descriptor vt_, const FT sq_dist_)
-    : vs(vs_), vt(vt_), sq_dist(sq_dist_)
-  { }
-
-  vertex_descriptor vs;
-  vertex_descriptor vt;
-  FT sq_dist;
-};
-
-template <typename PolygonMesh, typename GeomTraits,
-          typename DistanceMultiIndexContainer,
-          typename SVPM, typename TVPM,
-          typename ToleranceMap,
-          typename Box>
-struct Vertex_proximity_report
-{
-  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor       vertex_descriptor;
-  typedef typename boost::graph_traits<PolygonMesh>::edge_descriptor         edge_descriptor;
-
-  typedef typename GeomTraits::FT                                            FT;
-  typedef typename boost::property_traits<SVPM>::value_type                  Point;
-
-  Vertex_proximity_report(DistanceMultiIndexContainer& snapping_pairs,
-                          const SVPM& svpm, const PolygonMesh& smesh,
-                          const TVPM& tvpm, const PolygonMesh& tmesh,
-                          const ToleranceMap& tol_pmap,
-                          const GeomTraits& gt)
-    :
-      m_snapping_pairs(snapping_pairs),
-      is_same_mesh((&smesh == &tmesh)),
-      svpm(svpm), tvpm(tvpm),
-      tol_pmap(tol_pmap),
-      gt(gt)
-  { }
-
-  void operator()(const Box& a, const Box& b)
-  {
-    vertex_descriptor va = a.info();
-    vertex_descriptor vb = b.info();
-
-    if(is_same_mesh && va == vb)
-      return;
-
-    const Point sp = get(svpm, va);
-    const Point tp = get(tvpm, vb);
-    const FT tol = get(tol_pmap, va);
-
-    // Don't reject a '0' distance, it still needs to lock the points in place
-    const FT sq_dist = gt.compute_squared_distance_3_object()(sp, tp);
-    CGAL::Comparison_result res = CGAL::compare(sq_dist, tol * tol);
-
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-    std::cout << "distance between " /*<< va*/ << " [" << sp << "] and "
-                                     /*<< vb*/ << " [" << tp << "]: " << sq_dist
-                                     << " (bound: " << tol*tol << ") larger? " << (res == CGAL::LARGER)
-                                     << std::endl;
+  std::cout << "collapsed " << collapsed_n << " edges" << std::endl;
 #endif
 
-    if(res == CGAL::LARGER)
-      return;
+  std::vector<halfedge_descriptor> new_range;
+  new_range.reserve(halfedge_range.size());
 
-    m_snapping_pairs.insert(Snapping_pair<PolygonMesh, GeomTraits>(va, vb, sq_dist));
-  }
+  for(halfedge_descriptor h : halfedges(tm))
+    if(get(range_halfedges, h))
+      new_range.push_back(h);
 
-private:
-  DistanceMultiIndexContainer& m_snapping_pairs;
+  halfedge_range = HalfedgeRange(new_range.begin(), new_range.end());
 
-  const bool is_same_mesh;
-  const SVPM& svpm;
-  const TVPM& tvpm;
-  const ToleranceMap& tol_pmap;
-  const GeomTraits& gt;
-};
-
-} // namespace internal
-
-namespace experimental {
-
-// This is the function if you know what you're doing with the ranges
-//
-// \ingroup PMP_repairing_grp
-//
-// Attempts to snap the vertices in `source_hrange` onto the vertices in `target_hrange`.
-// A vertex of the source range is only snapped to a vertex of the target mesh
-// if its distance to the target mesh vertex is smaller than a user-chosen bound.
-// If a source vertex can be snapped onto multiple vertices of the target
-// range, the closest target vertex is used.
-// If multiple vertices within the source range could be snapped onto the same target vertex,
-// the source vertex closest to the target vertex will be snapped. Other source vertices will try to snap
-// to free target vertices until they find a valid target, or until there is no more target
-// to snap to (within the tolerance).
-//
-// @warning This function does not give any guarantee on the conformity between the source and target meshes after the snapping.
-// @warning This function does not merge vertices together.
-//
-// @tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
-// @tparam SourceHalfedgeRange a model of `Range` with value type `boost::graph_traits<PolygonMesh>::%halfedge_descriptor`
-// @tparam TargetHalfedgeRange a model of `Range` with value type `boost::graph_traits<PolygonMesh>::%halfedge_descriptor`
-// @tparam ToleranceMap a model of `ReadablePropertyMap` with key type `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
-//                      and value type `GetGeomTraits<PolygonMesh, SourceNamedParameters>::type::FT`
-// @tparam SourceNamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
-// @tparam TargetNamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
-//
-// @param source_hrange a range of vertices of the source mesh whose positions can be changed.
-//                      the vertices must be border vertices of `smesh`.
-// @param smesh the source mesh whose border vertices might be moved
-// @param target_hrange a range of vertices of the target mesh which are potential new positions
-//                      for the vertices in the source range
-// @param tmesh the target mesh to which the vertices in `target_hrange` belong
-// @param tol_pmap a tolerance map associating to each vertex of the source range a tolerance value:
-//               potential projection targets are sought in a sphere centered at the vertex and
-//               whose radius is the tolerance value.
-// @param snp optional \ref pmp_namedparameters "Named Parameters" related to the source mesh,
-//            amongst those described below:
-//
-// \cgalNamedParamsBegin
-//    \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of the source mesh.
-//                                      The type of this map is model of `ReadWritePropertyMap`.
-//                                      If this parameter is omitted, an internal property map for
-//                                      `CGAL::vertex_point_t` must be available in `PolygonMesh`
-//    \cgalParamEnd
-//    \cgalParamBegin{geom_traits} a geometric traits class instance.
-//       The traits class must provide the nested types `Point_3` and `Vector_3`,
-//       and the nested functors :
-//         - `Construct_bbox_3` to construct a bounding box of a point,
-//         - `Compute_squared_distance_3` to compute the distance between two points,
-//
-//       and, for each functor `Foo`, a function `Foo foo_object()`
-//   \cgalParamEnd
-// \cgalNamedParamsEnd
-//
-// @param tnp optional \ref pmp_namedparameters "Named Parameters" related to the target mesh,
-//            amongst those described below:
-//
-// \cgalNamedParamsBegin
-//    \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of the target mesh.
-//                                      The type of this map is model of `ReadablePropertyMap`.
-//                                      If this parameter is omitted, an internal property map for
-//                                      `CGAL::vertex_point_t` must be available in `PolygonMesh`
-//    \cgalParamEnd
-// \cgalNamedParamsEnd
-//
-// @return the number of snapped vertices
-//
-// @sa `merge_duplicated_vertices_in_boundary_cycles()`
-//
-template <typename PolygonMesh,
-          typename SourceHalfedgeRange, typename TargetHalfedgeRange,
-          typename ToleranceMap,
-          typename SourceNamedParameters, typename TargetNamedParameters>
-std::size_t snap_vertex_range_onto_vertex_range(const SourceHalfedgeRange& source_hrange,
-                                                PolygonMesh& smesh,
-                                                const TargetHalfedgeRange& target_hrange,
-                                                const PolygonMesh& tmesh,
-                                                const ToleranceMap& tol_pmap,
-                                                const SourceNamedParameters& snp,
-                                                const TargetNamedParameters& tnp)
-{
-  using parameters::get_parameter;
-  using parameters::choose_parameter;
-
-  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor      vertex_descriptor;
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
-
-  typedef CGAL::Box_intersection_d::Box_with_info_d<double, 3, vertex_descriptor>     Box;
-
-  typedef typename GetVertexPointMap<PolygonMesh, SourceNamedParameters>::type        SVPM;
-  typedef typename GetVertexPointMap<PolygonMesh, TargetNamedParameters>::const_type  TVPM;
-  typedef typename boost::property_traits<TVPM>::value_type                           Point;
-
-  typedef typename GetGeomTraits<PolygonMesh, SourceNamedParameters>::type            GT;
-  typedef typename GT::FT                                                             FT;
-
-  if(is_empty_range(source_hrange.begin(), source_hrange.end()) ||
-     is_empty_range(target_hrange.begin(), target_hrange.end()))
-    return 0;
-
-  CGAL_static_assertion((std::is_same<Point, typename GT::Point_3>::value));
-
-  GT gt = choose_parameter(get_parameter(snp, internal_np::geom_traits), GT());
-
-  SVPM svpm = choose_parameter(get_parameter(snp, internal_np::vertex_point),
-                               get_property_map(vertex_point, smesh));
-  TVPM tvpm = choose_parameter(get_parameter(tnp, internal_np::vertex_point),
-                               get_const_property_map(vertex_point, tmesh));
-
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "Snapping vertices to vertices. Range sizes: "
-            << std::distance(source_hrange.begin(), source_hrange.end()) << " and "
-            << std::distance(target_hrange.begin(), target_hrange.end()) << std::endl;
-
-  if(&smesh == &tmesh)
-    std::cout << "same mesh!" << std::endl;
-#endif
-
-  // Try to snap vertices
-  std::vector<Box> boxes;
-  std::unordered_set<vertex_descriptor> unique_vertices;
-  for(halfedge_descriptor hd : source_hrange)
-  {
-    const vertex_descriptor vd = target(hd, smesh);
-    if(!unique_vertices.insert(vd).second)
-      continue; // if 'vd' appears multiple times on the border, move it only once
-
-    // only making the box a little larger, but the final tolerance is not changed
-    const double eps = 1.01 * CGAL::to_double(get(tol_pmap, vd));
-
-    const Bbox_3 pb = gt.construct_bbox_3_object()(get(svpm, vd));
-    const Bbox_3 b(pb.xmin() - eps, pb.ymin() - eps, pb.zmin() - eps,
-                   pb.xmax() + eps, pb.ymax() + eps, pb.zmax() + eps);
-    boxes.push_back(Box(b, vd));
-  }
-
-  std::vector<Box> target_boxes;
-  for(halfedge_descriptor hd : target_hrange)
-  {
-    const vertex_descriptor vd = target(hd, tmesh);
-    const Point& p = get(tvpm, vd);
-    target_boxes.push_back(Box(gt.construct_bbox_3_object()(p), vd));
-  }
-
-  // Use a multi index to sort easily by sources, targets, AND distance.
-  // Then, look up the distances in increasing order, and snap whenever the source and the target
-  // have both not been snapped yet.
-  typedef internal::Snapping_pair<PolygonMesh, GT>                                    Snapping_pair;
-  typedef boost::multi_index::multi_index_container<
-    Snapping_pair,
-    boost::multi_index::indexed_by<
-      boost::multi_index::ordered_non_unique<
-        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, vertex_descriptor, vs)>,
-      boost::multi_index::ordered_non_unique<
-        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, vertex_descriptor, vt)>,
-      boost::multi_index::ordered_non_unique<
-        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, FT, sq_dist)>
-    >
-  >                                                                                   Snapping_pair_container;
-
-  typedef internal::Vertex_proximity_report<PolygonMesh, GT, Snapping_pair_container,
-                                            SVPM, TVPM, ToleranceMap, Box>            Reporter;
-
-  Snapping_pair_container snapping_pairs;
-  Reporter vpr(snapping_pairs, svpm, smesh, tvpm, tmesh, tol_pmap, gt);
-
-  // Shenanigans to pass a reference as callback (which is copied by value by 'box_intersection_d')
-  std::function<void(const Box&, const Box&)> callback(std::ref(vpr));
-
-  CGAL::box_intersection_d(boxes.begin(), boxes.end(),
-                           target_boxes.begin(), target_boxes.end(),
-                           callback);
-
-#ifdef CGAL_PMP_SNAP_DEBUG
-    std::cout << snapping_pairs.size() << " snappable pair(s)!" << std::endl;
-#endif
-
-  if(snapping_pairs.empty())
-    return 0;
-
-  // Sorted views of the container
-  typedef typename Snapping_pair_container::template nth_index<0>::type   Container_by_source;
-  typedef typename Snapping_pair_container::template nth_index<1>::type   Container_by_target;
-  typedef typename Snapping_pair_container::template nth_index<2>::type   Container_by_distance;
-
-  Container_by_source& container_by_source = snapping_pairs.template get<0>();
-  Container_by_target& container_by_target = snapping_pairs.template get<1>();
-  Container_by_distance& container_by_dist = snapping_pairs.template get<2>();
-
-  std::size_t counter = 0;
-
-  CGAL_assertion_code(FT prev = -1;)
-  while(!container_by_dist.empty())
-  {
-    const Snapping_pair& sp = *(container_by_dist.begin());
-    const vertex_descriptor vs = sp.vs;
-    const vertex_descriptor vt = sp.vt;
-    CGAL_assertion(sp.sq_dist >= prev);
-    CGAL_assertion_code(prev = sp.sq_dist;)
-
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-    std::cout << "Snapping " /*<< vs*/ << " (" << get(svpm, vs) << ") "
-              << " to " /*<< vt*/ << " (" << get(tvpm, vt) << ") at dist: " << sp.sq_dist << std::endl;
-#endif
-
-    // Collect all the source vertices projecting onto that target vertex
-   ++counter;
-    put(svpm, vs, get(tvpm, vt));
-
-    // 'vs' and 'vt' cannot be used anymore, remove them from the container
-    container_by_source.erase(vs);
-    container_by_target.erase(vt);
-  }
-
-  return counter;
+  CGAL_postcondition(halfedge_range.size() == initial_n - collapsed_n);
 }
 
-template <typename PolygonMesh, typename SourceHalfedgeRange, typename TargetHalfedgeRange,
-          typename SourceNamedParameters, typename TargetNamedParameters>
-std::size_t snap_vertex_range_onto_vertex_range(const SourceHalfedgeRange& source_hrange,
-                                                PolygonMesh& smesh,
-                                                const TargetHalfedgeRange& target_hrange,
-                                                const PolygonMesh& tmesh,
-                                                const SourceNamedParameters& snp,
-                                                const TargetNamedParameters& tnp)
-{
-  typedef typename GetGeomTraits<PolygonMesh, SourceNamedParameters>::type            GT;
-  typedef typename GT::FT                                                             FT;
-  typedef CGAL::dynamic_vertex_property_t<FT>                                         Vertex_property_tag;
-  typedef typename boost::property_map<PolygonMesh, Vertex_property_tag>::type        Tolerance_map;
-
-  Tolerance_map tol_pmap = get(Vertex_property_tag(), smesh);
-  const FT tol_mx(std::numeric_limits<double>::max());
-  internal::assign_tolerance_with_local_edge_length_bound(source_hrange, tol_pmap, tol_mx, smesh, snp);
-
-  return snap_vertex_range_onto_vertex_range(source_hrange, smesh, target_hrange, tmesh, tol_pmap, snp, tnp);
-}
-
-template <typename PolygonMesh, typename SourceHalfedgeRange, typename TargetHalfedgeRange, typename ToleranceMap>
-std::size_t snap_vertex_range_onto_vertex_range(const SourceHalfedgeRange& source_hrange,
-                                                PolygonMesh& smesh,
-                                                const TargetHalfedgeRange& target_hrange,
-                                                const PolygonMesh& tmesh,
-                                                const ToleranceMap& tol_pmap)
-{
-  return snap_vertex_range_onto_vertex_range(source_hrange, smesh, target_hrange, tmesh, tol_pmap,
-                                             CGAL::parameters::all_default(),
-                                             CGAL::parameters::all_default());
-}
-
-template <typename PolygonMesh, typename SourceHalfedgeRange, typename TargetHalfedgeRange>
-std::size_t snap_vertex_range_onto_vertex_range(const SourceHalfedgeRange& source_hrange,
-                                                PolygonMesh& smesh,
-                                                const TargetHalfedgeRange& target_hrange,
-                                                const PolygonMesh& tmesh)
-{
-  return snap_vertex_range_onto_vertex_range(source_hrange, smesh, target_hrange, tmesh,
-                                             CGAL::parameters::all_default(),
-                                             CGAL::parameters::all_default());
-}
-
-template <typename PolygonMesh>
-std::size_t snap_vertex_range_onto_vertex_range(PolygonMesh& smesh, const PolygonMesh& tmesh)
-{
-  return snap_vertex_range_onto_vertex_range(halfedges(smesh), smesh, halfedges(tmesh), tmesh);
-}
-
-template <typename PolygonMesh, typename HalfedgeRange, typename ToleranceMap>
-std::size_t snap_border_vertices_onto_vertex_range(PolygonMesh& smesh,
-                                                   const HalfedgeRange& target_hrange,
-                                                   const PolygonMesh& tmesh,
-                                                   const ToleranceMap& tol_pmap)
-{
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
-
-  std::vector<halfedge_descriptor> border_vertices;
-  border_halfedges(smesh, std::back_inserter(border_vertices));
-
-  return snap_vertex_range_onto_vertex_range(border_vertices, smesh, target_hrange, tmesh, tol_pmap);
-}
-
-template <typename PolygonMesh, typename HalfedgeRange>
-std::size_t snap_border_vertices_onto_vertex_range(PolygonMesh& smesh,
-                                                   const HalfedgeRange& target_hrange,
-                                                   const PolygonMesh& tmesh)
-{
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
-
-  std::vector<halfedge_descriptor> border_vertices;
-  border_halfedges(smesh, std::back_inserter(border_vertices));
-
-  return snap_vertex_range_onto_vertex_range(border_vertices, smesh, target_hrange, tmesh);
-}
-
-template <typename PolygonMesh, typename ToleranceMap>
-std::size_t snap_border_vertices_onto_border_vertices(PolygonMesh& smesh,
-                                                      const PolygonMesh& tmesh,
-                                                      const ToleranceMap& tol_pmap)
-{
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
-
-  std::vector<halfedge_descriptor> sborder_vertices;
-  border_halfedges(smesh, std::back_inserter(sborder_vertices));
-
-  std::vector<halfedge_descriptor> tborder_vertices;
-  border_halfedges(tmesh, std::back_inserter(tborder_vertices));
-
-  return snap_vertex_range_onto_vertex_range(sborder_vertices, smesh, tborder_vertices, tmesh, tol_pmap);
-}
-
-// \ingroup PMP_repairing_grp
-//
-// Attempts to snap the border vertices of the source mesh onto the vertices of the target mesh.
-//
-// A vertex of the source range is only snapped to a vertex of the target mesh
-// if its distance to the target mesh vertex is smaller than a user-chosen bound.
-// If any source vertex can be snapped onto multiple vertices of the target
-// range, the closest one is chosen.
-// If multiple vertices within the source range could be snapped onto the same target vertex,
-// the source vertex closest to the target vertex will be snapped. Other source vertices will try to snap
-// to free target vertices until they find a valid target, or until there is no more target
-// to snap to (within the tolerance).
-//
-// @tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
-// @tparam ToleranceMap a model of `ReadablePropertyMap` with key type `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
-//                      and value type the number type associated with the traits of the mesh.
-//
-// @param smesh the source mesh whose border vertices might be moved
-// @param tmesh the target mesh whose vertices are potential projection targets
-// @param tol_pmap a tolerance map associating to each vertex of the source range a tolerance value:
-//               potential projection targets are sought in a sphere centered at the vertex and
-//               whose radius is the tolerance value.
-//
-// @pre `smesh` and `tmesh` are different meshes
-//
-// \return the number of snapped vertices
-//
-template <typename PolygonMesh, typename ToleranceMap>
-std::size_t snap_border_vertices_onto_vertex_range(PolygonMesh& smesh,
-                                                   const PolygonMesh& tmesh,
-                                                   const ToleranceMap& tol_pmap)
-{
-  return snap_border_vertices_onto_vertex_range(smesh, halfedges(tmesh), tmesh, tol_pmap);
-}
-
-template <typename PolygonMesh>
-std::size_t snap_border_vertices_onto_vertex_range(PolygonMesh& smesh, const PolygonMesh& tmesh)
-{
-  return snap_border_vertices_onto_vertex_range(smesh, halfedges(tmesh), tmesh);
-}
-
-} // namespace experimental
-
-////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-namespace internal {
-
 // Adapted from <CGAL/internal/AABB_tree/AABB_traversal_traits.h>
-template <typename AABBTraits>
+template <typename TriangleMesh,
+          typename VPMS, typename VPMT, typename FacePatchMap,
+          typename AABBTraits>
 class Projection_traits
 {
-  typedef typename AABBTraits::FT                               FT;
-  typedef typename AABBTraits::Point_3                          Point;
-  typedef typename AABBTraits::Primitive                        Primitive;
-  typedef typename AABBTraits::Bounding_box                     Bounding_box;
-  typedef typename AABBTraits::Primitive::Id                    Primitive_id;
-  typedef typename AABBTraits::Point_and_primitive_id           Point_and_primitive_id;
-  typedef typename AABBTraits::Object_and_primitive_id          Object_and_primitive_id;
+  typedef typename AABBTraits::FT                                          FT;
+  typedef typename AABBTraits::Point_3                                     Point;
+  typedef typename AABBTraits::Primitive                                   Primitive;
+  typedef typename AABBTraits::Bounding_box                                Bounding_box;
+  typedef typename AABBTraits::Primitive::Id                               Primitive_id;
+  typedef typename AABBTraits::Point_and_primitive_id                      Point_and_primitive_id;
+  typedef typename AABBTraits::Object_and_primitive_id                     Object_and_primitive_id;
 
-  typedef CGAL::AABB_node<AABBTraits>                           Node;
+  typedef CGAL::AABB_node<AABBTraits>                                      Node;
+
+  typedef typename AABBTraits::Geom_traits                                 Geom_traits;
+  typedef typename Geom_traits::Vector_3                                   Vector;
+  typedef typename Geom_traits::Plane_3                                    Plane;
+
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor  halfedge_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::edge_descriptor      edge_descriptor;
+
+#ifdef CGAL_PMP_SNAP_USE_ANISOTROPIC_DISTANCE
+  void build_metric()
+  {
+    Vector hv(get(m_vpm_S, source(m_h, m_tm_S)), get(m_vpm_S, target(m_h, m_tm_S)));
+    Vector n = CGAL::Polygon_mesh_processing::compute_face_normal(face(opposite(m_h, m_tm_S), m_tm_S), m_tm_S,
+                                                                  CGAL::parameters::geom_traits(m_gt)
+                                                                                   .vertex_point_map(m_vpm_S));
+    Vector pn = m_gt.construct_cross_product_vector_3_object()(hv, n);
+    Plane pl(get(m_vpm_S, target(m_h, m_tm_S)), pn);
+
+    Vector b1 = pl.base1();
+    Vector b2 = pl.base2();
+
+    internal::normalize(b1, m_gt);
+    internal::normalize(b2, m_gt);
+    internal::normalize(pn, m_gt);
+
+    Eigen::Matrix3d eigen_m;
+    eigen_m(0,0) = b1.x(); eigen_m(0,1) = b2.x(); eigen_m(0,2) = pn.x();
+    eigen_m(1,0) = b1.y(); eigen_m(1,1) = b2.y(); eigen_m(1,2) = pn.y();
+    eigen_m(2,0) = b1.z(); eigen_m(2,1) = b2.z(); eigen_m(2,2) = pn.z();
+
+    Eigen::Matrix3d eigen_diag = Eigen::Matrix3d::Zero();
+    eigen_diag(0,0) = 1;
+    eigen_diag(1,1) = 1;
+    eigen_diag(2,2) = 100; // we scale by 1/sqrt(lambda_0) in the direction of n
+
+    Eigen::Matrix3d eigen_mtransp = eigen_m.transpose();
+    m_metric = eigen_m * eigen_diag * eigen_mtransp;
+  }
+#endif
+
+  FT squared_anisotropic_distance(const Point& p, const Point& q) const
+  {
+#ifdef CGAL_PMP_SNAP_USE_ANISOTROPIC_DISTANCE
+    Vector pq(p, q);
+    Eigen::Vector3d ev;
+    ev(0) = pq.x();
+    ev(1) = pq.y();
+    ev(2) = pq.z();
+
+    return ev.transpose() * m_metric * ev;
+#else
+    return CGAL::squared_distance(p, q);
+#endif
+  }
+
+  // The idea behind this function is to give priority to projections that are parallel to the edge 'e0'
+  // whom the query is the target of. This is done by considering an (anisotropic) distance that
+  // increases the distance if we are not projecting along the vector orthogonal to both the edge 'e0'
+  // and to the normal of the face, and also by checking the scalar product between the edges.
+  // The latter is because the distance to the projection point does not entirely reflect
+  // the alignment of the edges.
+  //
+  // This is WIP and likely to evolve...
+  bool is_better_than_current_best(const FT sq_dist,
+                                   const FT scalar_product)
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "is_better_than_current_best()" << std::endl;
+    std::cout << "sq_dist: " << sq_dist << std::endl;
+    std::cout << "m_sq_adist: " << m_sq_adist << std::endl;
+    std::cout << "scalar products: " << scalar_product << " " << m_sp_with_closest_edge << std::endl;
+#endif
+
+    // Automatically accept much closer tentative targets; automatically reject much farther tentative targets
+    const FT lambda = 4; // comparing squared distances
+    if(lambda * sq_dist < m_sq_adist)
+      return true;
+    if(lambda * m_sq_adist < sq_dist)
+      return false;
+
+    return (scalar_product > m_sp_with_closest_edge);
+  }
 
 public:
-  explicit Projection_traits(const AABBTraits& traits,
-                             const FT sq_tolerance)
-    : m_traits(traits),
+  explicit Projection_traits(const halfedge_descriptor h,
+                             const std::size_t patch_id,
+                             const FT sq_tolerance,
+                             const TriangleMesh& tm_S,
+                             const VPMS vpm_S,
+                             const TriangleMesh& tm_T,
+                             const FacePatchMap face_patch_map_T,
+                             const VPMT vpm_T,
+                             const AABBTraits& aabb_traits)
+    :
+      m_h(h),
+      m_patch_id(patch_id),
+      m_sq_tol(sq_tolerance),
+      m_tm_S(tm_S), m_vpm_S(vpm_S),
+      m_tm_T(tm_T), m_face_patch_map_T(face_patch_map_T), m_vpm_T(vpm_T),
+      m_is_same_mesh((&tm_S == &tm_T)),
+      m_continue(true),
       m_closest_point_initialized(false),
-      m_sq_dist(sq_tolerance)
-  {}
+      m_traits(aabb_traits),
+      m_gt(Geom_traits()) // blame AABB's traits management
+  {
+    // not fully convinced that it is still useful after adding scalar product shenanigans
+// #define CGAL_PMP_SNAP_USE_ANISOTROPIC_DISTANCE
+#ifdef CGAL_PMP_SNAP_USE_ANISOTROPIC_DISTANCE
+    build_metric();
+#endif
 
-  bool go_further() const { return true; }
+    Vector hv(get(vpm_S, source(h, tm_S)), get(vpm_S, target(h, tm_S)));
+    m_direction = hv;
+    CGAL::Polygon_mesh_processing::internal::normalize(m_direction, m_gt);
+  }
+
+  bool go_further() const { return m_continue; }
 
   void intersection(const Point& query, const Primitive& primitive)
   {
-    // skip the primitive if one of its endpoints is the query
-    const typename Primitive::Datum& s = primitive.datum(m_traits.shared_data());
-    if(m_traits.equal_3_object()(s[0], query) || m_traits.equal_3_object()(s[1], query))
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "~~~~ intersection with primitive: " << primitive.id() << std::endl;
+    std::cout << get(m_vpm_T, source(primitive.id(), m_tm_T)) << std::endl;
+    std::cout << get(m_vpm_T, target(primitive.id(), m_tm_T)) << std::endl;
+#endif
+
+    halfedge_descriptor h = halfedge(primitive.id(), m_tm_T);
+    if(is_border(h, m_tm_T))
+      h = opposite(h, m_tm_T);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+      std::cout << "patches: " << get(m_face_patch_map_T, face(h, m_tm_T)) << " " << m_patch_id << std::endl;
+#endif
+
+    if(get(m_face_patch_map_T, face(h, m_tm_T)) != m_patch_id)
       return;
 
-    if(!m_closest_point_initialized)
+    const typename Primitive::Datum& s = primitive.datum(m_traits.shared_data());
+    if(m_traits.equal_3_object()(s[0], query) || m_traits.equal_3_object()(s[1], query))
     {
-      m_closest_point_initialized = true;
-      m_closest_primitive = primitive.id();
-      m_closest_point = primitive.reference_point(m_traits.shared_data());
-      m_sq_dist = m_traits.squared_distance_object()(query, m_closest_point);
+      // If we are NOT using the same mesh and the query is (geometrically) equal to one extremity
+      // of the target edge, we don't want to move the source point away from the target point
+      // (because we cannot move the target point).
+      if(!m_is_same_mesh)
+      {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+        std::cout << "This vertex is stuck because it is equal to a vertex on the target mesh" << std::endl;
+#endif
+        m_closest_point_initialized = false;
+        m_continue = false;
+      }
+
+      // skip the primitive if one of its endpoints is the query
+      return;
     }
 
-    Point new_closest_point = m_traits.closest_point_object()(query, primitive, m_closest_point);
-    if(!m_traits.equal_3_object()(new_closest_point, m_closest_point))
+    // We are searching for a point on the target border that is close to target(h).
+    // To try and avoid foldings, we penalize potential matches that are roughly in the direction of 'h'
+    // by using an anisotropic distance that is the Euclidean on the plane orthogonal to the direction,
+    // and much larger when traveling in the rough direction of 'h'.
+    //
+    // Note that we apply this to points that fall within the tolerance ball, so if there is
+    // only a single candidate that is in a direction we don't like, we still take it.
+    //
+    // @todo should the construct_projected_point_3 be anisotropic too?
+    const Point new_closest_point = m_gt.construct_projected_point_3_object()(
+      CGAL::internal::Primitive_helper<AABBTraits>::get_datum(primitive, m_traits), query);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "closest point to primitive: " << new_closest_point << std::endl;
+#endif
+
+    const FT sq_ad_to_tentative_closest_pt = squared_anisotropic_distance(query, new_closest_point);
+
+    Vector tentative_dir(get(m_vpm_T, source(primitive.id(), m_tm_T)),
+                         get(m_vpm_T, target(primitive.id(), m_tm_T)));
+    CGAL::Polygon_mesh_processing::internal::normalize(tentative_dir, m_gt);
+    const FT sp_with_tentative = CGAL::abs(tentative_dir * m_direction);
+
+    if(!m_closest_point_initialized ||
+       is_better_than_current_best(sq_ad_to_tentative_closest_pt, sp_with_tentative))
     {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+      std::cout << "is better!" << std::endl;
+#endif
+
+      m_closest_point_initialized = true;
+
       m_closest_primitive = primitive.id();
       m_closest_point = new_closest_point;
-      m_sq_dist = m_traits.squared_distance_object()(query, m_closest_point);
+      m_sq_adist = sq_ad_to_tentative_closest_pt;
+      m_sp_with_closest_edge = sp_with_tentative;
     }
   }
 
   bool do_intersect(const Point& query, const Node& node) const
   {
-    return m_traits.compare_distance_object()(query, node.bbox(), m_sq_dist) == CGAL::SMALLER;
+    // This should NOT be the anisotropic distance, as we want to test all targets within the tolerance
+    return m_traits.compare_distance_object()(query, node.bbox(), m_sq_tol) == CGAL::SMALLER;
   }
 
   const Point& closest_point() const { return m_closest_point; }
   typename Primitive::Id closest_primitive_id() const { return m_closest_primitive; }
   bool closest_point_initialized() const { return m_closest_point_initialized; }
+  FT scalar_product_with_best() const { return m_sp_with_closest_edge; }
 
 private:
-  const AABBTraits& m_traits;
+  halfedge_descriptor m_h;
+  const std::size_t m_patch_id;
+  const FT m_sq_tol;
+  Vector m_direction;
+#ifdef CGAL_PMP_SNAP_USE_ANISOTROPIC_DISTANCE
+  Eigen::Matrix3d m_metric;
+#endif
+
+  const TriangleMesh& m_tm_S;
+  VPMS m_vpm_S;
+  const TriangleMesh& m_tm_T;
+  FacePatchMap m_face_patch_map_T;
+  VPMT m_vpm_T;
+  const bool m_is_same_mesh;
+
+  bool m_continue;
   bool m_closest_point_initialized;
-  Point m_closest_point;
-  FT m_sq_dist;
-
   typename Primitive::Id m_closest_primitive;
+  Point m_closest_point;
+  FT m_sq_adist;
+  FT m_sp_with_closest_edge; // scalar product between m_h and the current best edge candidate
+
+  const AABBTraits& m_traits;
+  Geom_traits m_gt;
 };
 
-template <typename PolygonMesh, typename GeomTraits, typename VPM>
-struct Compare_points_along_edge
+template <typename ConcurrencyTag>
+struct Edges_to_split_map_inserter // Parallel
 {
-  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
-  typedef typename GeomTraits::Point_3                                      Point;
-
-  Compare_points_along_edge(halfedge_descriptor support,
-                            const GeomTraits& gt, const VPM& vpm, const PolygonMesh& pm)
-    : gt(gt), m_src(get(vpm, source(support, pm)))
-  { }
-
-  bool operator()(const Point& p1, const Point& p2) const {
-    return gt.less_distance_to_point_3_object()(m_src, p1, p2);
+#ifdef CGAL_LINKED_WITH_TBB
+  template <typename EdgeToSplitMap, typename HalfedgeDescriptor, typename Point>
+  void operator()(EdgeToSplitMap& edges_to_split,
+                  const HalfedgeDescriptor closest_h,
+                  const HalfedgeDescriptor h,
+                  const Point& closest_p)
+  {
+    typename EdgeToSplitMap::accessor acc;
+    edges_to_split.insert(acc, closest_h);
+    acc->second.emplace_back(h, closest_p);
   }
-
-  const GeomTraits& gt;
-  Point m_src;
+#endif
 };
 
-template <typename TriangleMesh, typename EdgeToSplitContainer, typename AABBTree, typename VPM, typename GT>
-void find_splittable_edge(const std::pair<typename boost::property_traits<VPM>::value_type,
-                                          typename GT::FT>& point_with_tolerance,
-                          EdgeToSplitContainer& edges_to_split,
+template <>
+struct Edges_to_split_map_inserter<CGAL::Sequential_tag>
+{
+  template <typename EdgeToSplitMap, typename HalfedgeDescriptor, typename Point>
+  void operator()(EdgeToSplitMap& edges_to_split,
+                  const HalfedgeDescriptor closest_h,
+                  const HalfedgeDescriptor h,
+                  const Point& closest_p)
+  {
+    edges_to_split[closest_h].emplace_back(h, closest_p);
+  }
+};
+
+// The UniqueVertex is a pair of a container of vertex_descriptor and FT, representing
+// vertices with the same geometric position and their associated snapping tolerance
+// (defined as the minimum of the tolerances of the vertices of the bunch)
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename VertexWithTolerance, typename TriangleMesh,
+          typename EdgeToSplitMap, typename AABBTree,
+          typename VertexPatchMap_S, typename FacePatchMap_T,
+          typename VPMS, typename VPMT, typename GT>
+void find_splittable_edge(const VertexWithTolerance& vertex_with_tolerance,
+                          EdgeToSplitMap& edges_to_split,
                           const AABBTree* aabb_tree_ptr,
-                          const TriangleMesh& /* pms */,
-                          const VPM& /* vpms */,
-                          const TriangleMesh& pmt,
-                          const VPM& vpmt,
+                          const TriangleMesh& tm_S,
+                          VertexPatchMap_S vertex_patch_map_S,
+                          VPMS vpm_S,
+                          const TriangleMesh& tm_T,
+                          FacePatchMap_T face_patch_map_T,
+                          VPMT vpm_T,
                           const GT& gt)
 {
-  CGAL_USE(vpmt);
-  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor   halfedge_descriptor;
-  typedef typename boost::graph_traits<TriangleMesh>::edge_descriptor       edge_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor           vertex_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor         halfedge_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::edge_descriptor             edge_descriptor;
 
-  typedef typename GT::FT                                                   FT;
-  typedef typename boost::property_traits<VPM>::value_type                  Point;
+  typedef typename GT::FT                                                         FT;
+  typedef typename boost::property_traits<VPMS>::value_type                       Point;
+  typedef typename boost::property_traits<VPMS>::reference                        Point_ref;
 
-  typedef typename AABBTree::AABB_traits                                    AABB_traits;
+  typedef typename AABBTree::AABB_traits                                          AABB_traits;
 
-  const Point& query = point_with_tolerance.first;
-  const FT sq_tolerance = CGAL::square(point_with_tolerance.second);
+  typedef internal::Projection_traits<TriangleMesh, VPMS, VPMT, FacePatchMap_T, AABB_traits> Projection_traits;
 
-  // use the current halfedge as hint
-  internal::Projection_traits<AABB_traits> traversal_traits(aabb_tree_ptr->traits(), sq_tolerance);
+  // by construction the whole range has the same position
+  const halfedge_descriptor h = vertex_with_tolerance.first;
+  const vertex_descriptor v = target(h, tm_S);
+  const Point_ref query = get(vpm_S, v);
+  const FT sq_tolerance = CGAL::square(vertex_with_tolerance.second);
+  const std::size_t patch_id = get(vertex_patch_map_S, v);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+  std::cout << "--------------------------- Query: " << v << " (" << query << ")" << std::endl;
+#endif
+
+  Projection_traits traversal_traits(h, patch_id, sq_tolerance, tm_S, vpm_S,
+                                     tm_T, face_patch_map_T, vpm_T, aabb_tree_ptr->traits());
   aabb_tree_ptr->traversal(query, traversal_traits);
 
   if(!traversal_traits.closest_point_initialized())
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+  std::cout << "Couldn't find any single projection point" << std::endl;
+#endif
     return;
+  }
 
   const Point& closest_p = traversal_traits.closest_point();
 
   // The filtering in the AABB tree checks the dist query <-> node bbox, which might be smaller than
   // the actual distance between the query <-> closest point
-  const FT sq_dist_to_closest = gt.compute_squared_distance_3_object()(query, closest_p);
-  bool is_close_enough = (sq_dist_to_closest <= sq_tolerance);
+  edge_descriptor closest_e = traversal_traits.closest_primitive_id();
+  bool is_close_enough =
+    gt.compare_squared_distance_3_object()(query,
+                                           gt.construct_segment_3_object()(get(vpm_T, source(closest_e, tm_T)),
+                                                                           get(vpm_T, target(closest_e, tm_T))),
+                                           sq_tolerance) != LARGER;
 
 #ifdef CGAL_PMP_SNAP_DEBUG_PP
   std::cout << "  Closest point: (" << closest_p << ")" << std::endl
-            << "  at distance " << gt.compute_squared_distance_3_object()(query, closest_p)
-            << " with a tolerance of " << point_with_tolerance.second << " at vertex (squared tol: " << sq_tolerance
-            << " && close enough? " << is_close_enough << ")" << std::endl;
+            << "  on edge: " << traversal_traits.closest_primitive_id()
+            << "  at sq distance " << gt.compute_squared_distance_3_object()(query, closest_p)
+            << " with squared tolerance: " << sq_tolerance
+            << " && close enough? " << is_close_enough << std::endl;
 #endif
 
   if(!is_close_enough)
     return;
 
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-  std::cout << "\t and is thus beneath tolerance" << std::endl;
-#endif
 
-  edge_descriptor closest = traversal_traits.closest_primitive_id();
-  CGAL_assertion(get(vpmt, source(closest, pmt)) != query &&
-                                                    get(vpmt, target(closest, pmt)) != query);
+  CGAL_assertion(get(vpm_T, source(closest_e, tm_T)) != query &&
+                 get(vpm_T, target(closest_e, tm_T)) != query);
 
-  halfedge_descriptor clos_hd = halfedge(closest, pmt);
-  CGAL_assertion(is_border(edge(clos_hd, pmt), pmt));
+  halfedge_descriptor closest_h = halfedge(closest_e, tm_T);
+  CGAL_assertion(is_border(edge(closest_h, tm_T), tm_T));
 
-  if(!is_border(clos_hd, pmt))
-    clos_hd = opposite(clos_hd, pmt);
+  if(!is_border(closest_h, tm_T))
+    closest_h = opposite(closest_h, tm_T);
 
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-  std::cout << "splitting position: " << query << std::endl;
-#endif
-
-  edges_to_split.push_back(std::make_pair(query, clos_hd));
+  // Using a map because we need to know if the same halfedge is split multiple times
+  Edges_to_split_map_inserter<ConcurrencyTag>()(edges_to_split, closest_h, vertex_with_tolerance.first, closest_p);
 }
 
 #ifdef CGAL_LINKED_WITH_TBB
 template <typename PointWithToleranceContainer,
-          typename TriangleMesh, typename EdgeToSplitContainer,
-          typename AABBTree, typename VPM, typename GT>
+          typename TriangleMesh, typename EdgeToSplitMap, typename AABBTree,
+          typename VertexPatchMap_S, typename FacePatchMap_T,
+          typename VPMS, typename VPMT, typename GT>
 struct Find_splittable_edge_for_parallel_for
 {
   Find_splittable_edge_for_parallel_for(const PointWithToleranceContainer& points_with_tolerance,
-                                        EdgeToSplitContainer& edges_to_split,
+                                        EdgeToSplitMap& edges_to_split,
                                         const AABBTree* aabb_tree_ptr,
-                                        const TriangleMesh& pms,
-                                        const VPM& vpms,
-                                        const TriangleMesh& pmt,
-                                        const VPM& vpmt,
+                                        const TriangleMesh& tm_S,
+                                        const VertexPatchMap_S vertex_patch_map_S,
+                                        const VPMS vpm_S,
+                                        const TriangleMesh& tm_T,
+                                        const FacePatchMap_T face_patch_map_T,
+                                        const VPMT vpm_T,
                                         const GT& gt)
     :
       m_points_with_tolerance(points_with_tolerance),
       m_edges_to_split(edges_to_split), m_aabb_tree_ptr(aabb_tree_ptr),
-      m_pms(pms), m_vpms(vpms), m_pmt(pmt), m_vpmt(vpmt), m_gt(gt)
+      m_tm_S(tm_S), m_vertex_patch_map_S(vertex_patch_map_S), m_vpm_S(vpm_S),
+      m_tm_T(tm_T), m_face_patch_map_T(face_patch_map_T), m_vpm_T(vpm_T),
+      m_gt(gt)
   { }
 
   void operator()(const tbb::blocked_range<size_t>& r) const
   {
     for(std::size_t i=r.begin(); i!=r.end(); ++i)
     {
-      find_splittable_edge(m_points_with_tolerance[i], m_edges_to_split,
-                           m_aabb_tree_ptr,
-                           m_pms, m_vpms, m_pmt, m_vpmt,
-                           m_gt);
+      find_splittable_edge<CGAL::Parallel_tag>(m_points_with_tolerance[i], m_edges_to_split, m_aabb_tree_ptr,
+                                               m_tm_S, m_vertex_patch_map_S, m_vpm_S,
+                                               m_tm_T, m_face_patch_map_T, m_vpm_T, m_gt);
     }
   }
 
 private:
   const PointWithToleranceContainer& m_points_with_tolerance;
-  EdgeToSplitContainer& m_edges_to_split;
+  EdgeToSplitMap& m_edges_to_split;
   const AABBTree* m_aabb_tree_ptr;
-  const TriangleMesh& m_pms;
-  const VPM m_vpms;
-  const TriangleMesh& m_pmt;
-  const VPM m_vpmt;
+  const TriangleMesh& m_tm_S;
+  const VertexPatchMap_S m_vertex_patch_map_S;
+  const VPMS m_vpm_S;
+  const TriangleMesh& m_tm_T;
+  const FacePatchMap_T m_face_patch_map_T;
+  const VPMT m_vpm_T;
   const GT& m_gt;
 };
 #endif
 
-} // namespace internal
-
-namespace experimental {
-
-// Try to merge vertices in 'hrange' (vd = target(hd, pm)) onto the edges in the 'erange',
-// non-conformingly
-template <typename HalfedgeRange, typename TriangleMesh,
-          typename ToleranceMap, typename NamedParameters>
-std::size_t snap_vertex_range_onto_vertex_range_non_conforming(const HalfedgeRange& source_hrange,
-                                                               TriangleMesh& pms,
-                                                               const HalfedgeRange& target_hrange,
-                                                               TriangleMesh& pmt,
-                                                               const ToleranceMap& tol_pmap,
-                                                               const NamedParameters& nps,
-                                                               const NamedParameters& npt)
+template <typename EdgesToSplitContainer,
+          typename TriangleMesh, typename GeomTraits,
+          typename VPMS, typename VPMT>
+std::size_t split_edges(EdgesToSplitContainer& edges_to_split,
+                        TriangleMesh& tm_S,
+                        VPMS vpm_S,
+                        TriangleMesh& tm_T,
+                        VPMT vpm_T,
+                        const GeomTraits& gt,
+                        const bool is_source_mesh_fixed) // when snapping is B --> A and the mesh B is fixed
 {
-  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor     vertex_descriptor;
-  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor   halfedge_descriptor;
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "split " << edges_to_split.size() << " edges" << std::endl;
+#endif
 
-  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::type   VPM;
-  typedef typename boost::property_traits<VPM>::value_type                  Point;
-  typedef typename boost::property_traits<VPM>::reference                   Point_ref;
+  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor           vertex_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor         halfedge_descriptor;
 
-  typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type       GT;
-  typedef typename GT::FT                                                   FT;
-  typedef typename GT::Vector_3                                             Vector;
+  typedef typename boost::property_traits<VPMS>::value_type                       Point;
+  typedef typename boost::property_traits<VPMT>::reference                        Point_ref;
+  typedef typename GeomTraits::Vector_3                                           Vector;
 
-  typedef internal::Compare_points_along_edge<TriangleMesh, GT, VPM>        Point_along_edge_comparer;
-
-  typedef CGAL::AABB_halfedge_graph_segment_primitive<TriangleMesh, VPM>    Primitive;
-  typedef CGAL::AABB_traits<GT, Primitive>                                  AABB_Traits;
-  typedef CGAL::AABB_tree<AABB_Traits>                                      AABB_tree;
-
-  using parameters::get_parameter;
-  using parameters::choose_parameter;
-
-  // Need to have a triangle mesh to ensure that the refinement point of a border edge 'e' has visibility
-  // of the third p oint of the face 'f' incident to 'e'
-  CGAL_precondition(is_triangle_mesh(pmt));
+  typedef std::pair<halfedge_descriptor, Point>                                   Vertex_with_new_position;
+  typedef std::vector<Vertex_with_new_position>                                   Vertices_with_new_position;
+  typedef std::pair<const halfedge_descriptor, Vertices_with_new_position>        Edge_and_splitters;
 
   std::size_t snapped_n = 0;
 
-  VPM vpms = choose_parameter(get_parameter(nps, internal_np::vertex_point), get_property_map(vertex_point, pms));
-  VPM vpmt = choose_parameter(get_parameter(npt, internal_np::vertex_point), get_property_map(vertex_point, pmt));
+  CGAL::Real_timer timer;
+  timer.start();
 
-  const GT gt = choose_parameter(get_parameter(nps, internal_np::geom_traits), GT());
-
-  // start by snapping vertices together to simplify things
-  snapped_n = snap_vertex_range_onto_vertex_range(source_hrange, pms, target_hrange, pmt, tol_pmap, nps, npt);
-
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "Snapping vertices to edges. Range sizes: "
-            << std::distance(source_hrange.begin(), source_hrange.end()) << " and "
-            << std::distance(target_hrange.begin(), target_hrange.end()) << std::endl;
-#endif
-
-  // Collect border points that can be projected onto a border edge
-  typedef std::map<Point, FT>                       Unique_vertices_with_tolerance;  // unordered map is empirically slower
-
-  // If the point appears multiple times on the source border, use it only once to snap target edges
-  // use the smallest tolerance from all source vertices
-
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "gather unique points in source range" << std::endl;
-#endif
-
-  Unique_vertices_with_tolerance unique_source_vertices;
-  for(halfedge_descriptor hd : source_hrange)
+  for(Edge_and_splitters& es : edges_to_split)
   {
-    // Skip the source vertex if its two incident halfedges are geometrically identical (it means that
-    // the two halfedges are already stitchable and we don't want this common vertex to be used
-    // to split a halfedge somewhere else)
-    if(get(vpms, source(hd, pms)) == get(vpms, target(next(hd, pms), pms)))
-      continue;
+    halfedge_descriptor h_to_split = es.first;
+    CGAL_assertion(is_border(h_to_split, tm_T));
 
-    const vertex_descriptor vd = target(hd, pms);
-    const Point_ref query = get(vpms, vd);
-    const FT tolerance = get(tol_pmap, vd);
+    Vertices_with_new_position& splitters = es.second;
 
-    std::pair<typename Unique_vertices_with_tolerance::iterator, bool> is_insert_successful =
-      unique_source_vertices.insert(std::make_pair(query, tolerance));
-
-    // Keep the lowest tolerance out of all the source vertices with the same position
-    is_insert_successful.first->second = (std::min)(is_insert_successful.first->second, tolerance);
-
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-    if(is_insert_successful.second)
-      std::cout << "Query: " << vd << " (" << query << ")" << std::endl;
-#endif
-  }
-
-  // Since we're inserting primitives one by one, we can't pass this shared data in the constructor of the tree
-  AABB_Traits aabb_traits;
-  aabb_traits.set_shared_data(pmt, vpmt);
-  AABB_tree aabb_tree(aabb_traits);
-
-  for(halfedge_descriptor hd : target_hrange)
-  {
-    CGAL_precondition(is_border(edge(hd, pmt), pmt));
-    aabb_tree.insert(Primitive(edge(hd, pmt), pmt, vpmt));
-  }
-
-  // Now, check which edges of the target range ought to be split by source vertices
-#ifdef CGAL_PMP_SNAP_DEBUG_PP
-  std::cout << "Collect edges to split w/ " << unique_source_vertices.size() << " unique vertices" << std::endl;
-#endif
-
-#ifdef CGAL_LINKED_WITH_TBB
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "Parallel find splittable edges!" << std::endl;
-#endif
-
-  typedef tbb::concurrent_vector<std::pair<Point, halfedge_descriptor> >        Concurrent_edge_to_split_container;
-
-  // Can't parallel for a map...
-  std::vector<std::pair<Point, FT> > unique_vertices_with_tolerance_vector(unique_source_vertices.begin(),
-                                                                           unique_source_vertices.end());
-
-  typedef internal::Find_splittable_edge_for_parallel_for<std::vector<std::pair<Point, FT> >,
-                                                          TriangleMesh,
-                                                          Concurrent_edge_to_split_container,
-                                                          AABB_tree, VPM, GT>    Functor;
-
-  Concurrent_edge_to_split_container edges_to_split;
-  Functor f(unique_vertices_with_tolerance_vector, edges_to_split, &aabb_tree, pms, vpms, pmt, vpmt, gt);
-  tbb::parallel_for(tbb::blocked_range<std::size_t>(0, unique_vertices_with_tolerance_vector.size()), f);
-#else // CGAL_LINKED_WITH_TBB
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "Sequential find splittable edges!" << std::endl;
-#endif
-  typedef std::pair<Point, FT>                      Point_with_tolerance;
-
-  std::vector<std::pair<Point, halfedge_descriptor> > edges_to_split;
-  for(const Point_with_tolerance& point_with_tolerance : unique_source_vertices)
-  {
-    internal::find_splittable_edge(point_with_tolerance, edges_to_split, &aabb_tree,
-                                   pms, vpms, pmt, vpmt, gt);
-  }
-#endif
-
-  // Sort points falling on the same edge and split the edge
-  std::map<halfedge_descriptor, std::vector<Point> > points_per_edge;
-  typedef std::pair<Point, halfedge_descriptor> Pair_type;
-  for(const Pair_type& p : edges_to_split)
-    points_per_edge[p.second].push_back(p.first);
-
-#ifdef CGAL_PMP_SNAP_DEBUG
-  std::cout << "split " << points_per_edge.size() << " edges" << std::endl;
-#endif
-
-  typedef std::pair<const halfedge_descriptor, std::vector<Point> > Map_type;
-  for(Map_type& mt : points_per_edge)
-  {
-    const halfedge_descriptor mt_hd = mt.first;
-    const halfedge_descriptor mt_hd_opp = opposite(mt_hd, pmt);
-    CGAL_assertion(!is_border(mt_hd_opp, pmt));
-
-    if(mt.second.size() > 1)
+    if(splitters.size() > 1)
     {
 #ifdef CGAL_PMP_SNAP_DEBUG_PP
-      std::cout << " MUST SORT ON BORDER!" << std::endl;
+      std::cout << " _______ Multiple splitting points on the same halfedge" << std::endl;
 #endif
-      /// \todo Sorting the projected positions is too simple (for example, this doesn't work
-      ///       for a zigzaging polyline). Rather, points should be sorted following
-      ///       the order along the matching border. Note that this requires identifying
-      ///       matching polylines because a sequence of zigzaging points might not all project
-      ///       onto the same halfedge.
-      Point_along_edge_comparer cmp(mt_hd, gt, vpmt, pmt);
-      std::sort(mt.second.begin(), mt.second.end(), cmp);
+
+      const Point_ref hsp = get(vpm_T, source(h_to_split, tm_T));
+      std::sort(splitters.begin(), splitters.end(),
+                [&](const Vertex_with_new_position& l, const Vertex_with_new_position& r) -> bool
+                {
+                  return gt.less_distance_to_point_3_object()(hsp, l.second, r.second);
+                });
     }
 
-    halfedge_descriptor hd_to_split = mt_hd;
-    for(const Point& p : mt.second)
+    // Inserting new points ordered from the source to the target of (the initial) 'h'
+    bool first_split = true;
+    Point previous_split_position = get(vpm_S, *(vertices(tm_S).begin())); // dummy value to avoid "used uninitialized" warning
+    for(const Vertex_with_new_position& vnp : splitters)
     {
+      const halfedge_descriptor splitter_h = vnp.first;
+      const vertex_descriptor splitter_v = target(splitter_h, tm_S);
+      const Point new_position = is_source_mesh_fixed ? get(vpm_S, splitter_v) : vnp.second;
+
+      bool do_split = true;
+
+      // Some splits can create degenerate faces, avoid that
+      if((new_position == get(vpm_T, target(h_to_split, tm_T))) ||
+         (new_position == get(vpm_T, source(h_to_split, tm_T))))
+        do_split = false;
+
+      if(!first_split && new_position == previous_split_position)
+        do_split = false;
+
 #ifdef CGAL_PMP_SNAP_DEBUG_PP
-      std::cout << "SPLIT " << edge(hd_to_split, pmt) << " |||| "
-                << " vs " << source(hd_to_split, pmt) << " (" << pmt.point(source(hd_to_split, pmt)) << ")"
-                << " --- vt " << target(hd_to_split, pmt) << " (" << pmt.point(target(hd_to_split, pmt)) << ")" << std::endl;
-      std::cout << "  with pos " << p << std::endl;
+      std::cout << " -.-.-. Splitting " << edge(h_to_split, tm_T) << " |||| "
+                << " Vs " << source(h_to_split, tm_T) << " (" << tm_T.point(source(h_to_split, tm_T)) << ")"
+                << " --- Vt " << target(h_to_split, tm_T) << " (" << tm_T.point(target(h_to_split, tm_T)) << ")" << std::endl;
+      std::cout << "With point: " << vnp.second << std::endl;
+      std::cout << "Actually split? " << do_split << std::endl;
 #endif
 
-      halfedge_descriptor res = CGAL::Euler::split_edge(hd_to_split, pmt);
-      put(vpmt, target(res, pmt), p);
+      // Split and update positions
+      vertex_descriptor new_v = boost::graph_traits<TriangleMesh>::null_vertex();
+      if(do_split)
+      {
+        CGAL::Euler::split_edge(h_to_split, tm_T);
+        new_v = source(h_to_split, tm_T);
+        put(vpm_T, new_v, new_position); // position of the new point on the target mesh
+      }
+
+      if(!is_source_mesh_fixed)
+        put(vpm_S, splitter_v, new_position);
+
+      first_split = false;
+      previous_split_position = new_position;
       ++snapped_n;
 
-      // @todo ensuring hd_to_split is safe... but is it necessary?
-      hd_to_split = next(res, pmt);
-      halfedge_descriptor hd_to_split_opp = opposite(hd_to_split, pmt);
+      // Everything below is choosing the diagonal to triangulate the quad formed by the edge split
+      // So, it's only relevant if splitting has been performed
+      if(!do_split)
+        continue;
 
-      // Look at the geometry to determine which diagonal is better to use to split this new quad face
-
-      /*           p
+      /*          new_p
        *         /   \
-       *    res /     \ hd_to_split
+       *    res /     \ h_to_split
        *       /       \
        *      /         \
        *    left       right
@@ -962,22 +696,24 @@ std::size_t snap_vertex_range_onto_vertex_range_non_conforming(const HalfedgeRan
        *     |       /
        *     |      /
        *     |     /
-       *       opp
+       *     |    /
+       *      opp
        */
 
-      const Point_ref left_pt = get(vpmt, source(res, pmt));
-      const Point_ref right_pt = get(vpmt, target(hd_to_split, pmt));
-      const Point_ref opp = get(vpmt, target(next(opposite(res, pmt), pmt), pmt));
+      const halfedge_descriptor res = prev(h_to_split, tm_T);
+      const Point_ref left_pt = get(vpm_T, source(res, tm_T));
+      const Point_ref right_pt = get(vpm_T, target(h_to_split, tm_T));
+      const Point_ref opp = get(vpm_T, target(next(opposite(res, tm_T), tm_T), tm_T));
 
       // Check if 'p' is "visible" from 'opp' (i.e. its projection on the plane 'Pl(left, opp, right)'
       // falls in the cone with apex 'opp' and sides given by 'left' and 'right')
       const Vector n = gt.construct_orthogonal_vector_3_object()(right_pt, left_pt, opp);
-
       const Point trans_left_pt = gt.construct_translated_point_3_object()(left_pt, n);
       const Point trans_right_pt = gt.construct_translated_point_3_object()(right_pt, n);
 
-      const bool left_of_left = (gt.orientation_3_object()(trans_left_pt, left_pt, opp, p) == CGAL::POSITIVE);
-      const bool right_of_right = (gt.orientation_3_object()(right_pt, trans_right_pt, opp, p) == CGAL::POSITIVE);
+      const Point_ref new_p = get(vpm_T, new_v);
+      const bool left_of_left = (gt.orientation_3_object()(trans_left_pt, left_pt, opp, new_p) == CGAL::POSITIVE);
+      const bool right_of_right = (gt.orientation_3_object()(right_pt, trans_right_pt, opp, new_p) == CGAL::POSITIVE);
 
       const bool is_visible = (!left_of_left && !right_of_right);
 
@@ -986,17 +722,20 @@ std::size_t snap_vertex_range_onto_vertex_range_non_conforming(const HalfedgeRan
       std::cout << "visible from " << opp << " ? " << is_visible << std::endl;
 #endif
 
+      // h_to_split is equal to 'next(res)' after splitting
+      const halfedge_descriptor h_to_split_opp = opposite(h_to_split, tm_T);
+
       if(is_visible)
       {
-        halfedge_descriptor new_hd = CGAL::Euler::split_face(hd_to_split_opp,
-                                                             prev(prev(mt_hd_opp, pmt), pmt), pmt);
-        hd_to_split = opposite(prev(new_hd, pmt), pmt);
+        halfedge_descriptor new_hd = CGAL::Euler::split_face(h_to_split_opp,
+                                                             prev(prev(h_to_split_opp, tm_T), tm_T), tm_T);
+        h_to_split = opposite(prev(new_hd, tm_T), tm_T);
       }
       else
       {
-        halfedge_descriptor new_hd = CGAL::Euler::split_face(opposite(res, pmt),
-                                                             prev(hd_to_split_opp, pmt), pmt);
-        hd_to_split = opposite(next(new_hd, pmt), pmt);
+        halfedge_descriptor new_hd = CGAL::Euler::split_face(opposite(res, tm_T),
+                                                             prev(h_to_split_opp, tm_T), tm_T);
+        h_to_split = opposite(next(new_hd, tm_T), tm_T);
       }
     }
   }
@@ -1004,27 +743,465 @@ std::size_t snap_vertex_range_onto_vertex_range_non_conforming(const HalfedgeRan
   return snapped_n;
 }
 
-template <typename HalfedgeRange, typename TriangleMesh, typename ToleranceMap>
-std::size_t snap_vertex_range_onto_vertex_range_non_conforming(const HalfedgeRange& source_hrange,
-                                                               TriangleMesh& pms,
-                                                               const HalfedgeRange& target_hrange,
-                                                               TriangleMesh& pmt,
-                                                               const ToleranceMap& tol_pmap)
+// Collect border points that can be projected onto a border edge
+//
+// If multiple vertices on the source border have the same geometric position, they are moved
+// all at once and we use the smallest tolerance from all source vertices with that position.
+// This is done to solve situation such as:
+//          ||
+//          ||
+//      ____||____
+//      ----------
+// (vertex-vertex snapping into non-conformal snapping) in one go.
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename HalfedgeRange, typename TriangleMesh,
+          typename LockedVertexMap, typename LockedHalfedgeMap, typename ToleranceMap,
+          typename VertexPatchMap_S, typename FacePatchMap_T,
+          typename SourceNamedParameters, typename TargetNamedParameters>
+std::size_t snap_non_conformal_one_way(const HalfedgeRange& halfedge_range_S,
+                                       TriangleMesh& tm_S,
+                                       ToleranceMap tolerance_map_S,
+                                       VertexPatchMap_S vertex_patch_map_S,
+                                       LockedVertexMap locked_vertices_S,
+                                       const HalfedgeRange& halfedge_range_T,
+                                       TriangleMesh& tm_T,
+                                       FacePatchMap_T face_patch_map_T,
+                                       LockedHalfedgeMap locked_halfedges_T,
+                                       const bool is_source_mesh_fixed,
+                                       const SourceNamedParameters& snp,
+                                       const TargetNamedParameters& tnp)
 {
-  return snap_vertex_range_onto_vertex_range_non_conforming(source_hrange, pms, target_hrange, pmt,
-                                                            tol_pmap, parameters::all_default(),
-                                                            parameters::all_default());
+  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor           vertex_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor         halfedge_descriptor;
+
+  typedef typename GetGeomTraits<TriangleMesh, TargetNamedParameters>::type       GT;
+  typedef typename GT::FT                                                         FT;
+
+  typedef typename GetVertexPointMap<TriangleMesh, SourceNamedParameters>::type   VPMS;
+  typedef typename GetVertexPointMap<TriangleMesh, TargetNamedParameters>::type   VPMT;
+
+  typedef typename boost::property_traits<VPMT>::value_type                       Point;
+
+  typedef CGAL::AABB_halfedge_graph_segment_primitive<TriangleMesh, VPMT>         Primitive;
+  typedef CGAL::AABB_traits<GT, Primitive>                                        AABB_Traits;
+  typedef CGAL::AABB_tree<AABB_Traits>                                            AABB_tree;
+
+  typedef std::pair<halfedge_descriptor, Point>                                   Vertex_with_new_position;
+  typedef std::vector<Vertex_with_new_position>                                   Vertices_with_new_position;
+
+  using parameters::get_parameter;
+  using parameters::choose_parameter;
+
+  VPMS vpm_S = choose_parameter(get_parameter(snp, internal_np::vertex_point), get_property_map(vertex_point, tm_S));
+  VPMT vpm_T = choose_parameter(get_parameter(tnp, internal_np::vertex_point), get_property_map(vertex_point, tm_T));
+  const GT gt = choose_parameter(get_parameter(snp, internal_np::geom_traits), GT());
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "Gather unique points in source range..." << std::endl;
+#endif
+
+  typedef std::pair<halfedge_descriptor, FT>                                      Vertex_with_tolerance;
+  typedef std::vector<Vertex_with_tolerance>                                      Vertices_with_tolerance;
+
+  Vertices_with_tolerance vertices_to_snap;
+  vertices_to_snap.reserve(halfedge_range_S.size()); // ensures that iterators stay valid
+
+  // Take the min tolerance for all points that have the same coordinates
+  std::map<Point, FT> point_tolerance_map;
+
+  for(halfedge_descriptor h : halfedge_range_S)
+  {
+    if(get(locked_vertices_S, target(h, tm_S)))
+      continue;
+
+    // Skip the source vertex if its two incident halfedges are geometrically identical (it means that
+    // the two halfedges are already stitchable and we don't want this common vertex to be used
+    // to split a halfedge somewhere else)
+    if(get(vpm_S, source(h, tm_S)) == get(vpm_S, target(next(h, tm_S), tm_S)))
+      continue;
+
+    const vertex_descriptor v = target(h, tm_S);
+    const FT tolerance = get(tolerance_map_S, v);
+
+    vertices_to_snap.emplace_back(h, tolerance);
+
+    std::pair<Point, FT> entry(get(vpm_S, v), tolerance);
+    std::pair<typename std::map<Point, FT>::iterator, bool> is_insert_successful =
+      point_tolerance_map.insert(entry);
+    if(!is_insert_successful.second)
+      is_insert_successful.first->second = (std::min)(is_insert_successful.first->second, tolerance);
+
+    #ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "Non-conformal query: " << v << " (" << get(vpm_S, v) << "), tolerance: " << tolerance << std::endl;
+#endif
+  }
+
+  for(auto& p : vertices_to_snap)
+    p.second = point_tolerance_map[get(vpm_S, target(p.first, tm_S))];
+
+  // Since we're inserting primitives one by one, we can't pass this shared data in the constructor of the tree
+  AABB_Traits aabb_traits;
+  aabb_traits.set_shared_data(tm_T, vpm_T);
+  AABB_tree aabb_tree(aabb_traits);
+
+  for(halfedge_descriptor h : halfedge_range_T)
+  {
+    CGAL_precondition(is_border(edge(h, tm_T), tm_T));
+    if(get(locked_halfedges_T, h))
+    {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+      std::cout << edge(h, tm_T) << " is locked and not a valid target" << std::endl;
+#endif
+      continue;
+    }
+
+    aabb_tree.insert(Primitive(edge(h, tm_T), tm_T, vpm_T));
+  }
+
+  // Now, check which edges of the target range ought to be split by source vertices
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+  std::cout << "Collect edges to split with " << vertices_to_snap.size() << " vertices" << std::endl;
+#endif
+
+#ifndef CGAL_LINKED_WITH_TBB
+  CGAL_static_assertion_msg (!(std::is_convertible<ConcurrencyTag, Parallel_tag>::value),
+                             "Parallel_tag is enabled but TBB is unavailable.");
+#else
+  if(std::is_convertible<ConcurrencyTag, Parallel_tag>::value)
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG
+    std::cout << "Parallel find splittable edges!" << std::endl;
+#endif
+
+    typedef tbb::concurrent_hash_map<halfedge_descriptor,
+                                     Vertices_with_new_position>                 Concurrent_edge_to_split_container;
+    typedef internal::Find_splittable_edge_for_parallel_for<
+              Vertices_with_tolerance, TriangleMesh,
+              Concurrent_edge_to_split_container, AABB_tree,
+              VertexPatchMap_S, FacePatchMap_T, VPMS, VPMT, GT>                  Functor;
+
+    CGAL::Real_timer timer;
+    timer.start();
+
+    Concurrent_edge_to_split_container edges_to_split;
+    Functor f(vertices_to_snap, edges_to_split, &aabb_tree,
+              tm_S, vertex_patch_map_S, vpm_S, tm_T, face_patch_map_T, vpm_T, gt);
+    tbb::parallel_for(tbb::blocked_range<std::size_t>(0, vertices_to_snap.size()), f);
+
+    std::cout << "Time to gather edges: " << timer.time() << std::endl;
+
+    return split_edges(edges_to_split, tm_S, vpm_S,  tm_T, vpm_T, gt, is_source_mesh_fixed);
+  }
+  else
+#endif // CGAL_LINKED_WITH_TBB
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG
+    std::cout << "Sequential find splittable edges!" << std::endl;
+#endif
+
+    std::map<halfedge_descriptor, Vertices_with_new_position> edges_to_split;
+    for(const Vertex_with_tolerance& vt : vertices_to_snap)
+    {
+      internal::find_splittable_edge(vt, edges_to_split, &aabb_tree,
+                                     tm_S, vertex_patch_map_S, vpm_S,
+                                     tm_T, face_patch_map_T, vpm_T, gt);
+    }
+
+    return split_edges(edges_to_split, tm_S, vpm_S, tm_T, vpm_T,  gt, is_source_mesh_fixed);
+  }
 }
 
+// \ingroup PMP_repairing_grp
+//
+// Attempts to snap the vertices in `halfedge_range_A` onto edges of `halfedge_range_B`, and reciprocally.
+// A vertex from the first range is only snapped to an edge of the second range if the distance to
+// the edge is smaller than the tolerance prescribed at the vertex.
+//
+// \warning This function does not give any guarantee on the conformity between the two meshes after the snapping.
+// \warning This function does not merge vertices or the meshes, it is purely geometric.
+//
+// \tparam TriangleMesh a model of `FaceListGraph` and `MutableFaceGraph`
+// \tparam HalfedgeRange_A a model of `Range` with value type `boost::graph_traits<TriangleMesh>::%halfedge_descriptor`
+// \tparam HalfedgeRange_B a model of `Range` with value type `boost::graph_traits<TriangleMesh>::%halfedge_descriptor`
+// \tparam ToleranceMap_A a model of `ReadablePropertyMap` with key type `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
+//                        and value type `GetGeomTraits<TriangleMesh, NamedParameters_A>::type::FT`
+// \tparam ToleranceMap_B a model of `ReadablePropertyMap` with key type `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
+//                        and value type `GetGeomTraits<TriangleMesh, NamedParameters_A>::type::FT`
+// \tparam NamedParameters_A a sequence of \ref pmp_namedparameters "Named Parameters"
+// \tparam NamedParameters_B a sequence of \ref pmp_namedparameters "Named Parameters"
+//
+// \param halfedge_range_A a range of halfedges of the first mesh defining a set of vertices (as targets of the halfeges)
+// \param tm_A the first mesh to which the vertices in `halfedge_range_A` belong
+// \param tolerance_map_A a tolerance map associating to each vertex of the first range a tolerance value
+// \param halfedge_range_B a range of vertices of the second mesh defining a set of vertices (as targets of the halfeges)
+// \param tolerance_map_B a tolerance map associating to each vertex of the second range a tolerance value
+// \param tm_B the target mesh to which the vertices in `halfedge_range_B` belong
+// \param np_A optional \ref pmp_namedparameters "Named Parameters" related to the source mesh,
+//             amongst those described below:
+//
+// \cgalNamedParamsBegin
+//   \cgalParamBegin{vertex_point_map}
+//     the property map with the points associated to the vertices of the source mesh.
+//     The type of this map is model of `ReadWritePropertyMap`. If this parameter is omitted,
+//     an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMesh`.
+//   \cgalParamEnd
+//   \cgalParamBegin{geom_traits}
+//     a geometric traits class instance, must be a model of `Kernel`
+//   \cgalParamEnd
+// \cgalNamedParamsEnd
+//
+// \param np_B optional \ref pmp_namedparameters "Named Parameters" related to the target mesh,
+//             amongst those described below:
+//
+// \cgalNamedParamsBegin
+//   \cgalParamBegin{vertex_point_map}
+//     the property map with the points associated to the vertices of the target mesh.
+//     The type of this map is model of `ReadablePropertyMap`. If this parameter is omitted,
+//     an internal property map for `CGAL::vertex_point_t` must be available in `TriangleMesh`.
+//   \cgalParamEnd
+// \cgalNamedParamsEnd
+//
+// \return the number of snapped vertex pairs
+//
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename HalfedgeRange, typename TriangleMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_non_conformal(HalfedgeRange& halfedge_range_A,
+                               TriangleMesh& tm_A,
+                               ToleranceMap_A tolerance_map_A,
+                               HalfedgeRange& halfedge_range_B,
+                               TriangleMesh& tm_B,
+                               ToleranceMap_B tolerance_map_B,
+                               const bool is_self_snapping, // == true if range and meshes are equal
+                               const NamedParameters_A& np_A,
+                               const NamedParameters_B& np_B)
+{
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout.precision(17);
+  std::cerr.precision(17);
+#endif
+
+  typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor           vertex_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor         halfedge_descriptor;
+  typedef typename boost::graph_traits<TriangleMesh>::face_descriptor             face_descriptor;
+
+  typedef CGAL::dynamic_vertex_property_t<bool>                                   Vertex_bool_tag;
+  typedef CGAL::dynamic_vertex_property_t<std::size_t>                            Vertex_size_t_tag;
+  typedef CGAL::dynamic_halfedge_property_t<bool>                                 Halfedge_bool_tag;
+
+  typedef typename boost::property_map<TriangleMesh, Vertex_bool_tag>::type       Locked_vertices;
+  typedef typename boost::property_map<TriangleMesh, Halfedge_bool_tag>::type     Locked_halfedges;
+  typedef typename boost::property_map<TriangleMesh, Vertex_size_t_tag>::type     Vertex_patch;
+
+  typedef typename internal_np::Lookup_named_param_def <
+    internal_np::face_patch_t, NamedParameters_A,
+      Constant_property_map<face_descriptor, std::size_t> /*default*/ >::type     Face_patch_map_A;
+  typedef typename internal_np::Lookup_named_param_def <
+    internal_np::face_patch_t, NamedParameters_B,
+      Constant_property_map<face_descriptor, std::size_t> /*default*/ >::type     Face_patch_map_B;
+
+  using CGAL::parameters::choose_parameter;
+  using CGAL::parameters::is_default_parameter;
+  using CGAL::parameters::get_parameter;
+
+  const bool is_same_mesh = (&tm_A == &tm_B);
+  const bool simplify_first_mesh = choose_parameter(get_parameter(np_A, internal_np::do_simplify_border), false);
+  const bool simplify_second_mesh = choose_parameter(get_parameter(np_B, internal_np::do_simplify_border), false);
+  const bool is_second_mesh_fixed = choose_parameter(get_parameter(np_B, internal_np::do_lock_mesh), false);
+
+  // vertex-vertex and vertex-edge snapping is only considered within compatible patches
+  Face_patch_map_A face_patch_map_A = choose_parameter(get_parameter(np_A, internal_np::face_patch),
+                                                       Constant_property_map<face_descriptor, std::size_t>(-1));
+  Face_patch_map_B face_patch_map_B = choose_parameter(get_parameter(np_B, internal_np::face_patch),
+                                                       Constant_property_map<face_descriptor, std::size_t>(-1));
+
+  Vertex_patch vertex_patch_map_A = get(Vertex_size_t_tag(), tm_A);
+  Vertex_patch vertex_patch_map_B = get(Vertex_size_t_tag(), tm_B);
+
+  for(const halfedge_descriptor h : halfedge_range_A)
+  {
+    CGAL_precondition(is_border(h, tm_A));
+    halfedge_descriptor h_opp = opposite(h, tm_A);
+    for(const vertex_descriptor v : vertices_around_face(h_opp, tm_A))
+      put(vertex_patch_map_A, v, get(face_patch_map_A, face(h_opp, tm_A)));
+  }
+
+  // @todo avoid that when 'self_snapping' is true
+  for(const halfedge_descriptor h : halfedge_range_B)
+  {
+    CGAL_precondition(is_border(h, tm_B));
+    halfedge_descriptor h_opp = opposite(h, tm_B);
+    for(const vertex_descriptor v : vertices_around_face(h_opp, tm_B))
+      put(vertex_patch_map_B, v, get(face_patch_map_B, face(h_opp, tm_B)));
+  }
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "Non-conformal snapping... Range sizes: "
+            << std::distance(halfedge_range_A.begin(), halfedge_range_A.end()) << " and "
+            << std::distance(halfedge_range_B.begin(), halfedge_range_B.end()) << std::endl;
+#endif
+
+  CGAL_expensive_precondition(is_valid_polygon_mesh(tm_S) && is_triangle_mesh(tm_S));
+  CGAL_expensive_precondition(is_valid_polygon_mesh(tm_T) && is_triangle_mesh(tm_T));
+
+  // Steps:
+  // - #1 Simplify the source range
+  // - #1bis Simplify the target range (if it's not locked)
+  // - #2 two-way vertex-vertex snapping
+  // - #3 two-way vertex-edge snapping
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// #1 and #1bis (Simplification of borders)
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "Simplify ranges (" << simplify_first_mesh << " " << simplify_second_mesh << ")..." << std::endl;
+#endif
+
+  if(simplify_first_mesh)
+  {
+    internal::simplify_range(halfedge_range_A, tm_A, tolerance_map_A, np_A);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+    std::ofstream("results/simplified_A.off") << std::setprecision(17) << tm_A;
+#endif
+  }
+
+  if(!is_self_snapping && !is_second_mesh_fixed && simplify_second_mesh)
+  {
+    internal::simplify_range(halfedge_range_B, tm_B, tolerance_map_B, np_B);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+    std::ofstream("results/simplified_B.off") << std::setprecision(17) << tm_B;
+#endif
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// #2 (Two-way vertex-vertex snapping)
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+  // We keep in memory pairs of source/target edges that are stitchable after vertex-vertex snapping
+  // --> these halfedges should not be considered as targets in non-conformal snapping
+  // Similarly, matching vertices whose incident edges have matching directions are also locked
+  Locked_vertices locked_vertices_A = get(Vertex_bool_tag(), tm_A);
+  Locked_vertices locked_vertices_B = get(Vertex_bool_tag(), tm_B);
+  Locked_halfedges locked_halfedges_A = get(Halfedge_bool_tag(), tm_A);
+  Locked_halfedges locked_halfedges_B = get(Halfedge_bool_tag(), tm_B);
+
+  std::size_t snapped_n = 0;
+
+  std::vector<std::pair<vertex_descriptor, vertex_descriptor> > locked_vertices;
+  std::vector<halfedge_descriptor> locked_halfedges_A_vector, locked_halfedges_B_vector;
+
+  snapped_n += internal::snap_vertices_two_way<ConcurrencyTag>(
+                 halfedge_range_A, tm_A, tolerance_map_A, vertex_patch_map_A,
+                 halfedge_range_B, tm_B, tolerance_map_B, vertex_patch_map_B,
+                 std::back_inserter(locked_vertices),
+                 std::back_inserter(locked_halfedges_A_vector),
+                 std::back_inserter(locked_halfedges_B_vector),
+                 is_second_mesh_fixed, np_A, np_B);
+
+  for(const auto& vpair : locked_vertices)
+  {
+    put(locked_vertices_A, vpair.first, true);
+    put(locked_vertices_B, vpair.second, true);
+    if(is_same_mesh)
+    {
+      put(locked_vertices_B, vpair.first, true);
+      put(locked_vertices_A, vpair.second, true);
+    }
+  }
+
+  for(const halfedge_descriptor h : locked_halfedges_A_vector)
+    put(locked_halfedges_A, h, true);
+  for(const halfedge_descriptor h : locked_halfedges_B_vector)
+    put(locked_halfedges_B, h, true);
+
+  if(is_same_mesh)
+  {
+    for(const halfedge_descriptor h : locked_halfedges_A_vector)
+      put(locked_halfedges_B, h, true);
+    for(const halfedge_descriptor h : locked_halfedges_B_vector)
+      put(locked_halfedges_A, h, true);
+  }
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+  std::ofstream("results/vertex_vertex_A.off") << std::setprecision(17) << tm_A;
+  std::ofstream("results/vertex_vertex_B.off") << std::setprecision(17) << tm_B;
+#endif
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// #3 (Two one-way vertex-edge snapping)
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << " ///////////// Two one-way vertex-edge snapping (A --> B) " << std::endl;
+#endif
+
+  snapped_n += internal::snap_non_conformal_one_way<ConcurrencyTag>(
+                 halfedge_range_A, tm_A, tolerance_map_A, vertex_patch_map_A, locked_vertices_A,
+                 halfedge_range_B, tm_B, face_patch_map_B, locked_halfedges_B,
+                 false /*source is never fixed*/, np_A, np_B);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+  std::ofstream("results/vertex_edge_A.off") << std::setprecision(17) << tm_A;
+  std::ofstream("results/vertex_edge_B.off") << std::setprecision(17) << tm_B;
+#endif
+
+  if(!is_self_snapping)
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << " ///////////// Two one-way vertex-edge snapping (B --> A) " << std::endl;
+#endif
+
+    snapped_n += internal::snap_non_conformal_one_way<ConcurrencyTag>(
+                   halfedge_range_B, tm_B, tolerance_map_B, vertex_patch_map_B, locked_vertices_B,
+                   halfedge_range_A, tm_A, face_patch_map_A, locked_halfedges_A,
+                   is_second_mesh_fixed, np_B, np_A);
+  }
+
+  return snapped_n;
+}
+
+} // namespace internal
+
+namespace experimental {
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
+/// Convenience overloads
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
-// Attempt to snap the vertices of the border of 'pm1' onto border edges of 'pm2'.
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_borders(TriangleMesh& tm_A,
+                         ToleranceMap_A tolerance_map_A,
+                         TriangleMesh& tm_B,
+                         ToleranceMap_B tolerance_map_B,
+                         const NamedParameters_A& np_A,
+                         const NamedParameters_B& np_B)
+{
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor        halfedge_descriptor;
 
-template <typename TriangleMesh>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm1,
-                                                TriangleMesh& pm2)
+  std::vector<halfedge_descriptor> border_vertices_1;
+  border_halfedges(tm_A, std::back_inserter(border_vertices_1));
+  std::vector<halfedge_descriptor> border_vertices_2;
+  border_halfedges(tm_B, std::back_inserter(border_vertices_2));
+
+  return internal::snap_non_conformal<ConcurrencyTag>(border_vertices_1, tm_A, tolerance_map_A,
+                                                      border_vertices_2, tm_B, tolerance_map_B,
+                                                      false /*not self snapping*/, np_A, np_B);
+}
+
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_borders(TriangleMesh& tm_A,
+                         TriangleMesh& tm_B,
+                         const NamedParameters_A& np_A,
+                         const NamedParameters_B& np_B)
 {
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor        halfedge_descriptor;
 
@@ -1034,84 +1211,109 @@ std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm1,
   typedef CGAL::dynamic_vertex_property_t<FT>                                    Vertex_property_tag;
   typedef typename boost::property_map<TriangleMesh, Vertex_property_tag>::type  Tolerance_map;
 
-  std::vector<halfedge_descriptor> border_vertices1;
-  border_halfedges(pm1, std::back_inserter(border_vertices1));
+  std::vector<halfedge_descriptor> border_vertices_1;
+  std::vector<halfedge_descriptor> border_vertices_2;
+  border_halfedges(tm_A, std::back_inserter(border_vertices_1));
+  border_halfedges(tm_B, std::back_inserter(border_vertices_2));
 
-  std::vector<halfedge_descriptor> border_vertices2;
-  if(&pm1 == &pm2)
-    border_vertices2 = border_vertices1;
-  else
-    border_halfedges(pm2, std::back_inserter(border_vertices2));
-
-  Tolerance_map tol_pmap = get(Vertex_property_tag(), pm1);
   const FT tol_mx(std::numeric_limits<double>::max());
-  internal::assign_tolerance_with_local_edge_length_bound(border_vertices1, tol_pmap, tol_mx, pm1);
+  Tolerance_map tolerance_map_A = get(Vertex_property_tag(), tm_A);
+  internal::assign_tolerance_with_local_edge_length_bound(border_vertices_1, tolerance_map_A, tol_mx, tm_A, np_A);
+  Tolerance_map tolerance_map_B = get(Vertex_property_tag(), tm_A);
+  internal::assign_tolerance_with_local_edge_length_bound(border_vertices_2, tolerance_map_B, tol_mx, tm_B, np_B);
 
-  return snap_vertex_range_onto_vertex_range_non_conforming(border_vertices1, pm1,
-                                                            border_vertices2, pm2, tol_pmap,
-                                                            CGAL::parameters::all_default(),
-                                                            CGAL::parameters::all_default());
+  return internal::snap_non_conformal<ConcurrencyTag>(border_vertices_1, tm_A, tolerance_map_A,
+                                                      border_vertices_2, tm_B, tolerance_map_B,
+                                                      false /*no self snapping*/, np_A, np_B);
 }
 
-template <typename TriangleMesh, typename ToleranceMap, typename NamedParameters>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm1,
-                                                TriangleMesh& pm2,
-                                                const ToleranceMap& tol_pmap,
-                                                const NamedParameters& np1,
-                                                const NamedParameters& np2)
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B>
+std::size_t snap_borders(TriangleMesh& tm_A,
+                         ToleranceMap_A tolerance_map_A,
+                         TriangleMesh& tm_B,
+                         ToleranceMap_B tolerance_map_B)
+{
+  return snap_borders<ConcurrencyTag>(tm_A, tolerance_map_A, tm_B, tolerance_map_B,
+                                      CGAL::parameters::all_default(), CGAL::parameters::all_default());
+}
+
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh>
+std::size_t snap_borders(TriangleMesh& tm_A,
+                         TriangleMesh& tm_B)
+{
+  return snap_borders<ConcurrencyTag>(tm_A, tm_B, CGAL::parameters::all_default(), CGAL::parameters::all_default());
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////////////////////////
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Same as above, but with a single mesh
+
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename ToleranceMap,
+          typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
+std::size_t snap_borders(TriangleMesh& tm,
+                         ToleranceMap tolerance_map,
+                         const CGAL_PMP_NP_CLASS& np)
 {
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor        halfedge_descriptor;
 
-  std::vector<halfedge_descriptor> border_vertices1;
-  border_halfedges(pm1, std::back_inserter(border_vertices1));
+  std::vector<halfedge_descriptor> border_vertices;
+  border_halfedges(tm, std::back_inserter(border_vertices));
 
-  std::vector<halfedge_descriptor> border_vertices2;
-  border_halfedges(pm2, std::back_inserter(border_vertices2));
-
-  return snap_vertex_range_onto_vertex_range_non_conforming(border_vertices1, pm1,
-                                                            border_vertices2, pm2,
-                                                            tol_pmap, np1, np2);
+  return internal::snap_non_conformal<ConcurrencyTag>(border_vertices, tm, tolerance_map,
+                                                      border_vertices, tm, tolerance_map,
+                                                      true /*self snapping*/, np, np);
 }
 
-template <typename TriangleMesh, typename ToleranceMap>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm1,
-                                                TriangleMesh& pm2,
-                                                const ToleranceMap& tol_pmap)
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename ToleranceMap>
+std::size_t snap_borders(TriangleMesh& tm,
+                         ToleranceMap tolerance_map)
 {
-  return snap_border_vertices_non_conforming(pm1, pm2, tol_pmap,
-                                             CGAL::parameters::all_default(), CGAL::parameters::all_default());
+  return snap_borders<ConcurrencyTag>(tm, tolerance_map, CGAL::parameters::all_default());
 }
 
-////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////////////////////////
-
-template <typename TriangleMesh>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm)
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh,
+          typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
+std::size_t snap_borders(TriangleMesh& tm,
+                         const CGAL_PMP_NP_CLASS& np)
 {
-  return snap_border_vertices_non_conforming(pm, pm);
+  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor        halfedge_descriptor;
+
+  typedef typename GetGeomTraits<TriangleMesh>::type                             GT;
+  typedef typename GT::FT                                                        FT;
+
+  typedef CGAL::dynamic_vertex_property_t<FT>                                    Vertex_property_tag;
+  typedef typename boost::property_map<TriangleMesh, Vertex_property_tag>::type  Tolerance_map;
+
+  std::vector<halfedge_descriptor> border_vertices;
+  border_halfedges(tm, std::back_inserter(border_vertices));
+
+  const FT tol_mx(std::numeric_limits<double>::max());
+  Tolerance_map tolerance_map = get(Vertex_property_tag(), tm);
+  internal::assign_tolerance_with_local_edge_length_bound(border_vertices, tolerance_map, tol_mx, tm, np);
+
+  return internal::snap_non_conformal<ConcurrencyTag>(border_vertices, tm, tolerance_map,
+                                                      border_vertices, tm, tolerance_map,
+                                                      true /*self snapping*/, np, np);
 }
 
-template <typename TriangleMesh, typename ToleranceMap, typename NamedParameters>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm,
-                                                const ToleranceMap& tol_pmap,
-                                                const NamedParameters& np)
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename TriangleMesh>
+std::size_t snap_borders(TriangleMesh& tm)
 {
-  return snap_border_vertices_non_conforming(pm, pm, tol_pmap, np, np);
-}
-
-template <typename TriangleMesh, typename ToleranceMap>
-std::size_t snap_border_vertices_non_conforming(TriangleMesh& pm,
-                                                const ToleranceMap& tol_pmap)
-{
-  return snap_border_vertices_non_conforming(pm, pm, tol_pmap,
-                                             CGAL::parameters::all_default(), CGAL::parameters::all_default());
+  return snap_borders<ConcurrencyTag>(tm, CGAL::parameters::all_default());
 }
 
 } // end namespace experimental
-
 } // end namespace Polygon_mesh_processing
-
 } // end namespace CGAL
 
-#endif // CGAL_POLYGON_MESH_PROCESSING_INTERNAL_SNAP_H
+#endif // CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_H
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap_vertices.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap_vertices.h
new file mode 100644
index 00000000000..bb3a5f5297d
--- /dev/null
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Snapping/snap_vertices.h
@@ -0,0 +1,943 @@
+// Copyright (c) 2018, 2019 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Mael Rouxel-Labbé
+
+#ifndef CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_VERTICES_H
+#define CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_VERTICES_H
+
+#include <CGAL/license/Polygon_mesh_processing/repair.h>
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+ #ifndef CGAL_PMP_SNAP_DEBUG
+  #define CGAL_PMP_SNAP_DEBUG
+ #endif
+#endif
+
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/helper.h>
+#include <CGAL/Polygon_mesh_processing/internal/named_function_params.h>
+#include <CGAL/Polygon_mesh_processing/internal/named_params_helper.h>
+#include <CGAL/Polygon_mesh_processing/border.h>
+
+#include <CGAL/assertions.h>
+#include <CGAL/Bbox_3.h>
+#include <CGAL/boost/graph/helpers.h>
+#include <CGAL/boost/graph/iterator.h>
+#include <CGAL/boost/graph/selection.h>
+#include <CGAL/box_intersection_d.h>
+#include <CGAL/circulator.h>
+#include <CGAL/Dynamic_property_map.h>
+#include <CGAL/iterator.h>
+#include <CGAL/Kernel/global_functions.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/utility.h>
+#include <CGAL/Real_timer.h>
+#include <CGAL/tags.h>
+
+#include <boost/multi_index_container.hpp>
+#include <boost/multi_index/ordered_index.hpp>
+#include <boost/multi_index/member.hpp>
+
+#ifdef CGAL_LINKED_WITH_TBB
+# include <tbb/blocked_range.h>
+# include <tbb/concurrent_vector.h>
+# include <tbb/parallel_for.h>
+#endif
+
+#include <functional>
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+#include <fstream>
+#endif
+#include <iostream>
+#include <iterator>
+#include <limits>
+#include <map>
+#include <type_traits>
+#include <unordered_set>
+#include <utility>
+#include <vector>
+
+namespace CGAL {
+namespace Polygon_mesh_processing {
+namespace internal {
+
+// Data entry of the multi-index container
+template <typename PolygonMesh, typename GeomTraits>
+struct Snapping_pair
+{
+  typedef typename GeomTraits::FT                                                     FT;
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor              halfedge_descriptor;
+  typedef std::vector<halfedge_descriptor>                                            Vertex_container;
+  typedef std::pair<Vertex_container, FT>                                             Unique_vertex;
+  typedef const Unique_vertex*                                                        Unique_vertex_ptr;
+
+  Snapping_pair(Unique_vertex_ptr uv_a_, Unique_vertex_ptr uv_b_, const FT sq_dist_)
+    : uv_a(uv_a_), uv_b(uv_b_), sq_dist(sq_dist_)
+  { }
+
+  Unique_vertex_ptr uv_a;
+  Unique_vertex_ptr uv_b;
+  FT sq_dist;
+};
+
+// Functor that just forwards the pair of the two intersecting boxes
+template <class OutputIterator>
+struct Intersecting_boxes_pairs_report
+{
+  Intersecting_boxes_pairs_report(OutputIterator it) :  m_iterator(it) { }
+
+  template <class Box>
+  void operator()(const Box* b, const Box* c) const {
+    *m_iterator++ = std::make_pair(b->info(), c->info());
+  }
+
+  mutable OutputIterator m_iterator;
+};
+
+template <typename SnappingPairContainer,
+          typename PolygonMesh, typename GeomTraits,
+          typename VPM_A, typename VPM_B,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename VertexPatchMap_A, typename VertexPatchMap_B,
+          typename Box
+#ifdef CGAL_LINKED_WITH_TBB
+          , typename UniqueVertexPairContainer = void
+          , typename ToKeepContainer = void
+#endif
+          >
+struct Vertex_proximity_report
+{
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor                vertex_descriptor;
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor              halfedge_descriptor;
+  typedef typename boost::graph_traits<PolygonMesh>::edge_descriptor                  edge_descriptor;
+
+  typedef typename GeomTraits::FT                                                     FT;
+
+  typedef std::vector<halfedge_descriptor>                                            Vertex_container;
+  typedef std::pair<Vertex_container, FT>                                             Unique_vertex;
+  typedef const Unique_vertex*                                                        Unique_vertex_ptr;
+  typedef std::pair<Unique_vertex_ptr, Unique_vertex_ptr>                             Unique_vertex_pair;
+
+  Vertex_proximity_report(SnappingPairContainer& snapping_pairs,
+                          const PolygonMesh& tm_A,
+                          ToleranceMap_A tolerance_map_A,
+                          VertexPatchMap_A vertex_patch_map_A,
+                          const VPM_A& vpm_A,
+                          const PolygonMesh& tm_B,
+                          ToleranceMap_B tolerance_map_B,
+                          VertexPatchMap_B vertex_patch_map_B,
+                          const VPM_B& vpm_B,
+                          const GeomTraits& gt
+#ifdef CGAL_LINKED_WITH_TBB
+                          , const UniqueVertexPairContainer* uv_pairs = nullptr
+                          , ToKeepContainer* to_keep = nullptr
+#endif
+                          )
+    :
+      m_tm_A(tm_A),
+      m_tolerance_map_A(tolerance_map_A),
+      m_vertex_patch_map_A(vertex_patch_map_A),
+      m_vpm_A(vpm_A),
+      m_tm_B(tm_B),
+      m_tolerance_map_B(tolerance_map_B),
+      m_vertex_patch_map_B(vertex_patch_map_B),
+      m_vpm_B(vpm_B),
+      m_gt(gt),
+      m_snapping_pairs(snapping_pairs)
+#ifdef CGAL_LINKED_WITH_TBB
+    , m_uv_pairs(uv_pairs)
+    , m_to_keep(to_keep)
+#endif
+  { }
+
+  bool are_equal_vertices(Unique_vertex_ptr uv_a, Unique_vertex_ptr uv_b) const
+  {
+    if(&m_tm_A != &m_tm_B) // must be the same mesh
+      return false;
+
+    if(uv_a->first.size() != uv_b->first.size())
+      return false;
+
+    CGAL_assertion(!uv_a->first.empty() && !uv_b->first.empty());
+    const halfedge_descriptor ha = uv_a->first.front();
+    return (std::find(uv_b->first.begin(), uv_b->first.end(), ha) != uv_b->first.end());
+  }
+
+  std::pair<FT, bool> do_keep(Unique_vertex_ptr uv_a, Unique_vertex_ptr uv_b) const
+  {
+    const Vertex_container& vs_a = uv_a->first;
+    const Vertex_container& vs_b = uv_b->first;
+    const vertex_descriptor va = target(vs_a.front(), m_tm_A);
+    const vertex_descriptor vb = target(vs_b.front(), m_tm_B);
+
+    // Check for patch compatibility
+    if(get(m_vertex_patch_map_A, va) != get(m_vertex_patch_map_B, vb))
+      return std::make_pair(-1, false); // ignore
+
+    // Reject if same mesh and already grouped together
+    if(are_equal_vertices(uv_a, uv_b))
+      return std::make_pair(-1, false);
+
+    const FT tol_a = uv_a->second;
+    const FT tol_b = uv_b->second;
+    CGAL_assertion(tol_a >= FT(0));
+    CGAL_assertion(tol_b >= FT(0));
+
+    const FT upper_bound_squared = CGAL::square(0.5*(tol_a + tol_b));
+    CGAL::Comparison_result res =
+      m_gt.compare_squared_distance_3_object()(get(m_vpm_A, va), get(m_vpm_B, vb), upper_bound_squared);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "squared distance between "
+              << va << " [" << get(m_vpm_A, va) << "] and "
+              << vb << " [" << get(m_vpm_B, vb) << "]: " << sq_dist
+              << " (tol a/b: " << tol_a << " " << tol_b << ") larger? " << (res == CGAL::LARGER)
+              << std::endl;
+#endif
+
+    if(res == CGAL::LARGER)
+      return std::make_pair(-1, false); // ignore
+    else
+    {
+      const FT sq_dist = (min)(m_gt.compute_squared_distance_3_object()(get(m_vpm_A, va), get(m_vpm_B, vb)),
+                               upper_bound_squared);
+      return std::make_pair(sq_dist, true); // keep
+    }
+  }
+
+  // that's the sequential version
+  void operator()(const Box* a, const Box* b)
+  {
+    Unique_vertex_ptr uv_a = a->info(), uv_b = b->info();
+    const std::pair<FT, bool> res = do_keep(uv_a, uv_b);
+    if(res.second)
+      m_snapping_pairs.insert(Snapping_pair<PolygonMesh, GeomTraits>(uv_a, uv_b, res.first));
+  }
+
+#ifdef CGAL_LINKED_WITH_TBB
+  // that's the parallel version
+  void operator()(const tbb::blocked_range<std::size_t>& r) const
+  {
+    CGAL_assertion(m_uv_pairs != nullptr);
+    CGAL_assertion(m_to_keep != nullptr);
+
+    for(std::size_t ri = r.begin(); ri != r.end(); ++ri)
+    {
+      const Unique_vertex_pair& hp = (*m_uv_pairs)[ri];
+      m_to_keep->operator[](ri) = do_keep(hp.first, hp.second);
+    }
+  }
+#endif
+
+private:
+  const PolygonMesh& m_tm_A;
+  ToleranceMap_A m_tolerance_map_A;
+  VertexPatchMap_A m_vertex_patch_map_A;
+  VPM_A m_vpm_A;
+  const PolygonMesh& m_tm_B;
+  ToleranceMap_B m_tolerance_map_B;
+  VertexPatchMap_B m_vertex_patch_map_B;
+  VPM_B m_vpm_B;
+  const GeomTraits& m_gt;
+
+  SnappingPairContainer& m_snapping_pairs; // will only be filled here in the sequential setting
+
+#ifdef CGAL_LINKED_WITH_TBB
+  const UniqueVertexPairContainer* m_uv_pairs;
+  ToKeepContainer* m_to_keep;
+#endif
+};
+
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename VertexPatchMap_A, typename VertexPatchMap_B,
+          typename LockableVerticesOutputIterator, typename LockableHalfedgesOutputIterator,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_vertices_two_way(const HalfedgeRange_A& halfedge_range_A,
+                                  PolygonMesh& tm_A,
+                                  ToleranceMap_A tolerance_map_A,
+                                  VertexPatchMap_A vertex_patch_map_A,
+                                  const HalfedgeRange_B& halfedge_range_B,
+                                  PolygonMesh& tm_B,
+                                  ToleranceMap_B tolerance_map_B,
+                                  VertexPatchMap_B vertex_patch_map_B,
+                                  LockableVerticesOutputIterator lockable_vps_out,
+                                  LockableHalfedgesOutputIterator lockable_ha_out,
+                                  LockableHalfedgesOutputIterator lockable_hb_out,
+                                  const bool is_second_mesh_fixed,
+                                  const NamedParameters_A& np_A,
+                                  const NamedParameters_B& np_B)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor                vertex_descriptor;
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor              halfedge_descriptor;
+
+  typedef typename GetVertexPointMap<PolygonMesh, NamedParameters_A>::type            VPM_A;
+  typedef typename GetVertexPointMap<PolygonMesh, NamedParameters_B>::type            VPM_B;
+
+  typedef typename GetGeomTraits<PolygonMesh, NamedParameters_A>::type                GT;
+  typedef typename GT::FT                                                             FT;
+  typedef typename boost::property_traits<VPM_B>::value_type                          Point;
+
+  typedef std::vector<halfedge_descriptor>                                            Vertex_container;
+  typedef std::pair<Vertex_container, FT>                                             Unique_vertex;
+  typedef const Unique_vertex*                                                        Unique_vertex_ptr;
+  typedef std::map<std::pair<Point, std::size_t>, Unique_vertex>                      Unique_positions;
+
+  typedef Box_intersection_d::ID_FROM_BOX_ADDRESS                                             Box_policy;
+  typedef CGAL::Box_intersection_d::Box_with_info_d<double, 3, Unique_vertex_ptr, Box_policy> Box;
+
+  using parameters::get_parameter;
+  using parameters::choose_parameter;
+
+  CGAL_static_assertion((std::is_same<Point, typename GT::Point_3>::value));
+
+  GT gt = choose_parameter(get_parameter(np_A, internal_np::geom_traits), GT());
+  VPM_A vpm_A = choose_parameter(get_parameter(np_A, internal_np::vertex_point),
+                                 get_property_map(vertex_point, tm_A));
+  VPM_B vpm_B = choose_parameter(get_parameter(np_B, internal_np::vertex_point),
+                                 get_property_map(vertex_point, tm_B));
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "Finding snappables vertices. Range sizes: "
+            << std::distance(halfedge_range_A.begin(), halfedge_range_A.end()) << " and "
+            << std::distance(halfedge_range_B.begin(), halfedge_range_B.end()) << std::endl;
+#endif
+
+  if(is_empty_range(halfedge_range_A.begin(), halfedge_range_A.end()) ||
+     is_empty_range(halfedge_range_B.begin(), halfedge_range_B.end()))
+    return 0;
+
+  // Vertex-Vertex snapping is performed as follows:
+  // - Identify points which are already equal and group them together so that they are moved together
+  // - Create a single box for these points
+
+  std::vector<Box> boxes_A;
+  boxes_A.reserve(halfedge_range_A.size());
+  std::vector<Box> boxes_B;
+  boxes_B.reserve(halfedge_range_B.size());
+
+  Unique_positions unique_positions_A;
+  for(halfedge_descriptor h : halfedge_range_A)
+  {
+    const vertex_descriptor v = target(h, tm_A);
+    const FT tolerance = get(tolerance_map_A, v);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "Pos (A): " << v << " (" << get(vpm_A, v) << ")" << std::endl;
+#endif
+
+    Vertex_container nvc {{ h }};
+    std::pair<typename Unique_positions::iterator, bool> is_insert_successful =
+      unique_positions_A.insert(std::make_pair(
+                                  std::make_pair(get(vpm_A, v), get(vertex_patch_map_A, v)), // point and patch id
+                                  std::make_pair(nvc, tolerance)));
+
+    if(!is_insert_successful.second) // point was already met
+    {
+      Unique_vertex& uv = is_insert_successful.first->second;
+      Vertex_container& vc = uv.first; // second is the tolerance
+      CGAL_assertion(std::find(vc.begin(), vc.end(), h) == vc.end());
+      vc.push_back(h);
+      uv.second = (std::min)(uv.second, tolerance);
+    }
+  }
+
+  // same for tm_B (@todo avoid all that for self snapping + use self_intersection_d)
+  Unique_positions unique_positions_B;
+  for(halfedge_descriptor h : halfedge_range_B)
+  {
+    const vertex_descriptor v = target(h, tm_B);
+    const FT tolerance = get(tolerance_map_B, v);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "Pos (B): " << v << " (" << get(vpm_B, v) << ")" << std::endl;
+#endif
+
+    Vertex_container nvc {{ h }};
+    std::pair<typename Unique_positions::iterator, bool> is_insert_successful =
+      unique_positions_B.insert(std::make_pair(
+                                  std::make_pair(get(vpm_B, v), get(vertex_patch_map_B, v)), // point and patch id
+                                  std::make_pair(nvc, tolerance)));
+
+    if(!is_insert_successful.second) // point was already met
+    {
+      Unique_vertex& uv = is_insert_successful.first->second;
+      Vertex_container& vc = uv.first; // second is the tolerance
+      CGAL_assertion(std::find(vc.begin(), vc.end(), h) == vc.end());
+      vc.push_back(h);
+      uv.second = (std::min)(uv.second, tolerance);
+    }
+  }
+
+  // Actually build the boxes now
+  for(const auto& p : unique_positions_A)
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "Unique_vertex (A), pos: " << p.first.first << " vertices:";
+    for(const halfedge_descriptor h : p.second.first)
+      std::cout << " " << target(h, tm_A);
+    std::cout << std::endl;
+#endif
+
+    const Unique_vertex& ev = p.second;
+    CGAL_assertion(!ev.first.empty());
+
+    // this only makes the box a little larger to ease intersection computations,
+    // the final tolerance is not changed
+    const double eps = 1.01 * CGAL::to_double(ev.second);
+    const Bbox_3 pb = gt.construct_bbox_3_object()(p.first.first);
+    const Bbox_3 b(pb.xmin() - eps, pb.ymin() - eps, pb.zmin() - eps,
+                   pb.xmax() + eps, pb.ymax() + eps, pb.zmax() + eps);
+    boxes_A.push_back(Box(b, &ev));
+  }
+
+  for(const auto& p : unique_positions_B)
+  {
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    std::cout << "Unique_vertex (B), pos: " << p.first.first << " vertices:";
+    for(const halfedge_descriptor h : p.second.first)
+      std::cout << " " << target(h, tm_B);
+    std::cout << std::endl;
+#endif
+
+    const Unique_vertex& ev = p.second;
+    CGAL_assertion(!ev.first.empty());
+
+    const double eps = 1.01 * CGAL::to_double(ev.second);
+    const Bbox_3 pb = gt.construct_bbox_3_object()(p.first.first);
+    const Bbox_3 b(pb.xmin() - eps, pb.ymin() - eps, pb.zmin() - eps,
+                   pb.xmax() + eps, pb.ymax() + eps, pb.zmax() + eps);
+    boxes_B.push_back(Box(b, &ev));
+  }
+
+  // @fixme bench and don't use ptrs if not useful
+  std::vector<const Box*> boxes_A_ptr;
+  boxes_A_ptr.reserve(boxes_A.size());
+  for(const Box& b : boxes_A)
+    boxes_A_ptr.push_back(&b);
+
+  std::vector<const Box*> boxes_B_ptr;
+  boxes_B_ptr.reserve(boxes_B.size());
+  for(const Box& b : boxes_B)
+    boxes_B_ptr.push_back(&b);
+
+  // Use a multi index to sort easily by sources, targets, AND distance.
+  // Then, look up the distances in increasing order, and snap whenever the source and the target
+  // have both not been snapped yet.
+  typedef internal::Snapping_pair<PolygonMesh, GT>                                    Snapping_pair;
+  typedef boost::multi_index::multi_index_container<
+    Snapping_pair,
+    boost::multi_index::indexed_by<
+      boost::multi_index::ordered_non_unique<
+        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, Unique_vertex_ptr, uv_a)>,
+      boost::multi_index::ordered_non_unique<
+        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, Unique_vertex_ptr, uv_b)>,
+      boost::multi_index::ordered_non_unique<
+        BOOST_MULTI_INDEX_MEMBER(Snapping_pair, FT, sq_dist)>
+    >
+  >                                                                                   Snapping_pair_container;
+
+  Snapping_pair_container snapping_pairs;
+
+#if !defined(CGAL_LINKED_WITH_TBB)
+  CGAL_static_assertion_msg (!(std::is_convertible<ConcurrencyTag, Parallel_tag>::value),
+                             "Parallel_tag is enabled but TBB is unavailable.");
+#else
+  if(std::is_convertible<ConcurrencyTag, Parallel_tag>::value)
+  {
+    typedef std::pair<Unique_vertex_ptr, Unique_vertex_ptr>                           Unique_vertex_pair;
+    typedef tbb::concurrent_vector<Unique_vertex_pair>                                Unique_vertex_pairs;
+    typedef std::back_insert_iterator<Unique_vertex_pairs>                            UVP_output_iterator;
+
+    Unique_vertex_pairs uv_pairs;
+    Intersecting_boxes_pairs_report<UVP_output_iterator> callback(std::back_inserter(uv_pairs));
+
+    CGAL::Real_timer timer;
+    timer.start();
+
+    // Grab the boxes that are interesecting but don't do any extra filtering (in parallel)
+    CGAL::box_intersection_d<CGAL::Parallel_tag>(boxes_A_ptr.begin(), boxes_A_ptr.end(),
+                                                 boxes_B_ptr.begin(), boxes_B_ptr.end(),
+                                                 callback);
+
+    std::cout << "time for box_d: " << timer.time() << std::endl;
+
+    // Actually filter the range of intersecting boxes now (in parallel)
+    typedef std::vector<std::pair<FT, bool> >                                         Filters;
+    typedef Vertex_proximity_report<Snapping_pair_container,
+                                    PolygonMesh, GT, VPM_A, VPM_B,
+                                    ToleranceMap_A, ToleranceMap_B,
+                                    VertexPatchMap_A, VertexPatchMap_B,
+                                    Box, Unique_vertex_pairs, Filters>                Reporter;
+
+    Filters to_keep(uv_pairs.size());
+    Reporter proximity_filterer(snapping_pairs, tm_A, tolerance_map_A, vertex_patch_map_A, vpm_A,
+                                                tm_B, tolerance_map_B, vertex_patch_map_B, vpm_B,
+                                gt, &uv_pairs, &to_keep);
+    tbb::parallel_for(tbb::blocked_range<std::size_t>(0, uv_pairs.size()), proximity_filterer);
+
+    // Now fill the multi index, sequentially
+    for(std::size_t i=0, uvps = uv_pairs.size(); i<uvps; ++i)
+      if(to_keep[i].second)
+        snapping_pairs.insert(Snapping_pair(uv_pairs[i].first, uv_pairs[i].second, to_keep[i].first));
+  }
+  else
+#endif
+  {
+    typedef Vertex_proximity_report<Snapping_pair_container, PolygonMesh, GT,
+                                    VPM_A, VPM_B, ToleranceMap_A, ToleranceMap_B,
+                                    VertexPatchMap_A, VertexPatchMap_B, Box>          Reporter;
+
+    Reporter vpr(snapping_pairs, tm_A, tolerance_map_A, vertex_patch_map_A, vpm_A,
+                                 tm_B, tolerance_map_B, vertex_patch_map_B, vpm_B, gt);
+
+    // Shenanigans to pass a reference as callback (which is copied by value by 'box_intersection_d')
+    std::function<void(const Box*, const Box*)> callback(std::ref(vpr));
+
+    CGAL::box_intersection_d<CGAL::Sequential_tag>(boxes_A_ptr.begin(), boxes_A_ptr.end(),
+                                                   boxes_B_ptr.begin(), boxes_B_ptr.end(),
+                                                   callback);
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// Done collecting; start matching
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+  if(snapping_pairs.empty())
+    return 0;
+
+  typedef std::pair<Unique_vertex_ptr, Unique_vertex_ptr>                             Unique_vertex_pair;
+  std::vector<Unique_vertex_pair> snappable_vertices_pairs;
+
+  // Sorted views of the container
+  typedef typename Snapping_pair_container::template nth_index<0>::type               Container_by_source;
+  typedef typename Snapping_pair_container::template nth_index<1>::type               Container_by_target;
+  typedef typename Snapping_pair_container::template nth_index<2>::type               Container_by_distance;
+
+  Container_by_source& container_by_source = snapping_pairs.template get<0>();
+  Container_by_target& container_by_target = snapping_pairs.template get<1>();
+  Container_by_distance& container_by_dist = snapping_pairs.template get<2>();
+
+  // @todo this could be a best-match algorithm rather than a greedy algorithm,
+  // but is the increased complexity -and thus runtime- worth it?
+  CGAL_assertion_code(FT prev = -1;)
+  while(!container_by_dist.empty())
+  {
+    const Snapping_pair& sp = *(container_by_dist.begin());
+    Unique_vertex_ptr uv_a = sp.uv_a;
+    Unique_vertex_ptr uv_b = sp.uv_b;
+    CGAL_assertion(sp.sq_dist >= prev);
+    CGAL_assertion_code(prev = sp.sq_dist;)
+
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+    const Point& pa = get(vpm_A, target(uv_a->first.front(), tm_A));
+    const Point& pb = get(vpm_B, target(uv_b->first.front(), tm_B));
+    std::cout << "Snapping (" << pa << ") to (" << pb << ") at dist: " << sp.sq_dist << std::endl;
+    std::cout << "#verts A: " << uv_a->first.size() << " #verts B: " << uv_b->first.size() << std::endl;
+#endif
+
+    snappable_vertices_pairs.emplace_back(uv_a, uv_b);
+
+    // 'va' and 'vb' cannot be used anymore, remove them from the container
+    container_by_source.erase(uv_a);
+    container_by_target.erase(uv_b);
+
+    if((&tm_A == &tm_B))
+    {
+      container_by_source.erase(uv_b);
+      container_by_target.erase(uv_a);
+    }
+  }
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << snappable_vertices_pairs.size() << " snappable pair(s)" << std::endl;
+#endif
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// Done matching; start snapping
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+  std::size_t counter = 0;
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+  std::ofstream out_edges("results/snappable.polylines.txt");
+  out_edges.precision(17);
+#endif
+
+  for(const Unique_vertex_pair& uvp : snappable_vertices_pairs)
+  {
+    Unique_vertex_ptr uv_a = uvp.first;
+    Unique_vertex_ptr uv_b = uvp.second;
+    const Vertex_container& vs_a = uv_a->first;
+    const Vertex_container& vs_b = uv_b->first;
+    const vertex_descriptor va = target(vs_a.front(), tm_A);
+    const vertex_descriptor vb = target(vs_b.front(), tm_B);
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+    out_edges << "2 " << tm_A.point(va) << " " << tm_B.point(vb) << std::endl;
+#endif
+
+    if(!gt.equal_3_object()(get(vpm_A, va), get(vpm_B, vb)))
+    {
+      if(is_second_mesh_fixed)
+      {
+        for(const halfedge_descriptor ha : vs_a)
+          put(vpm_A, target(ha, tm_A), get(vpm_B, vb));
+      }
+      else
+      {
+        // Pick a point that is on the segment [va; vb], with a ratio based on the respective tolerances
+        const FT tol_s = uv_a->second;
+        const FT tol_t = uv_b->second;
+        CGAL_assertion(tol_s != FT(0) || tol_t != FT(0));
+
+        const FT lambda = tol_t / (tol_s + tol_t);
+        const Point new_p = get(vpm_A, va) + lambda * (get(vpm_B, vb) - get(vpm_A, va));
+#ifdef CGAL_PMP_SNAP_DEBUG_PP
+        std::cout << "new position of " << va << " " << vb << " --> " << new_p << std::endl;
+#endif
+
+        for(const halfedge_descriptor ha : vs_a)
+          put(vpm_A, target(ha, tm_A), new_p);
+
+        for(const halfedge_descriptor hb : vs_b)
+          put(vpm_B, target(hb, tm_B), new_p);
+      }
+
+      ++counter;
+    }
+  }
+
+#ifdef CGAL_PMP_SNAP_DEBUG_OUTPUT
+  out_edges.close();
+#endif
+
+#ifdef CGAL_PMP_SNAP_DEBUG
+  std::cout << "Snapped " << counter << " pair(s)!" << std::endl;
+#endif
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  /// Done snapping; start analyzing
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+
+  // Below is used in non-conformal snapping
+  // @todo could avoid doing it if not required
+  //
+  // Now that vertex-vertex snapping has been performed, look around to see if we can already
+  // lock some vertices and halfedges...
+  //
+  // #1 : If a pair of edges (1 incident to va, the other to vb) are already fully matching,
+  //      we don't want to project anything more onto any of those 2 edges
+  // #2 : If pairs on either side of the two matching vertices are compatible (not necessary fully matching),
+  //      then the two vertices should be locked as no better match can be obtained
+  // #3 : If a pair of incident edges are not fully matching, but still have compatible directions
+  //      (i.e. collinear and opposite directions), then we don't want to project onto the shorter
+  //      of the two
+  for(const Unique_vertex_pair& uvp : snappable_vertices_pairs)
+  {
+    Unique_vertex_ptr uv_a = uvp.first;
+    Unique_vertex_ptr uv_b = uvp.second;
+    const Vertex_container& vs_a = uv_a->first;
+    const Vertex_container& vs_b = uv_b->first;
+
+    // Quadratic, but all halfedges in vs_a and vs_b point to the same point. There shouldn't be many.
+    // @fixme this assumes compatible orientation...
+    for(const halfedge_descriptor ha : vs_a)
+    {
+      for(const halfedge_descriptor hb : vs_b)
+      {
+        if(!is_border(ha, tm_A) || !is_border(hb, tm_B))
+          continue;
+
+        const vertex_descriptor va = target(ha, tm_A);
+        const vertex_descriptor vb = target(hb, tm_B);
+
+        // The two folloing halfedges might not be in the range to snap, but it doesn't matter
+        const halfedge_descriptor nha = next(ha, tm_A);
+        const halfedge_descriptor nhb = next(hb, tm_B);
+        const bool is_stitchable_left = gt.equal_3_object()(get(vpm_A, source(ha, tm_A)),
+                                                            get(vpm_B, target(nhb, tm_B)));
+        const bool is_stitchable_right = gt.equal_3_object()(get(vpm_A, target(nha, tm_A)),
+                                                             get(vpm_B, source(hb, tm_B)));
+        bool is_collinear_left = false;
+        bool is_collinear_right = false;
+
+        if(is_stitchable_left)
+        {
+          *lockable_ha_out++ = ha; // #1
+          *lockable_hb_out++ = nhb; // #1
+          is_collinear_left = true;
+        }
+        else
+        {
+          const vertex_descriptor lva = source(ha, tm_A);
+          const vertex_descriptor lvb = target(nhb, tm_B);
+
+          is_collinear_left = is_collinear_with_tolerance(get(vpm_A, va), get(vpm_A, lva), get(vpm_B, lvb), gt);
+          if(is_collinear_left) // but not stitchable
+          {
+            if(gt.less_distance_to_point_3_object()(get(vpm_A, va), get(vpm_A, lva), get(vpm_B, lvb)))
+              *lockable_ha_out++ = ha; // #2
+            else
+              *lockable_hb_out++ = nhb; // #2
+          }
+        }
+
+        if(is_stitchable_right)
+        {
+          *lockable_ha_out++ = nha; // #1
+          *lockable_hb_out++ = hb; // #1
+          is_collinear_right = true;
+        }
+        else
+        {
+          const vertex_descriptor rva = target(nha, tm_A);
+          const vertex_descriptor rvb = source(hb, tm_B);
+
+          is_collinear_right = is_collinear_with_tolerance(get(vpm_A, va), get(vpm_A, rva), get(vpm_B, rvb), gt);
+          if(is_collinear_right) // but not stitchable
+          {
+            if(gt.less_distance_to_point_3_object()(get(vpm_A, va), get(vpm_A, rva), get(vpm_B, rvb)))
+              *lockable_ha_out++ = nha; // #2
+            else
+              *lockable_hb_out++ = hb; // #2
+          }
+        }
+
+        if(is_collinear_left && is_collinear_right) // #3
+        {
+#ifdef CGAL_PMP_SNAP_DEBUG
+          std::cout << va << " (" << get(vpm_A, va) << ") and " << vb << " (" << get(vpm_B, vb) << ") are locked vertices" << std::endl;
+#endif
+          *lockable_vps_out++ = std::make_pair(va, vb);
+        }
+      }
+    }
+  }
+
+  return counter;
+}
+
+// Convenience overload for snap_borders
+template <typename ConcurrencyTag = CGAL::Sequential_tag,
+          typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename LockableVerticesOutputIterator, typename LockableHalfedgesOutputIterator,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_vertices_two_way(const HalfedgeRange_A& halfedge_range_A,
+                                  PolygonMesh& tm_A,
+                                  ToleranceMap_A tolerance_map_A,
+                                  const HalfedgeRange_B& halfedge_range_B,
+                                  PolygonMesh& tm_B,
+                                  ToleranceMap_B tolerance_map_B,
+                                  LockableVerticesOutputIterator lockable_vps_out,
+                                  LockableHalfedgesOutputIterator lockable_ha_out,
+                                  LockableHalfedgesOutputIterator lockable_hb_out,
+                                  const NamedParameters_A& np_A,
+                                  const NamedParameters_B& np_B)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor             vertex_descriptor;
+
+  using CGAL::parameters::choose_parameter;
+  using CGAL::parameters::get_parameter;
+
+  return snap_vertices_two_way(halfedge_range_A, tm_A, tolerance_map_A,
+                               choose_parameter(get_parameter(np_A, internal_np::vertex_incident_patches),
+                                                Constant_property_map<vertex_descriptor, std::size_t>(-1)),
+                               halfedge_range_B, tm_B, tolerance_map_B,
+                               choose_parameter(get_parameter(np_B, internal_np::vertex_incident_patches),
+                                                Constant_property_map<vertex_descriptor, std::size_t>(-1)),
+                               lockable_vps_out, lockable_ha_out, lockable_hb_out,
+                               choose_parameter(get_parameter(np_B, internal_np::do_lock_mesh), false),
+                               np_A, np_B);
+}
+
+} // namespace internal
+
+namespace experimental {
+
+// \ingroup PMP_repairing_grp
+//
+// Attempts to snap the vertices in `halfedge_range_A` and `halfedge_range_B`.
+// A vertex from the first range and a vertex from the second range are only snapped
+// if the distance between both vertices is smaller than the sum of their user-prescribed tolerance.
+// All such pairs are collected and processed in a greedy order: the two vertices are moved
+// to a common vertex (more on this below), and both vertices are locked and cannot be used
+// in any other matches.
+//
+// \warning This function does not give any guarantee on the conformity between the two meshes after the snapping.
+// \warning This function does not merge vertices or the meshes, it is purely geometric.
+//
+// \tparam PolygonMesh a model of `FaceListGraph` and `MutableFaceGraph`
+// \tparam HalfedgeRange_A a model of `Range` with value type `boost::graph_traits<PolygonMesh>::%halfedge_descriptor`
+// \tparam HalfedgeRange_B a model of `Range` with value type `boost::graph_traits<PolygonMesh>::%halfedge_descriptor`
+// \tparam ToleranceMap_A a model of `ReadablePropertyMap` with key type `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
+//                        and value type `GetGeomTraits<PolygonMesh, NamedParameters_A>::type::FT`
+// \tparam ToleranceMap_B a model of `ReadablePropertyMap` with key type `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
+//                        and value type `GetGeomTraits<PolygonMesh, NamedParameters_A>::type::FT`
+// \tparam NamedParameters_A a sequence of \ref pmp_namedparameters "Named Parameters"
+// \tparam NamedParameters_B a sequence of \ref pmp_namedparameters "Named Parameters"
+//
+// \param halfedge_range_A a range of halfedges of the first mesh defining a set of vertices (as targets of the halfeges)
+// \param tm_A the first mesh to which the vertices in `halfedge_range_A` belong
+// \param tolerance_map_A a tolerance map associating to each vertex of the first range a tolerance value
+// \param halfedge_range_B a range of vertices of the second mesh defining a set of vertices (as targets of the halfeges)
+// \param tolerance_map_B a tolerance map associating to each vertex of the second range a tolerance value
+// \param tm_B the target mesh to which the vertices in `halfedge_range_B` belong
+// \param np_A optional \ref pmp_namedparameters "Named Parameters" related to the source mesh,
+//             amongst those described below:
+//
+// \cgalNamedParamsBegin
+//   \cgalParamBegin{vertex_point_map}
+//     the property map with the points associated to the vertices of the source mesh.
+//     The type of this map is model of `ReadWritePropertyMap`. If this parameter is omitted,
+//     an internal property map for `CGAL::vertex_point_t` must be available in `PolygonMesh`.
+//   \cgalParamEnd
+//   \cgalParamBegin{geom_traits}
+//     a geometric traits class instance, must be a model of `Kernel`
+//   \cgalParamEnd
+// \cgalNamedParamsEnd
+//
+// \param np_B optional \ref pmp_namedparameters "Named Parameters" related to the target mesh,
+//             amongst those described below:
+//
+// \cgalNamedParamsBegin
+//   \cgalParamBegin{vertex_point_map}
+//     the property map with the points associated to the vertices of the target mesh.
+//     The type of this map is model of `ReadablePropertyMap`. If this parameter is omitted,
+//     an internal property map for `CGAL::vertex_point_t` must be available in `PolygonMesh`.
+//   \cgalParamEnd
+// \cgalNamedParamsEnd
+//
+// \return the number of snapped vertex pairs
+//
+template <typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B,
+          typename NamedParameters_A, typename NamedParameters_B>
+std::size_t snap_vertices(const HalfedgeRange_A& halfedge_range_A,
+                          PolygonMesh& tm_A,
+                          ToleranceMap_A tolerance_map_A,
+                          const HalfedgeRange_B& halfedge_range_B,
+                          PolygonMesh& tm_B,
+                          ToleranceMap_B tolerance_map_B,
+                          const NamedParameters_A& np_A,
+                          const NamedParameters_B& np_B)
+{
+  CGAL::Emptyset_iterator unused_output_iterator;
+
+  return internal::snap_vertices_two_way(halfedge_range_A, tm_A, tolerance_map_A,
+                                         halfedge_range_B, tm_B, tolerance_map_B,
+                                         unused_output_iterator, unused_output_iterator,
+                                         unused_output_iterator, np_A, np_B);
+}
+
+template <typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh,
+          typename ToleranceMap_A, typename ToleranceMap_B>
+std::size_t snap_vertices(const HalfedgeRange_A& halfedge_range_A,
+                          PolygonMesh& tm_A,
+                          ToleranceMap_A tolerance_map_A,
+                          const HalfedgeRange_B& halfedge_range_B,
+                          PolygonMesh& tm_B,
+                          ToleranceMap_B tolerance_map_B)
+{
+  return snap_vertices(halfedge_range_A, tm_A, tolerance_map_A, halfedge_range_B, tm_B, tolerance_map_B,
+                       CGAL::parameters::all_default(), CGAL::parameters::all_default());
+}
+
+template <typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh,
+          typename T_A, typename Tag_A, typename Base_A,
+          typename T_B, typename Tag_B, typename Base_B>
+std::size_t snap_vertices(const HalfedgeRange_A& halfedge_range_A,
+                          PolygonMesh& tm_A,
+                          const HalfedgeRange_B& halfedge_range_B,
+                          PolygonMesh& tm_B,
+                          const CGAL::Named_function_parameters<T_A, Tag_A, Base_A>& np_A,
+                          const CGAL::Named_function_parameters<T_B, Tag_B, Base_B>& np_B)
+{
+  typedef CGAL::Named_function_parameters<T_A, Tag_A, Base_A>                         NamedParameters_A;
+  typedef typename GetGeomTraits<PolygonMesh, NamedParameters_A>::type                GT;
+  typedef typename GT::FT                                                             FT;
+  typedef CGAL::dynamic_vertex_property_t<FT>                                         Vertex_property_tag;
+  typedef typename boost::property_map<PolygonMesh, Vertex_property_tag>::type        Tolerance_map;
+
+  const FT max_tol(std::numeric_limits<double>::max());
+
+  Tolerance_map tolerance_map_A = get(Vertex_property_tag(), tm_A);
+  internal::assign_tolerance_with_local_edge_length_bound(halfedge_range_A, tolerance_map_A, max_tol, tm_A, np_A);
+  Tolerance_map tolerance_map_B = get(Vertex_property_tag(), tm_B);
+  internal::assign_tolerance_with_local_edge_length_bound(halfedge_range_B, tolerance_map_B, max_tol, tm_B, np_B);
+
+  return snap_vertices(halfedge_range_A, tm_A, tolerance_map_A, halfedge_range_B, tm_B, tolerance_map_B, np_A, np_B);
+}
+
+template <typename HalfedgeRange_A, typename HalfedgeRange_B, typename PolygonMesh>
+std::size_t snap_vertices(const HalfedgeRange_A& halfedge_range_A,
+                          PolygonMesh& tm_A,
+                          const HalfedgeRange_B& halfedge_range_B,
+                          PolygonMesh& tm_B)
+{
+  return snap_vertices(halfedge_range_A, tm_A, halfedge_range_B, tm_B,
+                       parameters::all_default(), parameters::all_default());
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+/// Border convenience overloads
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <typename PolygonMesh, typename ToleranceMap_A, typename ToleranceMap_B>
+std::size_t snap_border_vertices(PolygonMesh& tm_A,
+                                 ToleranceMap_A tolerance_map_A,
+                                 PolygonMesh& tm_B,
+                                 ToleranceMap_B tolerance_map_B)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
+
+  std::vector<halfedge_descriptor> border_A;
+  border_halfedges(tm_A, std::back_inserter(border_A));
+  std::vector<halfedge_descriptor> border_B;
+  border_halfedges(tm_B, std::back_inserter(border_B));
+
+  return snap_vertices(border_A, tm_A, tolerance_map_A,
+                       border_B, tm_B, tolerance_map_B);
+}
+
+template <typename PolygonMesh>
+std::size_t snap_border_vertices(PolygonMesh& tm_A,
+                                 PolygonMesh& tm_B)
+{
+  typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor    halfedge_descriptor;
+
+  std::vector<halfedge_descriptor> border_vertices_A;
+  border_halfedges(tm_A, std::back_inserter(border_vertices_A));
+
+  std::vector<halfedge_descriptor> border_vertices_B;
+  border_halfedges(tm_B, std::back_inserter(border_vertices_B));
+
+  return snap_vertices(border_vertices_A, tm_A, border_vertices_B, tm_B);
+}
+
+template <typename PolygonMesh, typename ToleranceMap>
+std::size_t snap_border_vertices(PolygonMesh& tm, ToleranceMap tolerance_map)
+{
+  return snap_border_vertices(tm, tolerance_map, tm, tolerance_map);
+}
+
+template <typename PolygonMesh>
+std::size_t snap_border_vertices(PolygonMesh& tm)
+{
+  return snap_border_vertices(tm, tm);
+}
+
+} // namespace experimental
+} // namespace Polygon_mesh_processing
+} // namespace CGAL
+
+#endif // CGAL_POLYGON_MESH_PROCESSING_SNAPPING_SNAP_VERTICES_H
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/merge_border_vertices.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/merge_border_vertices.h
index 891882f13d0..da6fb04d54e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/merge_border_vertices.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/merge_border_vertices.h
@@ -109,7 +109,7 @@ void detect_identical_mergeable_vertices(
 
   // check that intervals are disjoint or strictly nested
   // if there is only one issue we drop the whole cycle.
-  /// \todo shall we try to be more conservative?
+  // @todo shall we try to be more conservative?
   if (hedges_with_identical_point_target.empty()) return;
   std::set< std::pair<std::size_t, std::size_t> >::iterator it1 = intervals.begin(),
                                                             end2 = intervals.end(),
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
index 182a9a866f7..b70eefd073e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
@@ -438,8 +438,6 @@ void recursive_orient_volume_ccs( TriangleMesh& tm,
 * inward or outward oriented.
 *
 * @tparam TriangleMesh a model of `FaceListGraph` and `MutableFaceGraph` .
-*                      If `TriangleMesh` has an internal property map for `CGAL::face_index_t`,
-*                      as a named parameter, then it must be initialized.
 * @tparam NamedParameters a sequence of \ref pmp_namedparameters
 *
 * @param tm a closed triangulated surface mesh
@@ -461,16 +459,15 @@ void recursive_orient_volume_ccs( TriangleMesh& tm,
 * \cgalNamedParamsEnd
 */
 template<class TriangleMesh, class NamedParameters>
-void orient(TriangleMesh& tm, const NamedParameters& np)
+void orient(TriangleMesh& tm,
+            const NamedParameters& np)
 {
-  typedef boost::graph_traits<TriangleMesh> Graph_traits;
-  typedef typename Graph_traits::vertex_descriptor vertex_descriptor;
-  typedef typename Graph_traits::face_descriptor face_descriptor;
-  typedef typename Graph_traits::halfedge_descriptor halfedge_descriptor;
-  typedef typename GetVertexPointMap<TriangleMesh,
-      NamedParameters>::const_type Vpm;
-  typedef typename GetFaceIndexMap<TriangleMesh,
-      NamedParameters>::const_type Fid_map;
+  typedef boost::graph_traits<TriangleMesh>                                        Graph_traits;
+  typedef typename Graph_traits::vertex_descriptor                                 vertex_descriptor;
+  typedef typename Graph_traits::face_descriptor                                   face_descriptor;
+  typedef typename Graph_traits::halfedge_descriptor                               halfedge_descriptor;
+  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::const_type    Vpm;
+  typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::type FaceIndexMap;
 
   CGAL_assertion(is_triangle_mesh(tm));
   CGAL_assertion(is_valid_polygon_mesh(tm));
@@ -484,8 +481,7 @@ void orient(TriangleMesh& tm, const NamedParameters& np)
   Vpm vpm = CGAL::parameters::choose_parameter(get_parameter(np, internal_np::vertex_point),
                          get_const_property_map(boost::vertex_point, tm));
 
-  Fid_map fid_map = CGAL::parameters::choose_parameter(get_parameter(np, internal_np::face_index),
-                                 get_const_property_map(boost::face_index, tm));
+  FaceIndexMap fid_map = CGAL::get_initialized_face_index_map(tm, np);
 
   std::vector<std::size_t> face_cc(num_faces(tm), std::size_t(-1));
 
@@ -542,8 +538,6 @@ void orient(TriangleMesh& tm)
  * See \ref coref_def_subsec for a precise definition.
  *
  * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
- *                      If `TriangleMesh` has an internal property map for `CGAL::face_index_t`,
- *                      as a named parameter, then it must be initialized.
  * @tparam NamedParameters a sequence of \ref pmp_namedparameters
  *
  * @param tm a closed triangulated surface mesh
@@ -569,20 +563,20 @@ void orient(TriangleMesh& tm)
  */
 template <class TriangleMesh, class NamedParameters>
 void orient_to_bound_a_volume(TriangleMesh& tm,
-                                        const NamedParameters& np)
+                              const NamedParameters& np)
 {
-  typedef boost::graph_traits<TriangleMesh> Graph_traits;
-  typedef typename Graph_traits::vertex_descriptor vertex_descriptor;
-  typedef typename GetVertexPointMap<TriangleMesh,
-      NamedParameters>::const_type Vpm;
-  typedef typename GetFaceIndexMap<TriangleMesh,
-      NamedParameters>::const_type Fid_map;
-  typedef typename Kernel_traits<
-      typename boost::property_traits<Vpm>::value_type >::Kernel Kernel;
+  typedef boost::graph_traits<TriangleMesh>                                        Graph_traits;
+  typedef typename Graph_traits::vertex_descriptor                                 vertex_descriptor;
+
+  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::const_type    Vpm;
+  typedef typename boost::property_traits<Vpm>::value_type                         Point;
+  typedef typename Kernel_traits<Point>::Kernel                                    Kernel;
+
+  typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::type FaceIndexMap;
+
   if (!is_closed(tm)) return;
   if (!is_triangle_mesh(tm)) return;
 
-
   using parameters::get_parameter;
 
   bool orient_outward = CGAL::parameters::choose_parameter(
@@ -591,8 +585,7 @@ void orient_to_bound_a_volume(TriangleMesh& tm,
   Vpm vpm = CGAL::parameters::choose_parameter(get_parameter(np, internal_np::vertex_point),
                          get_const_property_map(boost::vertex_point, tm));
 
-  Fid_map fid_map = CGAL::parameters::choose_parameter(get_parameter(np, internal_np::face_index),
-                                 get_const_property_map(boost::face_index, tm));
+  FaceIndexMap fid_map = CGAL::get_initialized_face_index_map(tm, np);
 
   std::vector<std::size_t> face_cc(num_faces(tm), std::size_t(-1));
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
index c5a1b649f89..5290d6b03fc 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
@@ -41,9 +41,7 @@ namespace Polygon_mesh_processing {
 *         The descriptor types `boost::graph_traits<PolygonMesh>::%face_descriptor`
 *         and `boost::graph_traits<PolygonMesh>::%halfedge_descriptor` must be
 *         models of `Hashable`.
-*         If `PolygonMesh` has an internal property map for `CGAL::face_index_t`,
-*         and no `face_index_map` is given
-*         as a named parameter, then the internal one must be initialized
+*
 * @tparam FaceRange range of `boost::graph_traits<PolygonMesh>::%face_descriptor`,
           model of `Range`. Its iterator type is `ForwardIterator`.
 * @tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
@@ -160,9 +158,8 @@ void isotropic_remeshing(const FaceRange& faces
   VPMap vpmap = choose_parameter(get_parameter(np, internal_np::vertex_point),
                              get_property_map(vertex_point, pmesh));
 
-  typedef typename GetFaceIndexMap<PM, NamedParameters>::type FIMap;
-  FIMap fimap = choose_parameter(get_parameter(np, internal_np::face_index),
-                           get_property_map(face_index, pmesh));
+  typedef typename GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::type FIMap;
+  FIMap fimap = CGAL::get_initialized_face_index_map(pmesh, np);
 
   typedef typename internal_np::Lookup_named_param_def <
       internal_np::edge_is_constrained_t,
@@ -338,9 +335,8 @@ void split_long_edges(const EdgeRange& edges
   VPMap vpmap = choose_parameter(get_parameter(np, internal_np::vertex_point),
                              get_property_map(vertex_point, pmesh));
 
-  typedef typename GetFaceIndexMap<PM, NamedParameters>::type FIMap;
-  FIMap fimap = choose_parameter(get_parameter(np, internal_np::face_index),
-                             get_property_map(face_index, pmesh));
+  typedef typename GetInitializedFaceIndexMap<PolygonMesh, NamedParameters>::type FIMap;
+  FIMap fimap = CGAL::get_initialized_face_index_map(pmesh, np);
 
   typedef typename internal_np::Lookup_named_param_def <
         internal_np::edge_is_constrained_t,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
index f635af7bc95..3f2e8a6c03d 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
@@ -111,10 +111,6 @@ std::size_t remove_isolated_vertices(PolygonMesh& pmesh)
 /// As a consequence of the last sentence, the area or volume criteria can be disabled
 /// by passing zero (`0`) as threshold value.
 ///
-/// Property maps for `CGAL::face_index_t` and `CGAL::vertex_index_t`
-/// must be either available as internal property maps
-/// to `tmesh` or provided as \ref pmp_namedparameters "Named Parameters".
-///
 /// \tparam TriangleMesh a model of `FaceListGraph` and `MutableFaceGraph`
 /// \tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
 ///
@@ -129,8 +125,6 @@ std::size_t remove_isolated_vertices(PolygonMesh& pmesh)
 ///   \cgalParamBegin{edge_is_constrained_map} a property map containing the constrained-or-not status of each edge of `pmesh` \cgalParamEnd
 ///   \cgalParamBegin{face_index_map} a property map containing the index of each face of `tmesh` \cgalParamEnd
 ///   \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of `tmesh`.
-///                                     If this parameter is omitted, an internal property map for
-///                                     `CGAL::vertex_point_t` should be available in `TriangleMesh` \cgalParamEnd
 ///    \cgalParamBegin{geom_traits} an instance of a geometric traits class, model of `Kernel` \cgalParamEnd
 ///    \cgalParamBegin{dry_run} a Boolean parameter. If set to `true`, the mesh will not be altered,
 ///                             but the number of components that would be removed is returned. The default value is `false`.\cgalParamEnd
@@ -162,9 +156,8 @@ std::size_t remove_connected_components_of_negligible_size(TriangleMesh& tmesh,
   const VPM vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
                                    get_const_property_map(CGAL::vertex_point, tmesh));
 
-  typedef typename GetFaceIndexMap<TriangleMesh, NamedParameters>::type            FaceIndexMap;
-  FaceIndexMap fim = choose_parameter(get_parameter(np, internal_np::face_index),
-                                      get_property_map(boost::face_index, tmesh));
+  typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::type FaceIndexMap;
+  FaceIndexMap fim = CGAL::get_initialized_face_index_map(tmesh, np);
 
   FT area_threshold = choose_parameter(get_parameter(np, internal_np::area_threshold), FT(-1));
   FT volume_threshold = choose_parameter(get_parameter(np, internal_np::volume_threshold), FT(-1));
@@ -992,7 +985,7 @@ bool remove_degenerate_edges(const EdgeRange& edge_range,
           vertex_descriptor vd = remove_a_border_edge(ed, tmesh, degenerate_edges_to_remove, face_set);
           if (vd == GT::null_vertex())
           {
-            // TODO: if some border edges are later removed, the edge might be processable later
+            // @todo: if some border edges are later removed, the edge might be processable later
             // for example if it belongs to  boundary cycle of edges where the number of non-degenerate
             // edges is 2. That's what happen with fused_vertices.off in the testsuite where the edges
             // are not processed the same way with Polyhedron and Surface_mesh. In the case of Polyhedron
@@ -1198,7 +1191,7 @@ bool remove_degenerate_edges(const EdgeRange& edge_range,
           }
           while(true);
 
-          /// \todo use the area criteria? this means maybe continue exploration of larger cc
+          // @todo use the area criteria? this means maybe continue exploration of larger cc
           // mark faces of completetly explored cc
           for (index=0; index< nb_cc; ++index)
           {
@@ -1369,15 +1362,15 @@ bool remove_degenerate_edges(TriangleMesh& tmesh)
 //         - `Compare_distance_3` to compute the distance between 2 points
 //         - `Collinear_3` to check whether 3 points are collinear
 //         - `Less_xyz_3` to compare lexicographically two points
-///        - `Equal_3` to check whether 2 points are identical.
-///       For each functor Foo, a function `Foo foo_object()` must be provided.
+//        - `Equal_3` to check whether 2 points are identical.
+//       For each functor Foo, a function `Foo foo_object()` must be provided.
 //   \cgalParamEnd
 // \cgalNamedParamsEnd
 //
-// \todo the function might not be able to remove all degenerate faces.
+// @todo the function might not be able to remove all degenerate faces.
 //       We should probably do something with the return type.
 //
-/// \return `true` if all degenerate faces were successfully removed, and `false` otherwise.
+// \return `true` if all degenerate faces were successfully removed, and `false` otherwise.
 template <typename FaceRange, typename TriangleMesh, typename NamedParameters>
 bool remove_degenerate_faces(const FaceRange& face_range,
                              TriangleMesh& tmesh,
@@ -1478,7 +1471,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
   // Then, remove triangles made of 3 collinear points
 
   // start by filtering out border faces
-  // TODO: shall we avoid doing that in case a non-manifold vertex on the boundary or if a whole component disappear?
+  // @todo: shall we avoid doing that in case a non-manifold vertex on the boundary or if a whole component disappear?
   std::set<face_descriptor> border_deg_faces;
   for(face_descriptor f : degenerate_face_set)
   {
@@ -1685,7 +1678,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
           all_removed=false;
 #ifdef CGAL_PMP_REMOVE_DEGENERATE_FACES_DEBUG
           std::cout << "  WARNING: flip is not possible\n";
-          // \todo Let p and q be the vertices opposite to `edge_to_flip`, and let
+          // @todo Let p and q be the vertices opposite to `edge_to_flip`, and let
           //       r be the vertex of `edge_to_flip` that is the furthest away from
           //       the edge `pq`. In that case I think we should remove all the triangles
           //       so that the triangle pqr is in the mesh.
@@ -1786,7 +1779,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
           (cc_faces.size()+boundary_hedges.size())/2 != 1)
       {
         //cc_faces does not define a topological disk
-        /// \todo Find to way to handle that case
+        // @todo Find to way to handle that case
 #ifdef CGAL_PMP_REMOVE_DEGENERATE_FACES_DEBUG
         std::cout << "  WARNING: Cannot remove the component of degenerate faces: not a topological disk.\n";
 #endif
@@ -1932,7 +1925,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
       CGAL_assertion(get(vpmap,source(side_one.front(), tmesh))==side_points.front());
       CGAL_assertion(get(vpmap,target(side_one.back(), tmesh))==side_points.back());
 
-      //\todo the reordering could lead to the apparition of null edges.
+      // @todo the reordering could lead to the apparition of null edges.
       std::sort(side_points.begin(), side_points.end());
 
       CGAL_assertion(std::unique(side_points.begin(), side_points.end())==side_points.end());
@@ -1950,7 +1943,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
       CGAL_assertion(get(vpmap,source(side_two.front(), tmesh))==side_points.front());
       CGAL_assertion(get(vpmap,target(side_two.back(), tmesh))==side_points.back());
 
-      //\todo the reordering could lead to the apparition of null edges.
+      // @todo the reordering could lead to the apparition of null edges.
       std::sort(side_points.begin(), side_points.end());
 
       CGAL_assertion(std::unique(side_points.begin(), side_points.end())==side_points.end());
@@ -2993,7 +2986,7 @@ remove_self_intersections_one_step(TriangleMesh& tm,
         vertex_descriptor v = source(h, tm);
         hole_points.push_back( get(vpmap, v) );
         border_vertices.push_back(v);
-        third_points.push_back(get(vpmap, target(next(opposite(h, tm), tm), tm))); // TODO fix me for mesh border edges
+        third_points.push_back(get(vpmap, target(next(opposite(h, tm), tm), tm))); // @todo fix me for mesh border edges
       }
       CGAL_assertion(hole_points.size() >= 3);
 
@@ -3195,7 +3188,7 @@ bool remove_self_intersections(TriangleMesh& tm, const NamedParameters& np)
     {
       typedef std::pair<face_descriptor, face_descriptor> Face_pair;
       std::vector<Face_pair> self_inter;
-      // TODO : possible optimization to reduce the range to check with the bbox
+      // @todo : possible optimization to reduce the range to check with the bbox
       // of the previous patches or something.
       self_intersections(tm, std::back_inserter(self_inter));
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_polygon_soup.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_polygon_soup.h
index 096f1f60b08..8e4fc9c6f42 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_polygon_soup.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_polygon_soup.h
@@ -567,7 +567,8 @@ std::size_t merge_duplicate_points_in_polygon_soup(PointRange& points,
   const std::size_t removed_points_n = ini_points_n - points.size();
 
 #ifdef CGAL_PMP_REPAIR_POLYGON_SOUP_VERBOSE
-  std::cout << "Removed (merged) " << removed_points_n << " duplicate points" << std::endl;
+  if(removed_points_n > 0)
+    std::cout << "Removed (merged) " << removed_points_n << " duplicate points" << std::endl;
 #endif
 
   return removed_points_n;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
index 6a2a519fca4..9e565d205f8 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
@@ -185,10 +185,8 @@ collect_duplicated_stitchable_boundary_edges
   if(per_cc)
   {
     cc = get(Face_property_tag(), pmesh);
-    typedef typename GetFaceIndexMap<PM, CGAL_PMP_NP_CLASS>::const_type FIMap;
-    FIMap fim = parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                                             get_const_property_map(face_index, pmesh));
-    num_component = num_component_wrapper(pmesh, cc, fim);
+
+    num_component = num_component_wrapper(pmesh, cc, CGAL::get_initialized_face_index_map(pmesh, np));
     border_edges_per_cc.resize(num_component);
   }
   
@@ -862,16 +860,18 @@ std::size_t stitch_borders(PolygonMesh& pmesh,
 /// @param np optional sequence of \ref pmp_namedparameters "Named Parameters" among the ones listed below
 ///
 /// \cgalNamedParamsBegin
-///    \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of `pmesh`.
-/// If this parameter is omitted, an internal property map for
-/// `CGAL::vertex_point_t` must be available in `PolygonMesh`.\cgalParamEnd
-/// \cgalParamBegin{apply_per_connected_component}
-///  specifies if the borders should only be stitched inside their own connected component.
-/// In that case, a property map for `CGAL::face_index_t` should be either available as an internal property map 
-/// to `pmesh` or provided as the \ref pmp_namedparameters "Named Parameter" `face_index_map`. If this is not the case, 
-/// a default map will be created on the fly.
-/// Default value is `false`.\cgalParamEnd
-/// \cgalParamBegin{face_index_map} a property map containing the index of each face of `pmesh` \cgalParamEnd
+///   \cgalParamBegin{vertex_point_map}
+///     the property map with the points associated to the vertices of `pmesh`.
+///     If this parameter is omitted, an internal property map for
+///     `CGAL::vertex_point_t` must be available in `PolygonMesh`.
+///   \cgalParamEnd
+///   \cgalParamBegin{apply_per_connected_component}
+///     specifies if the borders should only be stitched inside their own connected component.
+///     Default value is `false`.
+///   \cgalParamEnd
+///   \cgalParamBegin{face_index_map}
+///     a property map containing for each face of `pmesh` a unique index between `0` and `num_faces(pmesh)-1`
+///   \cgalParamEnd
 /// \cgalNamedParamsEnd
 ///
 /// @return the number of pairs of halfedges that were stitched.
@@ -892,7 +892,7 @@ std::size_t stitch_borders(PolygonMesh& pmesh,
 
   typedef typename GetVertexPointMap<PolygonMesh, CGAL_PMP_NP_CLASS>::const_type VPMap;
   VPMap vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
-                           get_const_property_map(vertex_point, pmesh));
+                               get_const_property_map(vertex_point, pmesh));
 
 #ifdef CGAL_PMP_STITCHING_DEBUG
   std::cout << "------- Stitch cycles..." << std::endl;
diff --git a/Polygon_mesh_processing/include/CGAL/Rigid_triangle_mesh_collision_detection.h b/Polygon_mesh_processing/include/CGAL/Rigid_triangle_mesh_collision_detection.h
index ec20752cf83..2ce1278e7ae 100644
--- a/Polygon_mesh_processing/include/CGAL/Rigid_triangle_mesh_collision_detection.h
+++ b/Polygon_mesh_processing/include/CGAL/Rigid_triangle_mesh_collision_detection.h
@@ -537,11 +537,8 @@ public:
       std::vector<std::size_t> cc_ids(num_faces(tm));
 
       // face index map
-      typedef typename CGAL::GetFaceIndexMap<TriangleMesh, NamedParameters>::type Fid_map;
-
-      Fid_map fid_map =
-        parameters::choose_parameter(parameters::get_parameter(np, internal_np::face_index),
-                            get_const_property_map(boost::face_index, tm));
+      typedef typename GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::const_type FaceIndexMap;
+      FaceIndexMap fid_map = CGAL::get_initialized_face_index_map(tm, np);
 
       std::size_t nb_cc =
         Polygon_mesh_processing::connected_components(
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/CMakeLists.txt b/Polygon_mesh_processing/test/Polygon_mesh_processing/CMakeLists.txt
index b708ac434a8..6e480fbbdd2 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/CMakeLists.txt
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/CMakeLists.txt
@@ -35,14 +35,16 @@ find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
 find_package( TBB )
 
 if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-
   # Creating entries for all .cpp/.C files with "main" routine
   # ##########################################################
   create_single_source_cgal_program("fairing_test.cpp")
+  CGAL_target_use_Eigen(fairing_test)
   create_single_source_cgal_program("triangulate_hole_Polyhedron_3_no_delaunay_test.cpp" )
+  CGAL_target_use_Eigen(triangulate_hole_Polyhedron_3_no_delaunay_test)
   create_single_source_cgal_program("triangulate_hole_Polyhedron_3_test.cpp")
+  CGAL_target_use_Eigen(triangulate_hole_Polyhedron_3_test)
   create_single_source_cgal_program("test_shape_smoothing.cpp")
+  CGAL_target_use_Eigen(test_shape_smoothing)
 
 endif(EIGEN3_FOUND)
 
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/connected_component_polyhedron.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/connected_component_polyhedron.cpp
index 4a9fcec8ec7..35a7e3a75f0 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/connected_component_polyhedron.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/connected_component_polyhedron.cpp
@@ -37,8 +37,8 @@ void mesh_with_id(const char* argv1, const bool save_output)
   std::cerr << cc.size() << " faces in the CC of " << &*fd << std::endl;
 
   boost::vector_property_map<int,
-    boost::property_map<Mesh_with_id, boost::face_index_t>::type>
-      fccmap(get(boost::face_index,sm));
+    boost::property_map<Mesh_with_id, CGAL::face_index_t>::type>
+      fccmap(get(CGAL::face_index,sm));
 
   std::size_t num = PMP::connected_components(sm, fccmap);
   if (strcmp(argv1, "data/blobby_3cc.off") == 0)
@@ -84,17 +84,17 @@ void mesh_no_id(const char* argv1, const bool save_output)
   PMP::connected_component(fd, sm, std::back_inserter(cc));
 
   std::cerr << cc.size() << " faces in the CC of " << &*fd << std::endl;
-  boost::property_map<Mesh,boost::vertex_external_index_t>::type vim 
+  boost::property_map<Mesh,boost::vertex_external_index_t>::type vim
     = get(boost::vertex_external_index,sm);
 
-  boost::property_map<Mesh,boost::face_external_index_t>::type fim 
+  boost::property_map<Mesh,boost::face_external_index_t>::type fim
     = get(boost::face_external_index,sm);
 
   boost::vector_property_map<int,
     boost::property_map<Mesh, boost::face_external_index_t>::type>
       fccmap(fim);
 
-  std::size_t num = PMP::connected_components(sm, fccmap, PMP::parameters::face_index_map(fim));
+  std::size_t num = PMP::connected_components(sm, fccmap);
 
   if (strcmp(argv1, "data/blobby_3cc.off") == 0)
     assert(num == 3);
@@ -104,8 +104,7 @@ void mesh_no_id(const char* argv1, const bool save_output)
   //  std::cout  << &*f << " in connected component " << fccmap[f] << std::endl;
   //}
 
-  PMP::keep_largest_connected_components(sm, 2, PMP::parameters::vertex_index_map(vim)
-                                                                .face_index_map(fim));
+  PMP::keep_largest_connected_components(sm, 2, PMP::parameters::vertex_index_map(vim));
   if (save_output)
     return;
 
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/remeshing_test_P_SM_OM.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/remeshing_test_P_SM_OM.cpp
index 1769df9e09c..bed1ad1c583 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/remeshing_test_P_SM_OM.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/remeshing_test_P_SM_OM.cpp
@@ -31,15 +31,21 @@ int main()
   }
 
   {
-  typedef CGAL::Polyhedron_3<Epic> P;
-  std::map<boost::graph_traits<P>::face_descriptor, std::size_t> fim;
-  P p; 
-  std::ifstream in("data/elephant.off");
-  in >> p;
-  PMP::isotropic_remeshing(faces(p),
+    typedef CGAL::Polyhedron_3<Epic> P;
+
+    std::ifstream in("data/elephant.off");
+    P p;
+    in >> p;
+
+    std::map<boost::graph_traits<P>::face_descriptor, std::size_t> fim;
+    std::size_t fid = 0;
+    for(const boost::graph_traits<P>::face_descriptor f : faces(p))
+      fim[f] = fid++;
+
+    PMP::isotropic_remeshing(faces(p),
                              0.02,
-                           p,
-                           PMP::parameters::face_index_map(boost::make_assoc_property_map(fim)));
+                             p,
+                             PMP::parameters::face_index_map(boost::make_assoc_property_map(fim)));
     std::ofstream out("p.off");
     out << p << std::endl;
   }
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_orient_cc.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_orient_cc.cpp
index 34a54ecd273..8f846d3c455 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_orient_cc.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_orient_cc.cpp
@@ -1,5 +1,7 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Surface_mesh.h>
+
+#include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/Polygon_mesh_processing/orientation.h>
 #include <CGAL/Polygon_mesh_processing/corefinement.h>
 
@@ -12,13 +14,13 @@ typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef CGAL::Surface_mesh<Kernel::Point_3> SMesh;
 
 template<class TriangleMesh, class NamedParameters>
-bool test_orientation(TriangleMesh& tm, bool is_positive, const NamedParameters& np)
+bool test_orientation(const TriangleMesh& tm, bool is_positive, const NamedParameters& np)
 {
   typedef boost::graph_traits<TriangleMesh> Graph_traits;
   typedef typename Graph_traits::vertex_descriptor vertex_descriptor;
   typedef typename Graph_traits::face_descriptor face_descriptor;
   typedef typename CGAL::GetVertexPointMap<TriangleMesh, NamedParameters>::const_type Vpm;
-  typedef typename CGAL::GetFaceIndexMap<TriangleMesh, NamedParameters>::const_type Fid_map;
+  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters>::const_type Fid_map;
 
   using CGAL::parameters::choose_parameter;
   using CGAL::parameters::get_parameter;
@@ -26,8 +28,7 @@ bool test_orientation(TriangleMesh& tm, bool is_positive, const NamedParameters&
   Vpm vpm = choose_parameter(get_parameter(np, CGAL::internal_np::vertex_point),
                              CGAL::get_const_property_map(boost::vertex_point, tm));
 
-  Fid_map fid_map = choose_parameter(get_parameter(np, CGAL::internal_np::face_index),
-                                     CGAL::get_const_property_map(boost::face_index, tm));
+  Fid_map fid_map = CGAL::get_initialized_face_index_map(tm, np);
 
   std::vector<std::size_t> face_cc(num_faces(tm), std::size_t(-1));
 
@@ -127,5 +128,6 @@ int main()
     return 1;
   }
 
+  std::cout << "Done!" << std::endl;
   return 0;
 }
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_clip.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_clip.cpp
index 94572946c5a..0fb9319c9f3 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_clip.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_clip.cpp
@@ -22,325 +22,447 @@ template <class TriangleMesh>
 void test()
 {
   // test with a clipper mesh
-  TriangleMesh tm1, tm2;
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/elephant.off") >> tm1;
+    std::ifstream("data-coref/sphere.off") >> tm2;
 
-  std::ifstream input("data-coref/elephant.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/sphere.off");
-  input >> tm2;
-  input.close();
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
 
-  PMP::clip(tm1, tm2,
-            params::clip_volume(false)
-              .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-            params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2))
-  );
-  assert(!CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false).face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(!CGAL::is_closed(tm1));
+  }
 
-  input.open("data-coref/elephant.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/sphere.off");
-  input >> tm2;
-  input.close();
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/elephant.off") >> tm1;
+    std::ifstream("data-coref/sphere.off") >> tm2;
 
-  PMP::clip(tm1, tm2, params::clip_volume(true)
-              .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-            params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
 
+    PMP::clip(tm1, tm2,
+              params::clip_volume(true).face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(CGAL::is_closed(tm1));
+  }
 
   // test with a iso-cuboid
-  input.open("data-coref/elephant.off");
-  input >> tm1;
-  input.close();
-  K::Iso_cuboid_3 iso_cuboid(K::Point_3(0,0,0), K::Point_3(0.4, 0.6, 0.4));
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/elephant.off") >> tm1;
+    K::Iso_cuboid_3 iso_cuboid(K::Point_3(0,0,0), K::Point_3(0.4, 0.6, 0.4));
 
-  PMP::clip(tm1, iso_cuboid, params::clip_volume(true));
-  assert(CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+
+    PMP::clip(tm1, iso_cuboid, params::clip_volume(true).face_index_map(custom_face_index_map_1));
+    assert(CGAL::is_closed(tm1));
+  }
 
   // test with a plane
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    K::Plane_3 plane(0, 0, 1, -1);
 
-  K::Plane_3 plane(0, 0, 1, -1);
+    PMP::clip(tm1, plane, params::clip_volume(true));
+    assert(CGAL::is_closed(tm1));
+  }
 
-  PMP::clip(tm1, plane, params::clip_volume(true));
-  assert(CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    K::Plane_3 plane(0, 0, 1, -1);
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, plane, params::clip_volume(false)
-              .use_compact_clipper(false));
-  assert(!CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
+    PMP::clip(tm1, plane, params::clip_volume(false).use_compact_clipper(false));
+    assert(!CGAL::is_closed(tm1));
+  }
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, plane, params::clip_volume(false)
-                        .use_compact_clipper(true));
-  assert(CGAL::is_closed(tm1));
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    K::Plane_3 plane(0, 0, 1, -1);
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, K::Plane_3(-0.236474, 0.437732, 0.867451, -0.838791), params::clip_volume(true));
-  assert(CGAL::is_closed(tm1));
-  assert(!CGAL::is_empty(tm1));
-  CGAL::clear(tm1);
+    PMP::clip(tm1, plane, params::clip_volume(false).use_compact_clipper(true));
+    assert(CGAL::is_closed(tm1));
+  }
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, K::Plane_3(0, 0, 1, 2));
-  assert(CGAL::is_empty(tm1));
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, K::Plane_3(0, 0, 1, -2));
-  assert(!CGAL::is_empty(tm1));
-  CGAL::clear(tm1);
+    PMP::clip(tm1, K::Plane_3(-0.236474, 0.437732, 0.867451, -0.838791), params::clip_volume(true));
+    assert(CGAL::is_closed(tm1));
+    assert(!CGAL::is_empty(tm1));
+  }
+
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+
+    PMP::clip(tm1, K::Plane_3(0, 0, 1, 2));
+    assert(CGAL::is_empty(tm1));
+  }
+
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+
+    PMP::clip(tm1, K::Plane_3(0, 0, 1, -2));
+    assert(!CGAL::is_empty(tm1));
+  }
 
   // clipping with identity
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::clip(tm1, tm2,params::clip_volume(true)
-                      .use_compact_clipper(true)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(num_vertices(tm1)==8);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    std::ifstream("data-coref/cube.off") >> tm2;
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .use_compact_clipper(false)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(CGAL::is_empty(tm1));
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .use_compact_clipper(true)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(num_vertices(tm1)==8);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    PMP::clip(tm1, tm2,
+              params::clip_volume(true)
+                     .use_compact_clipper(true)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(num_vertices(tm1) == 8);
+  }
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::transform(K::Aff_transformation_3(CGAL::TRANSLATION, K::Vector_3(1,0,0)), tm2);
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .use_compact_clipper(false)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(CGAL::is_empty(tm1));
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    std::ifstream("data-coref/cube.off") >> tm2;
 
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::transform(K::Aff_transformation_3(CGAL::TRANSLATION, K::Vector_3(1,0,0)), tm2);
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .use_compact_clipper(true)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(vertices(tm1).size()==4);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .use_compact_clipper(false)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(CGAL::is_empty(tm1));
+  }
+
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    std::ifstream("data-coref/cube.off") >> tm2;
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .use_compact_clipper(true)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(num_vertices(tm1) == 8);
+  }
+
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    std::ifstream("data-coref/cube.off") >> tm2;
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::transform(K::Aff_transformation_3(CGAL::TRANSLATION, K::Vector_3(1,0,0)), tm2);
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .use_compact_clipper(false)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(CGAL::is_empty(tm1));
+  }
+
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+    std::ifstream("data-coref/cube.off") >> tm2;
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::transform(K::Aff_transformation_3(CGAL::TRANSLATION, K::Vector_3(1,0,0)), tm2);
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .use_compact_clipper(true)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(vertices(tm1).size() == 4);
+  }
 
   // test orientation + patch without input vertex
-  CGAL::make_tetrahedron(
-    K::Point_3(0.53, -1.3, 0.2),
-    K::Point_3(0.53, 1.1, 0.2),
-    K::Point_3(0.53, -1.3, 0.4),
-    K::Point_3(0.73, -1.3, 0.2),
-    tm2);
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(vertices(tm1).size()==6);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
 
-  CGAL::make_tetrahedron(
-    K::Point_3(0.53, -1.3, 0.2),
-    K::Point_3(0.53, 1.1, 0.2),
-    K::Point_3(0.53, -1.3, 0.4),
-    K::Point_3(0.73, -1.3, 0.2),
-    tm2);
-  PMP::reverse_face_orientations(tm2);
-  input.open("data-coref/cube.off");
-  input >> tm1;
-  input.close();
-  PMP::clip(tm1, tm2,params::clip_volume(false)
-                      .face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                     params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(vertices(tm1).size()==6+8);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    CGAL::make_tetrahedron(K::Point_3(0.53, -1.3, 0.2),
+                           K::Point_3(0.53, 1.1, 0.2),
+                           K::Point_3(0.53, -1.3, 0.4),
+                           K::Point_3(0.73, -1.3, 0.2),
+                           tm2);
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(vertices(tm1).size() == 6);
+  }
+
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-coref/cube.off") >> tm1;
+
+    CGAL::make_tetrahedron(K::Point_3(0.53, -1.3, 0.2),
+                           K::Point_3(0.53, 1.1, 0.2),
+                           K::Point_3(0.53, -1.3, 0.4),
+                           K::Point_3(0.73, -1.3, 0.2),
+                           tm2);
+    PMP::reverse_face_orientations(tm2);
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::clip_volume(false)
+                     .face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(vertices(tm1).size() == 6+8);
+  }
 
   // clip meshes with intersection polyline opened
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(1, 0, 0, -2));
-  assert(vertices(tm1).size()==4);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(1, 0, 0, -2));
+    assert(vertices(tm1).size() == 4);
+  }
 
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(-1, 0, 0, 2));
-  assert(vertices(tm1).size()==3);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(-1, 0, 0, 2));
+    assert(vertices(tm1).size() == 3);
+  }
 
   // test with clipper on border edge
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 1, 0), K::Point_3(1, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(0, 1, 0 , 0));
-  assert(vertices(tm1).size()==0);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 1, 0), K::Point_3(1, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(0, 1, 0 , 0));
+    assert(vertices(tm1).size() == 0);
+  }
 
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 1, 0), K::Point_3(1, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(0, -1, 0 , 0));
-  assert(vertices(tm1).size()==4);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 1, 0), K::Point_3(1, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(0, -1, 0 , 0));
+    assert(vertices(tm1).size() == 4);
+  }
 
   // test with clipper on border edge: full triangle
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(0, 0, 1, 0), params::use_compact_clipper(true));
-  assert(vertices(tm1).size()!=0);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(0, 0, 1, 0), params::use_compact_clipper(true));
+    assert(vertices(tm1).size()!=0);
+  }
 
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(0, 0, 1, 0), params::use_compact_clipper(false));
-  assert(vertices(tm1).size()==0);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 4, 0), K::Point_3(4, 0, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(0, 0, 1, 0), params::use_compact_clipper(false));
+    assert(vertices(tm1).size() == 0);
+  }
 
   // test tangencies
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 2, 0), K::Point_3(1, 1, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(1, 0, 0, -1));
-  assert(vertices(tm1).size()==3);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 2, 0), K::Point_3(1, 1, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(1, 0, 0, -1));
+    assert(vertices(tm1).size() == 3);
+  }
 
-  make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 2, 0), K::Point_3(1, 1, 0), tm1 );
-  PMP::clip(tm1, K::Plane_3(-1, 0, 0, 1));
-  assert(vertices(tm1).size()==0);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    make_triangle( K::Point_3(0, 0, 0), K::Point_3(0, 2, 0), K::Point_3(1, 1, 0), tm1 );
+    PMP::clip(tm1, K::Plane_3(-1, 0, 0, 1));
+    assert(vertices(tm1).size() == 0);
+  }
 
-  make_triangle( K::Point_3(0.5, 0, 0.5), K::Point_3(1, 0.5, 0.5), K::Point_3(0.5, 1, 0.5), tm1 );
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::clip(tm1, tm2, params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                      params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(vertices(tm1).size()==3);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+  {
+    TriangleMesh tm1, tm2;
+    make_triangle( K::Point_3(0.5, 0, 0.5), K::Point_3(1, 0.5, 0.5), K::Point_3(0.5, 1, 0.5), tm1 );
+    std::ifstream("data-coref/cube.off") >> tm2;
 
-  make_triangle( K::Point_3(0.5, 0, 0.5), K::Point_3(1, 0.5, 0.5), K::Point_3(0.5, 1, 0.5), tm1 );
-  input.open("data-coref/cube.off");
-  input >> tm2;
-  input.close();
-  PMP::reverse_face_orientations(tm2);
-  PMP::clip(tm1, tm2, params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                      params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(vertices(tm1).size()==0);
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(vertices(tm1).size() == 3);
+  }
+
+  {
+    TriangleMesh tm1, tm2;
+    make_triangle( K::Point_3(0.5, 0, 0.5), K::Point_3(1, 0.5, 0.5), K::Point_3(0.5, 1, 0.5), tm1 );
+    std::ifstream("data-coref/cube.off") >> tm2;
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::reverse_face_orientations(tm2);
+    PMP::clip(tm1, tm2,
+              params::face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(vertices(tm1).size() == 0);
+  }
+
+  // test combinaison of use_compact_clipper and clip_volume
+  {
+    TriangleMesh tm1;
+    std::ifstream("data-coref/cube.off") >> tm1;
+
+    //  -> closed mesh, true/true
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(true).clip_volume(true));
+    assert(faces(tm1).size() == 12);
+    assert(CGAL::is_closed(tm1));
+
+    //  -> closed mesh, false/true
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(false).clip_volume(true));
+    assert(faces(tm1).size() == 12);
+    assert(CGAL::is_closed(tm1));
+
+    //  -> closed mesh, true/false
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(true).clip_volume(false));
+    assert(faces(tm1).size() == 12);
+    assert(CGAL::is_closed(tm1));
+
+    //  -> closed mesh, false/false
+    PMP::clip(tm1, K::Plane_3(1,0,0,-1), params::use_compact_clipper(false).clip_volume(false));
+    assert(faces(tm1).size() == 10);
+    assert(!CGAL::is_closed(tm1));
+
+    // -> open mesh true/true
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(true).clip_volume(true));
+    assert(faces(tm1).size() == 10);
+
+    // -> open mesh true/false
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(true).clip_volume(false));
+    assert(faces(tm1).size() == 10);
+
+    // -> open mesh false/false
+    PMP::clip(tm1, K::Plane_3(-1,0,0,0), params::use_compact_clipper(false).clip_volume(false));
+    assert(faces(tm1).size() == 8);
+
+    // -> open mesh false/true
+    PMP::clip(tm1, K::Plane_3(0,-1,0,0), params::use_compact_clipper(false).clip_volume(true));
+    assert(faces(tm1).size() == 6);
+  }
 
   // test special case
-  input.open("data-clip/tm_1.off");
-  input >> tm1;
-  input.close();
-  input.open("data-clip/clipper_1.off");
-  input >> tm2;
-  input.close();
-  PMP::clip(tm1, tm2, params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm1)),
-                      params::face_index_map(get(CGAL::dynamic_face_property_t<std::size_t>(), tm2)));
-  assert(is_valid_polygon_mesh(tm1));
-  CGAL::clear(tm1);
-  CGAL::clear(tm2);
+  {
+    TriangleMesh tm1, tm2;
+    std::ifstream("data-clip/tm_1.off") >> tm2;
+    std::ifstream("data-clip/clipper_1.off") >> tm2;
+
+    auto custom_face_index_map_1 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm1);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_1, tm1);
+    auto custom_face_index_map_2 = get(CGAL::dynamic_face_property_t<std::size_t>(), tm2);
+    CGAL::BGL::internal::initialize_face_index_map(custom_face_index_map_2, tm2);
+
+    PMP::clip(tm1, tm2,
+              params::face_index_map(custom_face_index_map_1),
+              params::face_index_map(custom_face_index_map_2));
+    assert(is_valid_polygon_mesh(tm1));
+  }
 
   // non-manifold border vertices
-  std::stringstream ss;
-  ss << "OFF\n 5 2 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 0 1 4\n3 1 2 3\n";
-  ss >> tm1;
-  PMP::clip(tm1, K::Plane_3(-1,0,0,2));
-  assert(vertices(tm1).size()==3);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::stringstream ss;
+    ss << "OFF\n 5 2 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 0 1 4\n3 1 2 3\n";
+    ss >> tm1;
+    PMP::clip(tm1, K::Plane_3(-1,0,0,2));
+    assert(vertices(tm1).size() == 3);
+  }
 
-  ss.str(std::string());
-  ss << "OFF\n 7 4 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 3 5\n";
-  ss >> tm1;
-  CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
-  PMP::clip(tm1, K::Plane_3(-1,0,0,2));
-  assert(vertices(tm1).size()==6);
-  CGAL::clear(tm1);
-
-  ss.str(std::string());
-  ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
-  ss >> tm1;
-  for (int i=0;i<3;++i)
+  {
+    TriangleMesh tm1;
+    std::stringstream ss;
+    ss << "OFF\n 7 4 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 3 5\n";
+    ss >> tm1;
     CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
-  PMP::clip(tm1, K::Plane_3(-1,0,0,2));
-  assert(vertices(tm1).size()==7);
-  CGAL::clear(tm1);
+    PMP::clip(tm1, K::Plane_3(-1,0,0,2));
+    assert(vertices(tm1).size() == 6);
+  }
 
-  ss.str(std::string());
-  ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
-  ss >> tm1;
-  for (int i=0;i<3;++i)
-    CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
-  PMP::clip(tm1, K::Plane_3(0,1,0,0));
-  assert(vertices(tm1).size()==3);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::stringstream ss;
+    ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
+    ss >> tm1;
+    for (int i=0;i<3;++i)
+      CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
+    PMP::clip(tm1, K::Plane_3(-1,0,0,2));
+    assert(vertices(tm1).size() == 7);
+  }
 
-  ss.str(std::string());
-  ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
-  ss >> tm1;
-  for (int i=0;i<3;++i)
-    CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
-  PMP::clip(tm1, K::Plane_3(0,-1,0,0));
-  assert(vertices(tm1).size()==7);
-  CGAL::clear(tm1);
+  {
+    TriangleMesh tm1;
+    std::stringstream ss;
+    ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
+    ss >> tm1;
+    for (int i=0;i<3;++i)
+      CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
+    PMP::clip(tm1, K::Plane_3(0,1,0,0));
+    assert(vertices(tm1).size() == 3);
+  }
+
+  {
+    TriangleMesh tm1;
+    std::stringstream ss;
+    ss << "OFF\n 9 7 0\n 0 0 0\n2 0 0\n4 0 0\n4 1 0\n0 1 0\n3 1 0\n 1 1 0\n3 -1 0\n1 -1 0\n3 0 1 4\n3 1 2 3\n3 1 5 6\n3 1 8 7\n3 1 3 5\n3 1 6 4\n3 1 0 8\n";
+    ss >> tm1;
+    for (int i=0;i<3;++i)
+      CGAL::Euler::remove_face(halfedge(*std::prev(faces(tm1).end()),tm1),tm1);
+    PMP::clip(tm1, K::Plane_3(0,-1,0,0));
+    assert(vertices(tm1).size() == 7);
+  }
 }
 
 template <class Mesh>
@@ -396,20 +518,27 @@ void test_split()
 
 int main()
 {
-  std::cout << "running test with Surface_mesh\n";
+  std::cout << "Surface Mesh" << std::endl;
   test<Surface_mesh>();
-  std::cout << "running test with Polyhedron\n";
+
+  std::cout << "Polyhedron" << std::endl;
   test<Polyhedron>();
+  
   std::cout << "running test_split with Surface_mesh\n";
   test_split<Surface_mesh>();
+  
   std::cout << "running test_split_plane with Surface_mesh\n";
   test_split_plane<Surface_mesh>();
+  
   std::cout << "running test_split with Polyhedron\n";
   test_split<Polyhedron>();
+  
   std::cout << "running test_split_plane with Polyhedron\n";
   test_split_plane<Polyhedron>();
 
-  return 0;
+  std::cout << "Done!" << std::endl;
+
+  return EXIT_SUCCESS;
 }
 
 
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_non_conforming_snapping.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_non_conforming_snapping.cpp
index 7bdf106c1fa..5a5964ae604 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_non_conforming_snapping.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_non_conforming_snapping.cpp
@@ -1,3 +1,6 @@
+//#define CGAL_PMP_SNAP_DEBUG_PP
+//#define CGAL_PMP_SNAP_DEBUG_OUTPUT
+
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 
@@ -68,6 +71,7 @@ void read_mesh(const char* filename,
 template <typename Kernel, typename Mesh>
 void test(const char* filename,
           const double large_tolerance,
+          const double good_tolerance,
           const double small_tolerance)
 {
   typedef typename boost::graph_traits<Mesh>::vertex_descriptor       vertex_descriptor;
@@ -84,19 +88,19 @@ void test(const char* filename,
 
   // zero tolerance, just to test the API
   CGAL::Constant_property_map<vertex_descriptor, FT> tol_pmap_zero(0);
-  PMP::experimental::snap_border_vertices_non_conforming(sm_cpy, sm_cpy);
-  PMP::experimental::snap_border_vertices_non_conforming(sm_cpy, sm_cpy, tol_pmap_zero);
-  PMP::experimental::snap_border_vertices_non_conforming(sm_cpy, sm_cpy, tol_pmap_zero,
-                                                         CGAL::parameters::geom_traits(Kernel()),
-                                                         CGAL::parameters::geom_traits(Kernel()));
+  PMP::experimental::snap_borders(sm_cpy, sm_cpy);
+  PMP::experimental::snap_borders(sm_cpy, tol_pmap_zero, sm_cpy, tol_pmap_zero);
+  PMP::experimental::snap_borders(sm_cpy, tol_pmap_zero, sm_cpy, tol_pmap_zero,
+                                  CGAL::parameters::geom_traits(Kernel()),
+                                  CGAL::parameters::geom_traits(Kernel()));
 
   // too big, creates wrong snaps
   sm_cpy = sm;
   CGAL::Constant_property_map<vertex_descriptor, FT> tol_pmap_large(large_tolerance);
-  res = PMP::experimental::snap_border_vertices_non_conforming(sm_cpy, tol_pmap_large);
+  res = PMP::experimental::snap_borders(sm_cpy, tol_pmap_large);
   std::cout << "snapped: " << res << std::endl;
 
-  std::ofstream out1("out1.off");
+  std::ofstream out1("too_large.off");
   out1.precision(17);
   out1 << sm_cpy;
   out1.close();
@@ -104,53 +108,64 @@ void test(const char* filename,
   // too small
   sm_cpy = sm;
   CGAL::Constant_property_map<vertex_descriptor, FT> tol_pmap_small(small_tolerance);
-  res = PMP::experimental::snap_border_vertices_non_conforming(sm_cpy, tol_pmap_small,
-                                                               CGAL::parameters::geom_traits(Kernel()));
+  res = PMP::experimental::snap_borders(sm_cpy, tol_pmap_small,
+                                        CGAL::parameters::geom_traits(Kernel()));
   std::cout << "snapped: " << res << std::endl;
 
-  std::ofstream out2("out2.off");
+  std::ofstream out2("too_small.off");
   out2.precision(17);
   out2 << sm_cpy;
   out2.close();
 
-  // automatically computed, custom tolerance at each vertex
   sm_cpy = sm;
-  res = PMP::experimental::snap_border_vertices_non_conforming(sm_cpy);
+  CGAL::Constant_property_map<vertex_descriptor, FT> tol_pmap_good(good_tolerance);
+  res = PMP::experimental::snap_borders(sm_cpy, tol_pmap_good);
   std::cout << "snapped: " << res << std::endl;
 
-  std::ofstream out3("out3.off");
+  std::ofstream out3("good.off");
   out3.precision(17);
   out3 << sm_cpy;
   out3.close();
+
+  // automatically computed, custom tolerance at each vertex
+  sm_cpy = sm;
+  res = PMP::experimental::snap_borders(sm_cpy);
+  std::cout << "snapped: " << res << std::endl;
+
+  std::ofstream out4("custom.off");
+  out4.precision(17);
+  out4 << sm_cpy;
+  out4.close();
 }
 
 void test(const char* filename,
           const double large_tolerance,
+          const double good_tolerance,
           const double small_tolerance)
 {
   std::cout << "######################## TEST FILE: " << filename << " ################## " << std::endl;
 
   std::cout << "~~~~~~~~~~~ TEST EPECK POLYHEDRON ~~~~~~~~~~~" << std::endl;
-  test<EPECK, Exact_polyhedron>(filename, large_tolerance, small_tolerance);
+  test<EPECK, Exact_polyhedron>(filename, large_tolerance, good_tolerance, small_tolerance);
 
   std::cout << std::endl << "~~~~~~~~~~~ TEST EPICK POLYHEDRON ~~~~~~~~~~~" << std::endl;
-  test<EPICK, Polyhedron>(filename, large_tolerance, small_tolerance);
+  test<EPICK, Polyhedron>(filename, large_tolerance, good_tolerance, small_tolerance);
 
   std::cout << std::endl << "~~~~~~~~~~~ TEST EPICK SURFACE MESH ~~~~~~~~~~~" << std::endl;
-  test<EPICK, Surface_mesh>(filename, large_tolerance, small_tolerance);
+  test<EPICK, Surface_mesh>(filename, large_tolerance, good_tolerance, small_tolerance);
 }
 
 int main(int, char**)
 {
-  test("data_snapping/non_conform_snapping.off", 0.02, 0.001);
-  test("data_snapping/non-conform_snapping-hole.off", 0.02, 0.001);
-  test("data_snapping/non_conform_snapping-multiple_ccs.off", 0.02, 0.001);
-  test("data_snapping/non-conform_snapping-overlap.off", 0.02, 0.001);
+  test("data_snapping/non_conform_snapping.off", 0.2, 0.01, 0.0001);
+  test("data_snapping/non-conform_snapping-hole.off", 0.2, 0.01, 0.0001);
+  test("data_snapping/non_conform_snapping-multiple_ccs.off", 0.02, 0.01, 0.0001);
+  test("data_snapping/non-conform_snapping-overlap.off", 0.2, 0.01, 0.0001);
 
-  test("data_snapping/real_data.off", 1., 0.05);
-  test("data_snapping/real_data_2.off", 2, 0.1);
+  test("data_snapping/real_data.off", 1., 0.05, 0.0008);
+  test("data_snapping/real_data_2.off", 2, 0.05, 0.000001);
 
-  test("data_snapping/pig.stl", 20, 0.01);
+  test("data_snapping/pig.stl", 20, 0.3, 0.001);
 
   return EXIT_SUCCESS;
 }
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_snapping.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_snapping.cpp
index 3ae3d761799..5a9a535275d 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_snapping.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_snapping.cpp
@@ -1,3 +1,5 @@
+// #define CGAL_PMP_SNAP_DEBUG_PP
+
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 
@@ -6,6 +8,7 @@
 #include <CGAL/Surface_mesh.h>
 
 #include <CGAL/Polygon_mesh_processing/border.h>
+#include <CGAL/Polygon_mesh_processing/internal/Snapping/helper.h>
 #include <CGAL/Polygon_mesh_processing/internal/Snapping/snap.h>
 
 #include <CGAL/property_map.h>
@@ -37,7 +40,9 @@ void test_1()
   Mesh fg_source, fg_target;
 
   // empty meshes
-  std::size_t res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source, fg_target);
+  std::cout << "Empty meshes tests..." << std::endl;
+
+  std::size_t res = PMP::experimental::snap_border_vertices(fg_source, fg_target);
   assert(res == 0);
 
   std::ifstream source_input("data_snapping/border_snapping_source.off");
@@ -47,17 +52,12 @@ void test_1()
     return;
   }
 
-  std::vector<halfedge_descriptor> border_vertices;
-  PMP::border_halfedges(fg_source, std::back_inserter(border_vertices));
-  std::cout << border_vertices.size() << " border vertices" << std::endl;
-
   // one empty mesh
-  std::cout << "Empty meshes tests..." << std::endl;
-  res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source, fg_target);
+  res = PMP::experimental::snap_border_vertices(fg_source, fg_target);
   std::cout << "res: " << res << " (expected 0)" << std::endl;
   assert(res == 0);
 
-  res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_target, halfedges(fg_source), fg_source);
+  res = PMP::experimental::snap_border_vertices(fg_target, fg_source);
   std::cout << "res: " << res << " (expected 0)" << std::endl;
   assert(res == 0);
 
@@ -72,23 +72,35 @@ void test_1()
 
   // this epsilon value is too small, nothing happens
   std::cout << "*********************** EPS = 0.000000001 *************** " << std::endl;
+
   CGAL::Constant_property_map<vertex_descriptor, FT> tol_map_small(0.000000001);
-  res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source_cpy, fg_target, tol_map_small);
-  res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source_cpy, halfedges(fg_target), fg_target, tol_map_small);
+  res = PMP::experimental::snap_border_vertices(fg_source_cpy, tol_map_small, fg_target, tol_map_small);
+  std::cout << "res: " << res << " (expected 0)" << std::endl;
+  assert(res == 0);
+
+  std::vector<halfedge_descriptor> source_halfedge_range;
+  PMP::internal::vertices_as_halfedges(vertices(fg_source_cpy), fg_source_cpy, std::back_inserter(source_halfedge_range));
+  std::vector<halfedge_descriptor> target_halfedge_range;
+  PMP::internal::vertices_as_halfedges(vertices(fg_target), fg_target, std::back_inserter(target_halfedge_range));
+
+  res = PMP::experimental::snap_vertices(source_halfedge_range, fg_source_cpy, tol_map_small,
+                                         target_halfedge_range, fg_target, tol_map_small);
+
   std::cout << "res: " << res << " (expected 0)" << std::endl;
   assert(res == 0);
 
   // this epsilon value is too big; everything gets snapped!
   std::cout << "*********************** EPS = 0.1 *************** " << std::endl;
-  CGAL::Constant_property_map<vertex_descriptor, FT> tol_map_big(0.1);
-  fg_source_cpy = fg_source;
 
-  border_vertices.clear();
+  fg_source_cpy = fg_source;
+  std::vector<halfedge_descriptor> border_vertices;
   PMP::border_halfedges(fg_source_cpy, std::back_inserter(border_vertices));
 
-  res = PMP::experimental::snap_vertex_range_onto_vertex_range(border_vertices, fg_source_cpy,
-                                                               halfedges(fg_target), fg_target, tol_map_big,
-                                                               params::geom_traits(Kernel()), params::all_default());
+  CGAL::Constant_property_map<vertex_descriptor, FT> tol_map_big(0.1);
+  res = PMP::experimental::snap_vertices(border_vertices, fg_source_cpy, tol_map_big,
+                                         target_halfedge_range, fg_target, tol_map_big,
+                                         params::geom_traits(Kernel()),
+                                         params::do_lock_mesh(true));
 
   std::cout << "res: " << res << " (expected 154)" << std::endl;
   assert(res == 154);
@@ -96,24 +108,28 @@ void test_1()
   // this is a good value of 'epsilon', but not all expected vertices are projected
   // because the sampling of the border of the source mesh is not uniform
   std::cout << "*********************** EPS = 0.001 *************** " << std::endl;
-  CGAL::Constant_property_map<vertex_descriptor, FT> tol_map_good(0.001);
-  fg_source_cpy = fg_source;
 
+  fg_source_cpy = fg_source;
   border_vertices.clear();
   PMP::border_halfedges(fg_source_cpy, std::back_inserter(border_vertices));
 
-  res = PMP::experimental::snap_vertex_range_onto_vertex_range(border_vertices, fg_source_cpy,
-                                                               halfedges(fg_target), fg_target, tol_map_good);
+  CGAL::Constant_property_map<vertex_descriptor, FT> tol_map_good(0.001);
+  res = PMP::experimental::snap_vertices(border_vertices, fg_source_cpy, tol_map_good,
+                                         target_halfedge_range, fg_target, tol_map_good,
+                                         params::all_default(), params::do_lock_mesh(true));
   std::cout << "res: " << res << " vertices" << std::endl;
   assert(res == 76);
 
-  std::ofstream partial_snap_out("partially_snapped_mesh.off");
-  partial_snap_out << std::setprecision(17) << fg_source_cpy;
-
   // this one automatically computes an epsilon bound at each vertex
   std::cout << "*********************** EPS = LOCALLY COMPUTED *************** " << std::endl;
+
   fg_source_cpy = fg_source;
-  res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source_cpy, fg_target);
+  border_vertices.clear();
+  PMP::border_halfedges(fg_source_cpy, std::back_inserter(border_vertices));
+
+  res = PMP::experimental::snap_vertices(border_vertices, fg_source_cpy,
+                                         target_halfedge_range, fg_target,
+                                         params::all_default(), params::do_lock_mesh(true));
   std::cout << "res: " << res << " vertices" << std::endl;
   assert(res == 77);
 
@@ -147,9 +163,11 @@ void test_2()
   // if a target vertex is already occupied, the source vertex will go to the next one that is
   // within tolerance and is available
   CGAL::Constant_property_map<vertex_descriptor, FT> tol_map(0.5);
-  std::size_t res = PMP::experimental::snap_border_vertices_onto_vertex_range(fg_source, fg_target, tol_map);
+  std::size_t res = PMP::experimental::snap_border_vertices(fg_source, tol_map, fg_target, tol_map);
   std::cout << "res: " << res << " vertices" << std::endl;
   assert(res == 3);
+
+  std::ofstream("out.off") << fg_source;
 }
 
 template <typename K, typename Mesh>
diff --git a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/CMakeLists.txt b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/CMakeLists.txt
index 5572052eb2e..20d0abef1c2 100644
--- a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/CMakeLists.txt
+++ b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/CMakeLists.txt
@@ -36,58 +36,35 @@ endif()
 
 include( CGAL_CreateSingleSourceCGALProgram )
 
+find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
+if(NOT EIGEN3_FOUND)
+  message(STATUS "NOTICE: This project requires Eigen 3.1 (or greater) and will not be compiled.")
+  return()
+endif()
+
+find_package(SCIP QUIET)
+if (NOT SCIP_FOUND )
+  find_package( GLPK QUIET)
+  if ( NOT GLPK_FOUND )
+    message( STATUS "NOTICE: This project requires either SCIP or GLPK, and will not be compiled.")
+    return()
+  endif()
+endif()
+
 create_single_source_cgal_program( "polyfit_example_without_input_planes.cpp" )
 create_single_source_cgal_program( "polyfit_example_user_provided_planes.cpp" )
 create_single_source_cgal_program( "polyfit_example_model_complexty_control.cpp" )
 create_single_source_cgal_program( "polyfit_example_with_region_growing.cpp" )
 
-find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if(EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-
-  find_package( SCIP QUIET)
-
-  if ( NOT SCIP_FOUND )
-      find_package( GLPK QUIET)
-
-      if ( NOT GLPK_FOUND )
-        message( STATUS "NOTICE: This project requires either SCIP or GLPK, and will not be compiled. "
-                        "Please provide either 'SCIP_DIR' or 'GLPK_INCLUDE_DIR' and 'GLPK_LIBRARIES'")
-      else()
-        
-
-          include_directories( BEFORE ${GLPK_INCLUDE_DIR} )
-
-          target_link_libraries( polyfit_example_without_input_planes PRIVATE ${GLPK_LIBRARIES} )
-          target_compile_definitions(polyfit_example_without_input_planes PRIVATE -DCGAL_USE_GLPK)
-          target_link_libraries( polyfit_example_user_provided_planes PRIVATE ${GLPK_LIBRARIES} )
-          target_compile_definitions(polyfit_example_user_provided_planes PRIVATE -DCGAL_USE_GLPK)
-          target_link_libraries( polyfit_example_model_complexty_control PRIVATE ${GLPK_LIBRARIES} )
-          target_compile_definitions(polyfit_example_model_complexty_control PRIVATE -DCGAL_USE_GLPK)
-          target_link_libraries( polyfit_example_with_region_growing PRIVATE ${GLPK_LIBRARIES} )
-          target_compile_definitions(polyfit_example_with_region_growing PRIVATE -DCGAL_USE_GLPK)
-
-          message("GLPK found and used")
-
-      endif()
-
+foreach(target
+    polyfit_example_without_input_planes
+    polyfit_example_user_provided_planes
+    polyfit_example_model_complexty_control
+    polyfit_example_with_region_growing)
+  CGAL_target_use_Eigen(${target})
+  if (SCIP_FOUND)
+    CGAL_target_use_SCIP(${target})
   else()
-
-      include_directories( BEFORE ${SCIP_INCLUDE_DIRS} )
-
-      target_link_libraries( polyfit_example_without_input_planes PRIVATE ${SCIP_LIBRARIES} )
-      target_compile_definitions(polyfit_example_without_input_planes PRIVATE -DCGAL_USE_SCIP)
-      target_link_libraries( polyfit_example_user_provided_planes PRIVATE ${SCIP_LIBRARIES} )
-      target_compile_definitions(polyfit_example_user_provided_planes PRIVATE -DCGAL_USE_SCIP)
-      target_link_libraries( polyfit_example_model_complexty_control PRIVATE ${SCIP_LIBRARIES} )
-      target_compile_definitions(polyfit_example_model_complexty_control PRIVATE -DCGAL_USE_SCIP)
-      target_link_libraries( polyfit_example_with_region_growing PRIVATE ${SCIP_LIBRARIES} )
-      target_compile_definitions(polyfit_example_with_region_growing PRIVATE -DCGAL_USE_SCIP)
-
-      message("SCIP found and used")
-
+    CGAL_target_use_GLPK(${target})
   endif()
-
-else()
-  message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
-endif()
+endforeach()
diff --git a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_model_complexty_control.cpp b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_model_complexty_control.cpp
index 53d0a4ad1c3..5e48efa5552 100644
--- a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_model_complexty_control.cpp
+++ b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_model_complexty_control.cpp
@@ -5,10 +5,10 @@
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/Polygonal_surface_reconstruction.h>
 
-#ifdef CGAL_USE_SCIP
+#ifdef CGAL_USE_SCIP // defined (or not) by CMake scripts, do not define by hand
 #include <CGAL/SCIP_mixed_integer_program_traits.h>
 typedef CGAL::SCIP_mixed_integer_program_traits<double>			MIP_Solver;
-#elif defined(CGAL_USE_GLPK)
+#elif defined(CGAL_USE_GLPK) // defined (or not) by CMake scripts, do not define by hand
 #include <CGAL/GLPK_mixed_integer_program_traits.h>
 typedef CGAL::GLPK_mixed_integer_program_traits<double>			MIP_Solver;
 #endif
diff --git a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_user_provided_planes.cpp b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_user_provided_planes.cpp
index 8b56101a76f..e997b671ade 100644
--- a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_user_provided_planes.cpp
+++ b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_user_provided_planes.cpp
@@ -5,10 +5,10 @@
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/Polygonal_surface_reconstruction.h>
 
-#ifdef CGAL_USE_SCIP
+#ifdef CGAL_USE_SCIP  // defined (or not) by CMake scripts, do not define by hand
 #include <CGAL/SCIP_mixed_integer_program_traits.h>
 typedef CGAL::SCIP_mixed_integer_program_traits<double>			MIP_Solver;
-#elif defined(CGAL_USE_GLPK)
+#elif defined(CGAL_USE_GLPK)  // defined (or not) by CMake scripts, do not define by hand
 #include <CGAL/GLPK_mixed_integer_program_traits.h>
 typedef CGAL::GLPK_mixed_integer_program_traits<double>			MIP_Solver;
 #endif
diff --git a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_with_region_growing.cpp b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_with_region_growing.cpp
index 0cfe1cd02ff..4cc561a8ae6 100644
--- a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_with_region_growing.cpp
+++ b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_with_region_growing.cpp
@@ -7,12 +7,12 @@
 #include <CGAL/Shape_detection/Region_growing/Region_growing_on_point_set.h>
 #include <CGAL/Polygonal_surface_reconstruction.h>
 
-#ifdef CGAL_USE_SCIP
+#ifdef CGAL_USE_SCIP  // defined (or not) by CMake scripts, do not define by hand
 
 #include <CGAL/SCIP_mixed_integer_program_traits.h>
 typedef CGAL::SCIP_mixed_integer_program_traits<double> MIP_Solver;
 
-#elif defined(CGAL_USE_GLPK)
+#elif defined(CGAL_USE_GLPK)  // defined (or not) by CMake scripts, do not define by hand
 
 #include <CGAL/GLPK_mixed_integer_program_traits.h>
 typedef CGAL::GLPK_mixed_integer_program_traits<double>	MIP_Solver;
@@ -196,4 +196,4 @@ int main(int, char**)
     return EXIT_SUCCESS;
 }
 
-#endif  // defined(CGAL_USE_GLPK) || defined(CGAL_USE_SCIP)
\ No newline at end of file
+#endif  // defined(CGAL_USE_GLPK) || defined(CGAL_USE_SCIP)
diff --git a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_without_input_planes.cpp b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_without_input_planes.cpp
index 76531b62ed8..cd37cc996f1 100644
--- a/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_without_input_planes.cpp
+++ b/Polygonal_surface_reconstruction/examples/Polygonal_surface_reconstruction/polyfit_example_without_input_planes.cpp
@@ -6,12 +6,12 @@
 #include <CGAL/Shape_detection/Efficient_RANSAC.h>
 #include <CGAL/Polygonal_surface_reconstruction.h>
 
-#ifdef CGAL_USE_SCIP
+#ifdef CGAL_USE_SCIP  // defined (or not) by CMake scripts, do not define by hand
 
 #include <CGAL/SCIP_mixed_integer_program_traits.h>
 typedef CGAL::SCIP_mixed_integer_program_traits<double>			MIP_Solver;
 
-#elif defined(CGAL_USE_GLPK)
+#elif defined(CGAL_USE_GLPK)  // defined (or not) by CMake scripts, do not define by hand
 
 #include <CGAL/GLPK_mixed_integer_program_traits.h>
 typedef CGAL::GLPK_mixed_integer_program_traits<double>			MIP_Solver;
diff --git a/Polygonal_surface_reconstruction/test/Polygonal_surface_reconstruction/CMakeLists.txt b/Polygonal_surface_reconstruction/test/Polygonal_surface_reconstruction/CMakeLists.txt
index e5f6f23675a..9a88f8a5dc6 100644
--- a/Polygonal_surface_reconstruction/test/Polygonal_surface_reconstruction/CMakeLists.txt
+++ b/Polygonal_surface_reconstruction/test/Polygonal_surface_reconstruction/CMakeLists.txt
@@ -11,7 +11,7 @@ find_package( CGAL QUIET COMPONENTS  )
 
 if ( NOT CGAL_FOUND )
 
-  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  message(STATUS "NOTICE: This project requires the CGAL library, and will not be compiled.")
   return()  
 
 endif()
@@ -24,8 +24,11 @@ include( ${CGAL_USE_FILE} )
 find_package( Boost REQUIRED )
 
 if ( NOT Boost_FOUND )
-  message(STATUS "This project requires the Boost library, and will not be compiled.")
+
+  message(STATUS "NOTICE: This project requires the Boost library, and will not be compiled.")
+
   return()  
+
 endif()
 
 # Creating entries for all C++ files with "main" routine
@@ -33,49 +36,26 @@ endif()
 
 include( CGAL_CreateSingleSourceCGALProgram )
 
-create_single_source_cgal_program( "polygonal_surface_reconstruction_test.cpp" )
 
 find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if(EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-
-  # Executables that require Eigen 3.1
-  find_package( SCIP QUIET)
-
-  if (SCIP_FOUND)
-
-    include_directories( BEFORE ${SCIP_INCLUDE_DIRS} )
-
-    target_link_libraries( polygonal_surface_reconstruction_test PRIVATE ${SCIP_LIBRARIES} )
-
-    target_compile_definitions(polygonal_surface_reconstruction_test PRIVATE -DCGAL_USE_SCIP)
-
-    message("SCIP found and used")
-
-  endif()
-
-
-  find_package( GLPK QUIET)
-
-  if (GLPK_FOUND)
-
-    include_directories( BEFORE ${GLPK_INCLUDE_DIR} )
-
-    target_link_libraries( polygonal_surface_reconstruction_test PRIVATE ${GLPK_LIBRARIES} )
-
-    target_compile_definitions(polygonal_surface_reconstruction_test PRIVATE -DCGAL_USE_GLPK)
-
-    message("GLPK found and used")
-
-  endif()
-
-
-  if (NOT SCIP_FOUND AND NOT GLPK_FOUND)
-
-    message(STATUS "NOTICE: This project requires either SCIP or GLPK, some functions will not be tested. "
-      "Please provide either 'SCIP_DIR' or 'GLPK_INCLUDE_DIR' and 'GLPK_LIBRARIES'")
-
-  endif()
-else()
-  message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
+if(NOT EIGEN3_FOUND)
+  message(STATUS "NOTICE: This project requires Eigen 3.1 (or greater) and will not be compiled.")
+  return()
+endif()
+
+find_package(SCIP QUIET)
+if (NOT SCIP_FOUND )
+  find_package( GLPK QUIET)
+  if ( NOT GLPK_FOUND )
+    message( STATUS "NOTICE : This project requires either SCIP or GLPK, and will not be compiled.")
+    return()
+  endif()
+endif()
+
+create_single_source_cgal_program( "polygonal_surface_reconstruction_test.cpp")
+CGAL_target_use_Eigen(polygonal_surface_reconstruction_test)
+if (SCIP_FOUND)
+  CGAL_target_use_SCIP(polygonal_surface_reconstruction_test)
+else()
+  CGAL_target_use_GLPK(polygonal_surface_reconstruction_test)
 endif()
diff --git a/Polyhedron/demo/Polyhedron/CGAL_double_edit.cpp b/Polyhedron/demo/Polyhedron/CGAL_double_edit.cpp
index 07c630b7828..50b969ed1bc 100644
--- a/Polyhedron/demo/Polyhedron/CGAL_double_edit.cpp
+++ b/Polyhedron/demo/Polyhedron/CGAL_double_edit.cpp
@@ -1,5 +1,5 @@
 #include "CGAL_double_edit.h"
-
+#include <iostream>
 #include <QDoubleValidator>
 
 class DoubleValidator : public QDoubleValidator
@@ -59,7 +59,7 @@ public:
 
   void DoubleEdit::setRange(double min, double max)
   {
-    this->validator->setRange(min, max);
+    this->validator->setRange(min, max, this->validator->decimals());
   }
 
   double DoubleEdit::getValue()
diff --git a/Polyhedron/demo/Polyhedron/CMakeLists.txt b/Polyhedron/demo/Polyhedron/CMakeLists.txt
index 1b1cd817152..6d3f9dc346f 100644
--- a/Polyhedron/demo/Polyhedron/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/CMakeLists.txt
@@ -64,7 +64,7 @@ include(${CGAL_USE_FILE})
 find_package(Qt5
              QUIET
              COMPONENTS            OpenGL Script
-             OPTIONAL_COMPONENTS   ScriptTools)
+             OPTIONAL_COMPONENTS   ScriptTools WebSockets)
 
 if(Qt5_FOUND)
 
@@ -73,9 +73,6 @@ if(Qt5_FOUND)
 endif(Qt5_FOUND)
 
 find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-endif(EIGEN3_FOUND)
 
 find_package( METIS )
 
@@ -95,6 +92,11 @@ if( POLYHEDRON_DEMO_ACTIVATE_CONCURRENCY )
   endif()
 endif()
 
+#find libssh for scene sharing
+find_package(LibSSH)
+if( NOT LIBSSH_FOUND )
+  message("NOTICE : The SSH features will be disabled.")
+endif()
 
 # Activate concurrency ? (turned OFF by default)
 option(CGAL_ACTIVATE_CONCURRENT_MESH_3
@@ -131,7 +133,7 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
   qt5_wrap_ui( statisticsUI_FILES Statistics_on_item_dialog.ui)
   qt5_wrap_ui( FileLoaderDialogUI_files FileLoaderDialog.ui )
   qt5_wrap_ui( Show_point_dialogUI_FILES Show_point_dialog.ui )
-  qt5_wrap_ui( PreferencesUI_FILES   Preferences.ui Details.ui)
+  qt5_wrap_ui( PreferencesUI_FILES   Preferences.ui Details.ui SSH_dialog.ui)
   qt5_wrap_ui( Show_point_dialogUI_FILES Show_point_dialog.ui )
   qt5_wrap_ui( ViewerUI_FILES  LightingDialog.ui)
   qt5_generate_moc( "File_loader_dialog.h" "${CMAKE_CURRENT_BINARY_DIR}/File_loader_dialog_moc.cpp" )
@@ -195,6 +197,11 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
   target_link_libraries(demo_framework
     PUBLIC Qt5::OpenGL Qt5::Widgets Qt5::Gui Qt5::Script
     )
+  if(TARGET Qt5::WebSockets)
+    target_link_libraries(demo_framework PUBLIC Qt5::WebSockets)
+    message(STATUS "Qt5WebSockets was found. Using WebSockets is therefore possible.")
+  endif()
+
   cgal_add_compilation_test(demo_framework)
   # Let's define `three_EXPORT` during the compilation of `demo_framework`,
   # in addition of `demo_framework_EXPORT` (defined automatically by
@@ -276,12 +283,15 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
   
   if(EIGEN3_FOUND )
     add_item(scene_textured_item Scene_textured_surface_mesh_item.cpp texture.cpp)
+    CGAL_target_use_Eigen(scene_textured_item)
     qt5_wrap_ui( editionUI_FILES Plugins/Surface_mesh_deformation/Deform_mesh.ui )
     add_item(scene_edit_item Plugins/Surface_mesh_deformation/Scene_edit_polyhedron_item.cpp
       ${editionUI_FILES})
+    CGAL_target_use_Eigen(scene_edit_item)
     target_link_libraries(scene_edit_item PUBLIC scene_surface_mesh_item scene_k_ring_selection
       scene_basic_objects)
     add_item(scene_mcf_item Plugins/PMP/Scene_mcf_item.cpp)
+    CGAL_target_use_Eigen(scene_mcf_item)
   endif()
 
   add_item(scene_implicit_function_item Scene_implicit_function_item.cpp )
@@ -293,19 +303,19 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
   add_item(scene_nef_polyhedron_item Scene_nef_polyhedron_item.cpp)
   target_link_libraries(scene_nef_polyhedron_item PUBLIC scene_surface_mesh_item)
   
+  add_item(scene_points_with_normal_item Scene_points_with_normal_item.cpp)
+  if (EIGEN3_FOUND)
+    CGAL_target_use_Eigen(scene_points_with_normal_item)
+  endif()
+  
   find_package(LASLIB)
   if (LASLIB_FOUND)
-    include(${LASLIB_USE_FILE})
-    include_directories(${LASLIB_INCLUDE_DIR})
-    include_directories(${LASZIP_INCLUDE_DIR})
-    add_item(scene_points_with_normal_item Scene_points_with_normal_item.cpp)
+    CGAL_target_use_LASLIB(scene_points_with_normal_item)
     if (MSVC)
       target_compile_definitions( scene_points_with_normal_item PUBLIC "-D_CRT_SECURE_NO_DEPRECATE -D_CRT_SECURE_NO_WARNINGS")
     endif()
-    target_link_libraries( scene_points_with_normal_item PUBLIC ${LASLIB_LIBRARIES})
-  else()
-    add_item(scene_points_with_normal_item Scene_points_with_normal_item.cpp)
   endif()
+  
   if(TBB_FOUND)
     CGAL_target_use_TBB(scene_points_with_normal_item)
   endif()
@@ -329,11 +339,20 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND)
     MainWindow.cpp
     Polyhedron_demo.cpp
     File_loader_dialog_moc.cpp
+    Use_ssh.cpp
     ${CGAL_Qt5_RESOURCE_FILES} ${CGAL_Qt5_MOC_FILES}
     ${FileLoaderDialogUI_files} ${MainWindowUI_files} ${PreferencesUI_FILES} 
     ${statisticsUI_FILES} ${SubViewerUI_files})
   target_link_libraries(polyhedron_demo PUBLIC
     demo_framework point_dialog Qt5::Gui Qt5::OpenGL Qt5::Widgets Qt5::Script)
+  if(LIBSSH_FOUND)
+    add_definitions(-DCGAL_USE_SSH)
+    target_link_libraries(polyhedron_demo PUBLIC ${LIBSSH_LIBRARIES})
+  endif() #libssh
+  if(TARGET Qt5::WebSockets)
+    add_definitions(-DCGAL_USE_WEBSOCKETS)
+    target_link_libraries(polyhedron_demo PUBLIC Qt5::WebSockets)
+  endif()
   add_executable  ( Polyhedron_3 Polyhedron_3.cpp )
   target_link_libraries( Polyhedron_3 PRIVATE polyhedron_demo )
   add_to_cached_list( CGAL_EXECUTABLE_TARGETS Polyhedron_3 )
diff --git a/Polyhedron/demo/Polyhedron/MainWindow.cpp b/Polyhedron/demo/Polyhedron/MainWindow.cpp
index b91b64069fd..d8872fd851f 100644
--- a/Polyhedron/demo/Polyhedron/MainWindow.cpp
+++ b/Polyhedron/demo/Polyhedron/MainWindow.cpp
@@ -1,3 +1,6 @@
+#ifdef CGAL_USE_SSH
+#  include "CGAL/Use_ssh.h"
+#endif
 #include <cmath>
 
 #include "config.h"
@@ -7,6 +10,7 @@
 #include <CGAL/Three/TextRenderer.h>
 #include <CGAL/Three/exceptions.h>
 #include <CGAL/Qt/debug.h>
+#include <CGAL/double.h>
 
 #include <QJsonArray>
 #include <QtDebug>
@@ -42,6 +46,7 @@
 #include <QWidgetAction>
 #include <QJsonArray>
 #include <QSequentialIterable>
+#include <QDir>
 #ifdef QT_SCRIPT_LIB
 #  include <QScriptValue>
 #  ifdef QT_SCRIPTTOOLS_LIB
@@ -58,6 +63,7 @@
 #include "ui_Preferences.h"
 #include "ui_Details.h"
 #include "ui_Statistics_on_item_dialog.h"
+#include "ui_SSH_dialog.h"
 #include "Show_point_dialog.h"
 #include "File_loader_dialog.h"
 #include "Viewer.h"
@@ -69,6 +75,14 @@
 #  include <QScriptEngine>
 #  include <QScriptValue>
 #include "Color_map.h"
+
+
+#ifdef CGAL_USE_WEBSOCKETS
+#include <QWebSocketServer>
+#include <QWebSocket>
+#include <QNetworkInterface>
+#endif
+
 using namespace CGAL::Three;
 QScriptValue
 myScene_itemToScriptValue(QScriptEngine *engine,
@@ -150,6 +164,7 @@ MainWindow::MainWindow(const QStringList &keywords, bool verbose, QWidget* paren
   // remove the Load Script menu entry, when the demo has not been compiled with QT_SCRIPT_LIB
 #if !defined(QT_SCRIPT_LIB)
   ui->menuBar->removeAction(ui->actionLoadScript);
+  ui->menuBar->removeAction(ui->on_actionLoad_a_Scene_from_a_Script_File);
 #endif
   // Save some pointers from ui, for latter use.
   sceneView = ui->sceneView;
@@ -158,9 +173,9 @@ MainWindow::MainWindow(const QStringList &keywords, bool verbose, QWidget* paren
   CGAL::Three::Three::s_mainviewer = viewer;
   viewer->setObjectName("mainViewer");
   viewer_window->showMaximized();
-  viewer_window->setWindowFlags( 
+  viewer_window->setWindowFlags(
         Qt::SubWindow
-        | Qt::CustomizeWindowHint 
+        | Qt::CustomizeWindowHint
         | Qt::WindowMaximizeButtonHint
         | Qt::WindowSystemMenuHint
         | Qt::WindowTitleHint
@@ -353,7 +368,7 @@ MainWindow::MainWindow(const QStringList &keywords, bool verbose, QWidget* paren
 
   // Load plugins, and re-enable actions that need it.
   operationSearchBar.setPlaceholderText("Filter...");
-  searchAction->setDefaultWidget(&operationSearchBar);  
+  searchAction->setDefaultWidget(&operationSearchBar);
   connect(&operationSearchBar, &QLineEdit::textChanged,
           this, [=](){filterOperations(true);});
   loadPlugins();
@@ -689,7 +704,7 @@ bool MainWindow::load_plugin(QString fileName, bool blacklisted)
     else{
       //qdebug << "error: " << qPrintable(loader.errorString());
       pluginsStatus_map[name] = loader.errorString();
-      
+
     }
     PathNames_map[name].push_back(fileinfo.absoluteDir().absolutePath());
     return true;
@@ -933,7 +948,7 @@ void MainWindow::viewerShow(float xmin,
 }
 
 void MainWindow::viewerShow(Viewer_interface* vi, float x, float y, float z) {
-  
+
   CGAL::qglviewer::ManipulatedCameraFrame backup_frame(*vi->camera()->frame());
   vi->camera()->fitSphere(CGAL::qglviewer::Vec(x, y, z),
                           vi->camera()->sceneRadius()/100);
@@ -1000,20 +1015,25 @@ void MainWindow::computeViewerBBox(CGAL::qglviewer::Vec& min, CGAL::qglviewer::V
   const double xmax = bbox.xmax();
   const double ymax = bbox.ymax();
   const double zmax = bbox.zmax();
-  
-  
-  
+
+
+
   min = CGAL::qglviewer::Vec(xmin, ymin, zmin);
   max= CGAL::qglviewer::Vec(xmax, ymax, zmax);
-  
+
   CGAL::qglviewer::Vec bbox_center((xmin+xmax)/2, (ymin+ymax)/2, (zmin+zmax)/2);
   
-  CGAL::qglviewer::Vec offset(0,0,0);
+  double bbox_diag = CGAL::approximate_sqrt(
+        CGAL::square(xmax - xmin)
+        + CGAL::square(ymax - ymin)
+        + CGAL::square(zmax - zmin));
   
+  CGAL::qglviewer::Vec offset(0,0,0);
+
   double l_dist = (std::max)((std::abs)(bbox_center.x - viewer->offset().x),
                              (std::max)((std::abs)(bbox_center.y - viewer->offset().y),
                                         (std::abs)(bbox_center.z - viewer->offset().z)));
-  if((std::log2)(l_dist) > 13.0 )
+  if((std::log2)(l_dist/bbox_diag) > 13.0 )
     for(int i=0; i<3; ++i)
     {
       offset[i] = -bbox_center[i];
@@ -1235,7 +1255,7 @@ void MainWindow::open(QString filename)
   settings.setValue("OFF open directory",
                     fileinfo.absoluteDir().absolutePath());
   loadItem(fileinfo, findLoader(load_pair.first), ok);
- 
+
   if(!ok)
     return;
   this->addToRecentFiles(fileinfo.absoluteFilePath());
@@ -1422,7 +1442,7 @@ void MainWindow::selectionChanged()
   {
     if(vi == NULL)
       continue;
-    
+
     if(item != NULL && item->manipulatable()) {
       vi->setManipulatedFrame(item->manipulatedFrame());
     } else {
@@ -1493,6 +1513,7 @@ void MainWindow::showSceneContextMenu(int selectedItemIndex,
     }
   }
   menu->addMenu(ui->menuOperations);
+
   if(menu)
     menu->exec(global_pos);
 }
@@ -1556,7 +1577,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
               menu_actions["line width"] = action->menu()->actions().last();
             }
           }
-          
+
         }
         Q_FOREACH(Scene::Item_id index, scene->selectionIndices())
         {
@@ -1589,7 +1610,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
                   )->value());
             slider->setOrientation(Qt::Horizontal);
             sliderAction->setDefaultWidget(slider);
-            
+
             connect(slider, &QSlider::valueChanged, [this, slider]()
             {
               Q_FOREACH(Scene::Item_id id, scene->selectionIndices())
@@ -1624,7 +1645,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
                   )->value());
             slider->setOrientation(Qt::Horizontal);
             sliderAction->setDefaultWidget(slider);
-            
+
             connect(slider, &QSlider::valueChanged, [this, slider]()
             {
               Q_FOREACH(Scene::Item_id id, scene->selectionIndices())
@@ -1659,7 +1680,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
                   )->value());
             slider->setOrientation(Qt::Horizontal);
             sliderAction->setDefaultWidget(slider);
-            
+
             connect(slider, &QSlider::valueChanged, [this, slider]()
             {
               Q_FOREACH(Scene::Item_id id, scene->selectionIndices())
@@ -1702,7 +1723,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
                   )->value());
             slider->setOrientation(Qt::Horizontal);
             sliderAction->setDefaultWidget(slider);
-            
+
             connect(slider, &QSlider::valueChanged, [this, slider]()
             {
               Q_FOREACH(Scene::Item_id id, scene->selectionIndices())
@@ -1755,6 +1776,7 @@ void MainWindow::showSceneContextMenu(const QPoint& p) {
         QAction* saveas = menu.addAction(tr("&Save as..."));
         connect(saveas,  SIGNAL(triggered()),
                 this, SLOT(on_actionSaveAs_triggered()));
+        menu.addMenu(ui->menuOperations);
         menu.exec(sender->mapToGlobal(p));
         return;
       }
@@ -1825,6 +1847,7 @@ void MainWindow::readSettings()
     this->default_point_size = settings.value("points_size").toInt();
     this->default_normal_length = settings.value("normals_length").toInt();
     this->default_lines_width = settings.value("lines_width").toInt();
+    setProperty("ws_url", settings.value("ws_server_url").toString());
 }
 
 void MainWindow::writeSettings()
@@ -1899,14 +1922,7 @@ void MainWindow::throw_exception() {
 void MainWindow::on_actionLoadScript_triggered()
 {
 #if defined(QT_SCRIPT_LIB)
-  QString filename = QFileDialog::getOpenFileName(
-        this,
-        tr("Select a script to run..."),
-        ".",
-        "QTScripts (*.js);;All Files (*)");
-  if(filename.isEmpty())
-    return;
-  loadScript(QFileInfo(filename));
+
 #endif
 }
 
@@ -1936,7 +1952,7 @@ void MainWindow::on_actionLoad_triggered()
       filters << filter;
     }
   }
-  
+
   QString directory = settings.value("OFF open directory",
                                      QDir::current().dirName()).toString();
 
@@ -1964,7 +1980,7 @@ void MainWindow::on_actionLoad_triggered()
                     static_cast<unsigned>(nb_files),
                     std::back_inserter(colors_));
   std::size_t nb_item = -1;
-  
+
   Q_FOREACH(const QString& filename, dialog.selectedFiles()) {
 
     CGAL::Three::Scene_item* item = NULL;
@@ -2189,7 +2205,7 @@ void MainWindow::on_actionShowHide_triggered()
     item->redraw();
   }
   scene->setUpdatesEnabled(true);
-  updateViewersBboxes(false);
+//  updateViewersBboxes(false); //Not usable :when the scene changes scale, smaller items disappear.
 }
 
 void MainWindow::on_actionSetPolyhedronA_triggered()
@@ -2209,7 +2225,6 @@ void MainWindow::on_actionPreferences_triggered()
   QDialog dialog(this);
   Ui::PreferencesDialog prefdiag;
   prefdiag.setupUi(&dialog);
-  
   float lineWidth[2];
   if(!viewer->isOpenGL_4_3())
     viewer->glGetFloatv(GL_LINE_WIDTH_RANGE, lineWidth);
@@ -2220,22 +2235,22 @@ void MainWindow::on_actionPreferences_triggered()
   }
   prefdiag.linesHorizontalSlider->setMinimum(lineWidth[0]);
   prefdiag.linesHorizontalSlider->setMaximum(lineWidth[1]);
-  
+
   prefdiag.offset_updateCheckBox->setChecked(
         settings.value("offset_update", false).toBool());
   connect(prefdiag.offset_updateCheckBox, SIGNAL(toggled(bool)),
           scene, SLOT(enableVisibilityRecentering(bool)));
-  
+
   prefdiag.antialiasingCheckBox->setChecked(settings.value("antialiasing", false).toBool());
   connect(prefdiag.antialiasingCheckBox, SIGNAL(toggled(bool)),
           viewer, SLOT(setAntiAliasing(bool)));
-  
+
   prefdiag.quick_cameraCheckBox->setChecked(
         settings.value("quick_camera_mode", true).toBool());
   connect(prefdiag.quick_cameraCheckBox, SIGNAL(toggled(bool)),
           viewer, SLOT(setFastDrawing(bool)));
   prefdiag.max_itemsSpinBox->setValue(viewer->textRenderer()->getMax_textItems());
-  
+
   connect(prefdiag.max_itemsSpinBox,static_cast<void (QSpinBox::*)(int)>(&QSpinBox::valueChanged),
           this, [this](int i){
     setMaxTextItemsDisplayed(i);
@@ -2266,20 +2281,20 @@ void MainWindow::on_actionPreferences_triggered()
   });
   connect(prefdiag.background_colorPushButton, &QPushButton::clicked,
           this, &MainWindow::setBackgroundColor);
-  
+
   connect(prefdiag.default_save_asPushButton, &QPushButton::clicked,
           this, &MainWindow::setDefaultSaveDir);
-  
+
   connect(prefdiag.lightingPushButton, &QPushButton::clicked,
           this, &MainWindow::setLighting_triggered);
-  
+
   prefdiag.surface_meshComboBox->setCurrentText(CGAL::Three::Three::modeName(
                                                   CGAL::Three::Three::s_defaultSMRM));
   connect(prefdiag.surface_meshComboBox, &QComboBox::currentTextChanged,
           this, [this](const QString& text){
     this->s_defaultSMRM = CGAL::Three::Three::modeFromName(text);
   });
-  
+
   prefdiag.point_setComboBox->setCurrentText(CGAL::Three::Three::modeName(
                                                CGAL::Three::Three::s_defaultPSRM));
   connect(prefdiag.point_setComboBox, &QComboBox::currentTextChanged,
@@ -2353,6 +2368,70 @@ void MainWindow::on_actionPreferences_triggered()
     });
     dialog.exec();
   });
+  connect(prefdiag.sshButton, &QPushButton::clicked,
+          this, [this](){
+    QDialog dialog(this);
+    Ui::SSHDialog sshdiag;
+    sshdiag.setupUi(&dialog);
+
+#ifdef CGAL_USE_SSH
+    sshdiag.userBox->setEnabled(true);
+    sshdiag.serverBox->setEnabled(true);
+    sshdiag.pkBox->setEnabled(true);
+    sshdiag.privkBox->setEnabled(true);
+    sshdiag.userEdit->setText(settings.value("ssh_user", QString()).toString());
+    sshdiag.serverEdit->setText(settings.value("ssh_server", QString()).toString());
+    sshdiag.publicEdit->setText(settings.value("ssh_public_key", QString()).toString());
+    sshdiag.privkEdit->setText(settings.value("ssh_priv_key", QString()).toString());
+    connect(sshdiag.pubButton, &QPushButton::clicked,
+            this, [this, sshdiag](){
+      QFileDialog diag(this,
+                       "Public Key",
+                       "",
+                       "All Files (*)");
+      diag.setFilter(QDir::Hidden|QDir::Files|QDir::Dirs|QDir::NoDotAndDotDot);
+      if(!diag.exec())
+        return;
+      sshdiag.publicEdit->setText(diag.selectedFiles().front());
+    });
+    connect(sshdiag.privButton, &QPushButton::clicked,
+            this, [this, sshdiag](){
+      QFileDialog diag(this,
+                       "Private Key",
+                       "",
+                       "All Files (*)");
+      diag.setFilter(QDir::Hidden|QDir::Files|QDir::Dirs|QDir::NoDotAndDotDot);
+      if(!diag.exec())
+        return;
+      sshdiag.privkEdit->setText(diag.selectedFiles().front());
+    });
+#else
+    sshdiag.userBox->setEnabled(false);
+    sshdiag.serverBox->setEnabled(false);
+    sshdiag.pkBox->setEnabled(false);
+    sshdiag.privkBox->setEnabled(false);
+#endif
+    sshdiag.wsEdit->setText(settings.value("ws_server_url", QString()).toString());
+
+    dialog.exec();
+    if ( dialog.result() )
+    {
+#ifdef CGAL_USE_SSH
+      settings.setValue("ssh_user",
+                        sshdiag.userEdit->text());
+      settings.setValue("ssh_server",
+                        sshdiag.serverEdit->text());
+      settings.setValue("ssh_public_key",
+                        sshdiag.publicEdit->text());
+      settings.setValue("ssh_priv_key",
+                        sshdiag.privkEdit->text());
+#endif
+      settings.setValue("ws_server_url",
+                        sshdiag.wsEdit->text());
+      setProperty("ws_url", sshdiag.wsEdit->text());
+    }
+  });
+
   dialog.exec();
 
   if ( dialog.result() )
@@ -2365,7 +2444,7 @@ void MainWindow::on_actionPreferences_triggered()
       if (item->checkState(0)==Qt::Unchecked)
         plugin_blacklist.insert(item->text(1));
     }
-    
+
     //write settings
     settings.setValue("antialiasing",
                       prefdiag.antialiasingCheckBox->isChecked());
@@ -2385,7 +2464,7 @@ void MainWindow::on_actionPreferences_triggered()
     settings.setValue("points_size", this->default_point_size);
     settings.setValue("normals_length", this->default_normal_length);
     settings.setValue("lines_width", this->default_lines_width);
-    
+
   }
   else
   {
@@ -2405,7 +2484,7 @@ void MainWindow::setBackgroundColor()
       v->update();
     }
   }
-  
+
 }
 
 void MainWindow::setLighting_triggered()
@@ -2567,7 +2646,7 @@ QString MainWindow::get_item_stats()
   Q_FOREACH(int id, scene->selectionIndices())
   {
     Scene_item* item = scene->item(id);
-    QString classname = item->property("classname").toString(); 
+    QString classname = item->property("classname").toString();
     if(classname.isEmpty())
        classname = item->metaObject()->className();
     if(!classnames.contains(classname))
@@ -2794,53 +2873,183 @@ void MainWindow::propagate_action()
   }
 }
 
+QString make_fullpath(const QString& filename, bool duplicate = false)
+{
+  QString fullpath = QString("%1/%2").arg(QDir::tempPath()).arg(filename);
+  QString tmp_fullpath = fullpath;
+  if(duplicate)
+  {
+    int i=0;
+    while(QFileInfo(tmp_fullpath).exists())
+    {
+      QString basename = QFileInfo(tmp_fullpath).baseName();
+      QString dir = QFileInfo(tmp_fullpath).dir().path();
+      QString suffix= QFileInfo(fullpath).completeSuffix();
+      tmp_fullpath=QString("%1/%2%3.%4").arg(dir).arg(basename).arg(++i).arg(suffix);
+    }
+  }
+  return tmp_fullpath;
+}
+/*
+ The two following functions allow to create files from string and strings from files.
+ This is used as a workaround of the absence of stream management in our IO system.
+ The whole to/from Base64 is used to avoid problems with binary formats. Everything is written
+ as a base64 binary string, and converted back to what it was.
+*/
+QByteArray file_to_string(const char* filename)
+{
+  std::ifstream f(filename, std::ifstream::binary);
+  // get size of file
+  f.seekg (0,f.end);
+  long size = f.tellg();
+  f.seekg (0);
+  std::ostringstream ss;
+  // allocate memory for file content
+    char* buffer = new char[size];
+
+    // read content of infile
+    f.read(buffer,size);
+
+    // write to outfile
+    ss.write(buffer,size);
+    // release dynamically-allocated memory
+    delete[] buffer;
+  //ss.write( << f.rdbuf(); // reading data
+  f.close();
+  std::string st = ss.str();
+  QByteArray ba(st.c_str(), static_cast<int>(st.size()));
+  return ba;
+}
+
+QString MainWindow::write_string_to_file(const QString& str, const QString &filename)
+{
+  QString fullpath = make_fullpath(filename);
+  std::ofstream f(fullpath.toStdString().c_str(), std::ofstream::binary);
+  QByteArray compressed_item(str.toStdString().c_str());
+  QByteArray item = qUncompress(QByteArray::fromBase64(compressed_item));
+  QByteArray bb = item;
+  f.write(bb.constData(),bb.toStdString().size());
+  f.close();
+  return fullpath;
+}
+
 void MainWindow::on_actionSa_ve_Scene_as_Script_triggered()
 {
-  QString filename =
-      QFileDialog::getSaveFileName(this,
-                                   "Save the Scene as a Script File",
-                                   last_saved_dir,
-                                   "Qt Script files (*.js)");
-  std::ofstream os(filename.toUtf8());
+  if(scene->numberOfEntries() == 0)
+    return;
+  bool do_upload = false;
+#ifdef CGAL_USE_SSH
+  QString user = settings.value("ssh_user", QString()).toString();
+  QString pass;
+  if(!user.isEmpty())
+  {
+    QMessageBox::StandardButton doyou =
+        QMessageBox::question(this, tr("Upload ?"), tr("Do you wish to upload the scene"
+                                                       " using the SSH preferences ?"));
+    bool ok;
+    do_upload = (doyou == QMessageBox::Yes);
+    if(do_upload)
+    {
+      pass = QInputDialog::getText(this, "SSH Password",
+                                   "Enter ssh key password:",
+                                   QLineEdit::Password,
+                                   tr(""),
+                                   &ok);
+      if(!ok)
+        return;
+      pass = pass.trimmed();
+    }
+  }
+#endif
+
+  QString filename;
+
+  if(do_upload){
+    filename = QString("%1/save_scene.js").arg(QDir::tempPath());
+  }else{
+    filename = QFileDialog::getSaveFileName(this,
+                                            "Save the Scene as a Script File",
+                                            last_saved_dir,
+                                            "Qt Script files (*.js)");
+  }
+  std::ofstream os(filename.toUtf8(), std::ofstream::binary);
   if(!os)
     return;
-  std::vector<QString> names;
-  std::vector<QString> loaders;
+  CGAL::Three::Three::CursorScopeGuard cs(Qt::WaitCursor);
+  std::vector<std::pair<QString, QString> > names;
+  std::vector<std::pair<QString, QString> > loaders;
   std::vector<QColor> colors;
   std::vector<int> rendering_modes;
   QStringList not_saved;
   for(int i = 0; i < scene->numberOfEntries(); ++i)
   {
     Scene_item* item = scene->item(i);
-    QString loader = item->property("loader_name").toString();
-    QString source = item->property("source filename").toString();
+    QString loader;// = item->property("loader_name").toString();
+    QString ext;
+    for(Polyhedron_demo_io_plugin_interface* iop : io_plugins)
+    {
+      if(iop->isDefaultLoader(item))
+      {
+        QString sf = iop->saveNameFilters().split(";;").first();
+        //OFF Files (*.off)
+        QRegularExpression re("\\(\\*\\.(.*)\\)");
+        QRegularExpressionMatch rem = re.match(sf);
+        if(!rem.hasMatch())
+          continue;
+        ext = rem.captured(1);
+        QList<Scene_item*>to_save;
+        to_save.append(item);
+        QString savename(tr("%1.%2").arg(item->name()).arg(ext));
+        QString fullpath = make_fullpath(savename, true);
+        savename = QFileInfo(fullpath).fileName();
+        iop->save(QFileInfo(fullpath), to_save);
+        names.push_back(std::make_pair(savename, item->name()));
+        loader=iop->name();
+        break;
+      }
+    }
     if(loader.isEmpty())
     {
-      not_saved.push_back(item->name());
+      QMessageBox::warning(this, "", tr("No plugin found for %1. Not saved.").arg(item->name()));
       continue;
     }
-    names.push_back(source);
-    loaders.push_back(loader);
+    loaders.push_back(std::make_pair(loader, ext));
     colors.push_back(item->color());
     rendering_modes.push_back(item->renderingMode());
   }
+  if(loaders.empty())
+    return;
   //path
   os << "var camera = \""<<viewer->dumpCameraCoordinates().toStdString()<<"\";\n";
   os << "var items = [";
   for(std::size_t i = 0; i< names.size() -1; ++i)
   {
-    os << "\'" << names[i].toStdString() << "\', ";
+    QString fullpath = make_fullpath(names[i].first);
+
+    QByteArray item = file_to_string(fullpath.toStdString().c_str());
+    os<<"[\'";
+    os<<qCompress(item, 9).toBase64().toStdString().c_str();
+    os << "\', \'"<<names[i].second.toStdString().c_str()<<"\']," ;
+    //delete temp file
+    QFile tmp_file(fullpath);
+    tmp_file.remove();
   }
-  os<<"\'"<<names.back().toStdString()<<"\'];\n";
-  
+  QString fullpath = make_fullpath(names.back().first);
+  QByteArray item = file_to_string(fullpath.toStdString().c_str());
+  os<<"[\'";
+  os<<qCompress(item, 9).toBase64().toStdString().c_str();
+  os << "\', \'"<<names.back().second.toStdString().c_str()<<"\']];\n";
+  //delete temp file
+  QFile tmp_file(fullpath);
+  tmp_file.remove();
   //plugin
   os << "var loaders = [";
   for(std::size_t i = 0; i< names.size() -1; ++i)
   {
-    os << "\'" << loaders[i].toStdString() << "\', ";
+    os << "[\'" << loaders[i].first.toStdString() << "\', \'"<<loaders[i].second.toStdString()<< "\'],";
   }
-  os<<"\'"<<loaders.back().toStdString()<<"\'];\n";
-  
+  os << "[\'" << loaders.back().first.toStdString() << "\', \'"<<loaders.back().second.toStdString()<< "\']];\n";
+
   //color
   os << "var colors = [";
   for(std::size_t i = 0; i< names.size() -1; ++i)
@@ -2848,7 +3057,7 @@ void MainWindow::on_actionSa_ve_Scene_as_Script_triggered()
     os << "[" << colors[i].red() <<", "<< colors[i].green() <<", "<< colors[i].blue() <<"], ";
   }
   os<<"[" << colors.back().red() <<", "<< colors.back().green() <<", "<< colors.back().blue() <<"]];\n";
-  
+
   //rendering mode
   os << "var rendering_modes = [";
   for(std::size_t i = 0; i< names.size() -1; ++i)
@@ -2856,10 +3065,13 @@ void MainWindow::on_actionSa_ve_Scene_as_Script_triggered()
     os << rendering_modes[i] << ", ";
   }
   os << rendering_modes.back()<<"];\n";
-  os <<"var initial_scene_size = scene.numberOfEntries;\n";
   os << "items.forEach(function(item, index, array){\n";
-  os << "        main_window.open(item, loaders[index]);\n";
-  os << "        var it = scene.item(initial_scene_size+index);\n";
+  os<<"          var path=items[index][1];\n";
+  os<<"          path+='.';\n";
+  os<<"          path+=loaders[index][1];\n";
+  os<<"          var fullpath = main_window.write_string_to_file(item[0], path);\n";
+  os<<"          main_window.open(fullpath,loaders[index][0]);\n";
+  os << "        var it = scene.item(scene.numberOfEntries-1);\n";
   os << "        var r = colors[index][0];\n";
   os << "        var g = colors[index][1];\n";
   os << "        var b = colors[index][2];\n";
@@ -2873,6 +3085,60 @@ void MainWindow::on_actionSa_ve_Scene_as_Script_triggered()
                          "Items Not  Saved",
                          QString("The following items could not be saved: %1").arg(
                            not_saved.join(", ")));
+#ifdef CGAL_USE_SSH
+  using namespace CGAL::ssh_internal;
+  if(do_upload)
+  {
+    QString server = settings.value("ssh_server", QString()).toString();
+    QString pk = settings.value("ssh_public_key", QString()).toString();
+    QString privK = settings.value("ssh_priv_key", QString()).toString();
+    user = user.trimmed();
+    server = server.trimmed();
+    pk = pk.trimmed();
+    privK=privK.trimmed();
+    if(user.isEmpty()){
+      return;
+    }
+    QString path;
+    path = QInputDialog::getText(this,
+                                 "",
+                                 tr("Enter the destination path for your file."));
+    if(path.isEmpty())
+      return;
+    try{
+      ssh_session session;
+      bool res = establish_ssh_session(session,
+                            user.toStdString().c_str(),
+                            server.toStdString().c_str(),
+                            pk.toStdString().c_str(),
+                            privK.toStdString().c_str(),
+                            pass.toStdString().c_str());
+      if(!res)
+      {
+        QMessageBox::warning(this,
+                             "Error",
+                             "The SSH session could not be started.");
+        return;
+      }
+      res = push_file(session,path.toStdString().c_str(), filename.toStdString().c_str());
+      if(!res)
+      {
+        QMessageBox::warning(this,
+                             "Error",
+                             "The file could not be uploaded. Check your console for more information.");
+        close_connection(session);
+        return;
+      }
+      close_connection(session);
+      QFile tmp_file(filename);
+      tmp_file.remove();
+    } catch( ssh::SshException e )
+    {
+      std::cout << "Error during connection : ";
+      std::cout << e.getError() << std::endl;
+    }
+  }
+#endif
 }
 void MainWindow::setTransparencyPasses(int val)
 {
@@ -2900,7 +3166,7 @@ void MainWindow::toggleFullScreen()
       dock->show();
     }
     visibleDockWidgets.clear();
-    
+
   }
 }
 
@@ -2923,7 +3189,7 @@ void MainWindow::setupViewer(Viewer* viewer, SubViewer* subviewer)
           viewer, SLOT(update()));
   connect(scene, SIGNAL(updated()),
           viewer, SLOT(update()));
-  
+
   QAction* action = subviewer->findChild<QAction*>("actionRecenter");
   connect(action, SIGNAL(triggered()),
           viewer, SLOT(update()));
@@ -2985,16 +3251,43 @@ void MainWindow::setupViewer(Viewer* viewer, SubViewer* subviewer)
           this, SLOT(selectSceneItem(int)));
   connect(viewer, SIGNAL(selectedPoint(double, double, double)),
           this, SLOT(showSelectedPoint(double, double, double)));
-  
+
   connect(viewer, SIGNAL(selectionRay(double, double, double,
                                       double, double, double)),
           scene, SIGNAL(selectionRay(double, double, double,
                                      double, double, double)));
-  
+
   connect(viewer, &Viewer::sendMessage,
           this, [](QString s){
     information(s);
   });
+
+#ifdef CGAL_USE_WEBSOCKETS
+  action= subviewer->viewer->findChild<QAction*>("actionShareCamera");
+  connect(action, &QAction::toggled,
+          this, [this, viewer](bool b)
+  {
+    if(!viewer){
+      return;
+    }
+    QString session;
+    if(b){
+      bool ok;
+      session = QInputDialog::getText(
+            this,"Session",
+            "Please enter the session name.\n"
+            "Only the machines that enter the same session name will be connected.\n"
+            "Several sessions can run simultaneously on a same server. ",
+            QLineEdit::Normal, QString(), &ok);
+      if(session.isEmpty() || !ok)
+      {
+        viewer->setShareCam(false, session);
+        return;
+      }
+    }
+    viewer->setShareCam(b, session);
+  });
+#endif
   
 }
 
@@ -3014,7 +3307,7 @@ void MainWindow::on_actionAdd_Viewer_triggered()
     scene->removeViewer(viewer2);
     viewerDestroyed(viewer2);
   });
-  
+
   setupViewer(viewer2, subviewer);
   viewer2->camera()->interpolateToFitScene();
   subviewer->show();
@@ -3147,11 +3440,20 @@ SubViewer::SubViewer(QWidget *parent, MainWindow* mw, Viewer* mainviewer)
   QAction* actionTotalPass = new QAction("Set Transparency Pass &Number...",this);
   actionTotalPass->setObjectName("actionTotalPass");
   viewMenu->addAction(actionTotalPass);
+#ifdef CGAL_USE_WEBSOCKETS
+  QAction* actionShareCamera= new QAction("Join &WS Server",viewer);
+  actionShareCamera->setObjectName("actionShareCamera");
+  actionShareCamera->setCheckable(true);
+  actionShareCamera->setChecked(false);
+  viewMenu->addAction(actionShareCamera);
+#endif
+
   QAction* actionBackFrontShading = new QAction("Activate Back/Front shading.",this);
   actionBackFrontShading->setObjectName("actionBackFrontShading");
   actionBackFrontShading->setCheckable(true);
   actionBackFrontShading->setChecked(false);
   viewMenu->addAction(actionBackFrontShading);
+
   if(mainviewer)
     setAttribute(Qt::WA_DeleteOnClose);
   setWindowIcon(QIcon(":/cgal/icons/resources/menu.png"));
@@ -3199,7 +3501,7 @@ void SubViewer::color()
 
 void SubViewer::closeEvent(QCloseEvent *closeEvent)
 {
-  
+
   if(is_main)
   {
     QMessageBox::information(mw, "", "This is the main viewer. It cannot be closed.");
@@ -3220,9 +3522,9 @@ void SubViewer::changeEvent(QEvent *event)
       {
         menu->addAction(action);
       }
-      setWindowFlags( 
+      setWindowFlags(
               Qt::SubWindow
-              | Qt::CustomizeWindowHint 
+              | Qt::CustomizeWindowHint
               | Qt::WindowMaximizeButtonHint
               //| Qt::WindowSystemMenuHint
               | Qt::WindowTitleHint
@@ -3238,9 +3540,9 @@ void SubViewer::changeEvent(QEvent *event)
       {
         menu->removeAction(action);
       }
-      setWindowFlags( 
+      setWindowFlags(
               Qt::SubWindow
-              | Qt::CustomizeWindowHint 
+              | Qt::CustomizeWindowHint
               | Qt::WindowMaximizeButtonHint
               | Qt::WindowSystemMenuHint
               | Qt::WindowTitleHint
@@ -3262,7 +3564,7 @@ void MainWindow::invalidate_bbox(bool do_recenter)
 
 void MainWindow::on_action_Save_triggered()
 {
-  if(QMessageBox::question(this, "Save", "Are you sure you want to override these files ?") 
+  if(QMessageBox::question(this, "Save", "Are you sure you want to override these files ?")
      == QMessageBox::No)
     return;
   QList<Scene_item*> to_save;
@@ -3278,3 +3580,187 @@ void MainWindow::on_action_Save_triggered()
     }
   }
 }
+
+void MainWindow::on_actionLoad_a_Scene_from_a_Script_File_triggered()
+{
+  bool do_download = false;
+  QString filename;
+
+#ifdef CGAL_USE_SSH
+  QString user = settings.value("ssh_user", QString()).toString();
+  QString pass;
+  if(!user.isEmpty())
+  {
+    QMessageBox::StandardButton doyou =
+        QMessageBox::question(this, tr("Download ?"), tr("Do you wish to download the scene"
+                                                         " using the SSH preferences ?"));
+    bool ok;
+    do_download= (doyou == QMessageBox::Yes);
+    if(do_download)
+    {
+      pass = QInputDialog::getText(this, "SSH Password",
+                                   "Enter ssh key password:",
+                                   QLineEdit::Password,
+                                   tr(""),
+                                   &ok);
+      if(!ok)
+        return;
+      pass = pass.trimmed();
+    }
+  }
+#endif
+
+  if(do_download)
+  {
+    #ifdef CGAL_USE_SSH
+    using namespace CGAL::ssh_internal;
+    QString server = settings.value("ssh_server", QString()).toString();
+    QString pk = settings.value("ssh_public_key", QString()).toString();
+    QString privK = settings.value("ssh_priv_key", QString()).toString();
+    user = user.trimmed();
+    server = server.trimmed();
+    pk = pk.trimmed();
+    privK=privK.trimmed();
+    QString path;
+    path = QInputDialog::getText(this,
+                                 "",
+                                 tr("Enter the remote path for your file."));
+    if(path.isEmpty())
+      return;
+    try{
+      ssh_session session;
+      bool res = establish_ssh_session(session,
+                            user.toStdString().c_str(),
+                            server.toStdString().c_str(),
+                            pk.toStdString().c_str(),
+                            privK.toStdString().c_str(),
+                            pass.toStdString().c_str());
+      if(!res)
+      {
+        QMessageBox::warning(this,
+                             "Error",
+                             "The SSH session could not be started.");
+        return;
+      }
+      filename = QString("%1/load_scene.js").arg(QDir::tempPath());
+      path = tr("/tmp/%2").arg(path);
+      res = pull_file(session,path.toStdString().c_str(), filename.toStdString().c_str());
+      if(!res)
+      {
+        QMessageBox::warning(this,
+                             "Error",
+                             "The file could not be fetched. Check your console for more info.");
+        close_connection(session);
+        return;
+      }
+      close_connection(session);
+    } catch( ssh::SshException e )
+    {
+      std::cout << "Error during connection : ";
+      std::cout << e.getError() << std::endl;
+    }
+    #endif
+  }
+  else
+  {
+    filename =  QFileDialog::getOpenFileName(
+          this,
+          tr("Select a Whole Scene file..."),
+          ".",
+          "Whole Scene files (*.js)");
+    if(filename.isEmpty())
+      return;
+  }
+  loadScript(QFileInfo(filename));
+  if(do_download){
+    QFile tmp_file(filename);
+    tmp_file.remove();
+  }
+}
+
+#ifdef CGAL_USE_WEBSOCKETS
+void MainWindow::on_action_Start_a_Session_triggered()
+{
+  QAction * action= findChild<QAction*>("action_Start_a_Session");
+  static EchoServer *server =nullptr;
+  if(action->isChecked()){
+     server = new EchoServer(1234);
+    QObject::connect(server, &EchoServer::closed, server,&EchoServer::deleteLater);
+  }
+  else
+  {
+    server->deleteLater();
+  }
+}
+
+EchoServer::EchoServer(quint16 port) :
+    QObject(CGAL::Three::Three::mainWindow()),
+    m_pWebSocketServer(new QWebSocketServer(QStringLiteral("Echo Server"),
+                                            QWebSocketServer::NonSecureMode, this))
+{
+    if (m_pWebSocketServer->listen(QHostAddress::Any, port)) {
+        connect(m_pWebSocketServer, &QWebSocketServer::newConnection,
+                this, &EchoServer::onNewConnection);
+        connect(m_pWebSocketServer, &QWebSocketServer::closed, this, &EchoServer::closed);
+    }
+    QHostAddress local_host("0.0.0.0");
+
+    //to avoid printing 127.0.0.1. Not realy sure it won't ever print the external ipv4 though.
+    const QHostAddress &localhost = QHostAddress(QHostAddress::LocalHost);
+    for (const QHostAddress &address: QNetworkInterface::allAddresses()) {
+      if (address.protocol() == QAbstractSocket::IPv4Protocol && address != localhost)
+      {
+        local_host= address;
+        break;
+      }
+    }
+    QMessageBox mb(QMessageBox::NoIcon, "WS Server",
+                   tr("WebSockets Server started.\nEnter the following address in\nyour Network Preferences to be able to join it :\n"
+                      "ws://%1:%2").arg(local_host.toString()).arg(port), QMessageBox::Ok, CGAL::Three::Three::mainWindow());
+    mb.setTextInteractionFlags(Qt::TextSelectableByMouse);
+    mb.exec();
+}
+
+EchoServer::~EchoServer()
+{
+    m_pWebSocketServer->close();
+    qDeleteAll(m_clients.begin(), m_clients.end());
+}
+
+void EchoServer::onNewConnection()
+{
+    QWebSocket *pSocket = m_pWebSocketServer->nextPendingConnection();
+
+    connect(pSocket, &QWebSocket::textMessageReceived, this, &EchoServer::processTextMessage);
+    connect(pSocket, &QWebSocket::binaryMessageReceived, this, &EchoServer::processBinaryMessage);
+    connect(pSocket, &QWebSocket::disconnected, this, &EchoServer::socketDisconnected);
+
+    m_clients << pSocket;
+}
+
+void EchoServer::processTextMessage(QString message)
+{
+    QWebSocket *pClient = qobject_cast<QWebSocket *>(sender());
+    for(auto *client : m_clients) {
+      if(client != pClient)
+        client->sendTextMessage(message);
+    }
+}
+
+void EchoServer::processBinaryMessage(QByteArray message)
+{
+    QWebSocket *pClient = qobject_cast<QWebSocket *>(sender());
+    if (pClient) {
+        pClient->sendBinaryMessage(message);
+    }
+}
+
+void EchoServer::socketDisconnected()
+{
+    QWebSocket *pClient = qobject_cast<QWebSocket *>(sender());
+    if (pClient) {
+        m_clients.removeAll(pClient);
+        pClient->deleteLater();
+    }
+}
+#endif
diff --git a/Polyhedron/demo/Polyhedron/MainWindow.h b/Polyhedron/demo/Polyhedron/MainWindow.h
index e4bd6d5b3b1..b7650b52b34 100644
--- a/Polyhedron/demo/Polyhedron/MainWindow.h
+++ b/Polyhedron/demo/Polyhedron/MainWindow.h
@@ -138,6 +138,8 @@ public Q_SLOTS:
    This slot is for use by scripts.*/
   bool open(QString filename, QString loader_name);
 
+  QString write_string_to_file(const QString &str, const QString& filename);
+
   /*! Reloads an item. Expects to be called by a QAction with the
    index of the item to be reloaded as data attached to the action.
    The index must identify a valid `Scene_item`.*/
@@ -352,6 +354,10 @@ protected Q_SLOTS:
   void save(QString filename, QList<CGAL::Three::Scene_item*>& to_save);
   //!Calls the function saveSnapShot of the viewer.
   void on_actionSaveSnapshot_triggered();
+#ifdef CGAL_USE_WEBSOCKETS
+  //!Starts a new WS server if none is already exist. Else, does nothing.
+  void on_action_Start_a_Session_triggered();
+#endif
   //!Opens a Dialog to choose a color and make it the background color.
   void setBackgroundColor();
   //!Opens a Dialog to change the lighting settings
@@ -447,6 +453,7 @@ public:
 #endif
 public Q_SLOTS:
   void on_actionSa_ve_Scene_as_Script_triggered();
+  void on_actionLoad_a_Scene_from_a_Script_File_triggered();
   void toggleFullScreen();
   void setDefaultSaveDir();
   void invalidate_bbox(bool do_recenter);
@@ -494,4 +501,30 @@ protected:
 private:
   bool is_main;
 };
+#ifdef CGAL_USE_WEBSOCKETS
+QT_FORWARD_DECLARE_CLASS(QWebSocketServer)
+QT_FORWARD_DECLARE_CLASS(QWebSocket)
+
+class EchoServer : public QObject
+{
+    Q_OBJECT
+public:
+    explicit EchoServer(quint16 port);
+    ~EchoServer();
+
+
+Q_SIGNALS:
+    void closed();
+
+private Q_SLOTS:
+    void onNewConnection();
+    void processTextMessage(QString message);
+    void processBinaryMessage(QByteArray message);
+    void socketDisconnected();
+
+private:
+    QWebSocketServer *m_pWebSocketServer;
+    QList<QWebSocket *> m_clients;
+};
+#endif
 #endif // ifndef MAINWINDOW_H
diff --git a/Polyhedron/demo/Polyhedron/MainWindow.ui b/Polyhedron/demo/Polyhedron/MainWindow.ui
index a011dedab64..6273a37bd16 100644
--- a/Polyhedron/demo/Polyhedron/MainWindow.ui
+++ b/Polyhedron/demo/Polyhedron/MainWindow.ui
@@ -58,6 +58,7 @@
     <addaction name="action_Save"/>
     <addaction name="actionSaveAs"/>
     <addaction name="actionSa_ve_Scene_as_Script"/>
+    <addaction name="actionLoad_a_Scene_from_a_Script_File"/>
     <addaction name="actionSaveSnapshot"/>
     <addaction name="separator"/>
     <addaction name="actionLoadScript"/>
@@ -96,6 +97,7 @@
     <addaction name="action_Rearrange_Viewers"/>
     <addaction name="menuDockWindows"/>
     <addaction name="separator"/>
+    <addaction name="action_Start_a_Session"/>
    </widget>
    <addaction name="menuFile"/>
    <addaction name="menuEdit"/>
@@ -463,6 +465,22 @@
     <string>&amp;Save</string>
    </property>
   </action>
+  <action name="actionLoad_a_Scene_from_a_Script_File">
+   <property name="text">
+    <string>Load a Scene &amp;from a Script File...</string>
+   </property>
+  </action>
+  <action name="action_Start_a_Session">
+   <property name="checkable">
+    <bool>true</bool>
+   </property>
+   <property name="text">
+    <string>&amp;Start a Session</string>
+   </property>
+   <property name="toolTip">
+    <string>Start a WebSocket Server to Share your Camera with Others on your Network.</string>
+   </property>
+  </action>
  </widget>
  <resources>
   <include location="Polyhedron_3.qrc"/>
diff --git a/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
index 0cf39f89ccb..d23ff947d9a 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/AABB_tree/Cut_plugin.cpp
@@ -860,6 +860,12 @@ public:
     return ok;
   }
 
+  bool isDefaultLoader(const Scene_item* item) const Q_DECL_OVERRIDE{
+    if(qobject_cast<const Scene_edges_item*>(item))
+      return true;
+    return false;
+  }
+
   using Polyhedron_demo_io_plugin_interface::init;
   void init(QMainWindow* mainWindow, CGAL::Three::Scene_interface* scene_interface,
             Messages_interface* m) override;
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Classification/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/Classification/CMakeLists.txt
index c0b3eded9c2..f272d98b4cd 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Classification/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/Classification/CMakeLists.txt
@@ -2,73 +2,51 @@ include( polyhedron_demo_macros )
 
 if(EIGEN3_FOUND)
 
-  set(classification_linked_libraries)
-  set(classification_compile_definitions)
-  
-  find_package(Boost OPTIONAL_COMPONENTS serialization iostreams)
+  set(Classification_dependencies_met TRUE)
 
-  if( WIN32 )
-# to avoid a warning with old cmake
-    set(_Boost_BZIP2_HEADERS             "boost/iostreams/filter/bzip2.hpp")
-    set(_Boost_ZLIB_HEADERS              "boost/iostreams/filter/zlib.hpp")
-    find_package( Boost OPTIONAL_COMPONENTS serialization iostreams bzip2 zlib)
-    if( Boost_ZLIB_FOUND AND Boost_BZIP2_FOUND)
-      if(TARGET Boost::bzip2 AND TARGET Boost::zlib)
-        set(classification_linked_libraries ${classification_linked_libraries}
-          Boost::bzip2 Boost::zlib)
-      else()
-        set(classification_linked_libraries ${classification_linked_libraries}
-          ${Boost_ZLIB_LIBRARY} ${Boost_BZIP2_LIBRARY})
-      endif()
-    endif()
+  find_package( Boost OPTIONAL_COMPONENTS serialization iostreams )
+  if (NOT Boost_SERIALIZATION_FOUND)
+    message(STATUS "NOTICE: Boost Serialization not found. Classification plugin won't be available.")
+    set(Classification_dependencies_met FALSE)
+  endif()
+  
+  if (NOT Boost_IOSTREAMS_FOUND)
+    message(STATUS "NOTICE: Boost IOStreams not found. Classification plugin won't be available.")
+    set(Classification_dependencies_met FALSE)
   endif()
 
-  if (Boost_SERIALIZATION_FOUND AND Boost_IOSTREAMS_FOUND AND (NOT WIN32 OR Boost_ZLIB_FOUND))
+  find_package(OpenCV QUIET COMPONENTS core ml) # Need core + machine learning
+  if (NOT OpenCV_FOUND)
+    message(STATUS "NOTICE: OpenCV was not found. OpenCV random forest predicate for classification won't be available.")
+  endif()
+
+  find_package(TensorFlow QUIET) 
+  if (NOT TensorFlow_FOUND)
+    message(STATUS "NOTICE: TensorFlow not found, Neural Network predicate for classification won't be available.")
+  endif()
+
+  if (Classification_dependencies_met)
     qt5_wrap_ui( classificationUI_FILES Classification_widget.ui Classification_advanced_widget.ui )
     polyhedron_demo_plugin(classification_plugin Classification_plugin Point_set_item_classification Cluster_classification Surface_mesh_item_classification ${classificationUI_FILES} KEYWORDS Classification)
-
-    if(TARGET Boost::serialization AND TARGET Boost::iostreams)
-      set(classification_linked_libraries ${classification_linked_libraries}
-        Boost::serialization Boost::iostreams)
-    else()
-      set(classification_linked_libraries ${classification_linked_libraries}
-        ${Boost_SERIALIZATION_LIBRARY}
-        ${Boost_IOSTREAMS_LIBRARY})
+    target_link_libraries(classification_plugin PUBLIC scene_points_with_normal_item
+      scene_polylines_item scene_polygon_soup_item scene_surface_mesh_item scene_selection_item scene_color_ramp)
+    
+    CGAL_target_use_Eigen(classification_plugin)
+    CGAL_target_use_Boost_IOStreams(classification_plugin)
+    CGAL_target_use_Boost_Serialization(classification_plugin)
+    if(OpenCV_FOUND)
+      CGAL_target_use_OpenCV(classification_plugin)
     endif()
-
-    find_package(OpenCV QUIET COMPONENTS core ml) # Need core + machine learning
-    if (OpenCV_FOUND)
-      message(STATUS "Found OpenCV ${OpenCV_VERSION}")
-      include_directories(${OpenCV_INCLUDE_DIRS})
-      set(classification_linked_libraries ${classification_linked_libraries}
-        ${OpenCV_LIBS})
-      set(classification_compile_definitions ${classification_compile_definitions}
-        "-DCGAL_LINKED_WITH_OPENCV")
-    else()
-      message(STATUS "NOTICE: OpenCV was not found. OpenCV random forest predicate for classification won't be available.")
+    if(TensorFlow_FOUND)
+      CGAL_target_use_TensorFlow(classification_plugin)
     endif()
-
-    find_package(TensorFlow QUIET)
-    if (TensorFlow_FOUND)
-      message(STATUS "Found TensorFlow")
-      set(classification_linked_libraries ${classification_linked_libraries}
-        ${TensorFlow_LIBRARY})
-      set(classification_compile_definitions ${classification_compile_definitions}
-        "-DCGAL_LINKED_WITH_TENSORFLOW")
-      include_directories( ${TensorFlow_INCLUDE_DIR} )
-    else()
-      message(STATUS "NOTICE: TensorFlow not found, Neural Network predicate for classification won't be available.")
+    if(TBB_FOUND)
+      CGAL_target_use_TBB(classification_plugin)
     endif()
     
-    target_link_libraries(classification_plugin PUBLIC scene_points_with_normal_item
-      scene_polylines_item scene_polygon_soup_item scene_surface_mesh_item scene_selection_item scene_color_ramp ${classification_linked_libraries})
     add_dependencies(classification_plugin point_set_selection_plugin selection_plugin)
-    target_compile_definitions(classification_plugin PUBLIC ${classification_compile_definitions})
-  else()
-    message(STATUS "NOTICE: Boost Serialization or IO Streams or ZLIB not found. Classification plugin won't be available.")
   endif()
 
-
 else(EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Classification plugin will not be available.")
 endif()
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Convex_hull/Convex_hull_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/Convex_hull/Convex_hull_plugin.cpp
index 3722f916e42..b973eeae32f 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Convex_hull/Convex_hull_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/Convex_hull/Convex_hull_plugin.cpp
@@ -80,28 +80,15 @@ void Polyhedron_demo_convex_hull_plugin::on_actionConvexHull_triggered()
 
     // add convex hull as new polyhedron
     SMesh *pConvex_hull  = new SMesh;
-    typedef boost::property_map<SMesh,CGAL::vertex_point_t>::type Vpmap;
-    typedef CGAL::Property_map_to_unary_function<Vpmap> Vpmap_fct;
     if(selection_item) {
       SMesh* pMesh = selection_item->polyhedron();
-      Vpmap vpm = get(CGAL::vertex_point,*pMesh);
-      
-      Vpmap_fct v2p(vpm);
       CGAL::convex_hull_3(
-        boost::make_transform_iterator(selection_item->selected_vertices.begin(), v2p),
-        boost::make_transform_iterator(selection_item->selected_vertices.end(), v2p),
-        *pConvex_hull);
+            *pMesh,
+            *pConvex_hull);
     }
     else if ( sm_item ){
       SMesh* pMesh = sm_item->polyhedron();
-      Vpmap vpm = get(CGAL::vertex_point,*pMesh);
-      
-      Vpmap_fct v2p(vpm);
-      boost::graph_traits<SMesh>::vertex_iterator b,e;
-      boost::tie(b,e) = vertices(*pMesh);
-      
-      CGAL::convex_hull_3(boost::make_transform_iterator(b,v2p),
-                          boost::make_transform_iterator(e,v2p),
+      CGAL::convex_hull_3(*pMesh,
                           *pConvex_hull);
                           
     }
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Display/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/Display/CMakeLists.txt
index 88145266135..c783cd751ac 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Display/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/Display/CMakeLists.txt
@@ -3,4 +3,5 @@ if(EIGEN3_FOUND)
   qt5_wrap_ui( display_propertyUI_FILES Display_property.ui )
   polyhedron_demo_plugin(display_property_plugin Display_property_plugin ${display_propertyUI_FILES})
   target_link_libraries(display_property_plugin PUBLIC scene_surface_mesh_item scene_points_with_normal_item scene_color_ramp)
+  CGAL_target_use_Eigen(display_property_plugin)
 endif(EIGEN3_FOUND)
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/3mf_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/3mf_io_plugin.cpp
index d2e34e4e00e..90f036e8cea 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/3mf_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/3mf_io_plugin.cpp
@@ -78,61 +78,6 @@ class Io_3mf_plugin:
     std::vector<std::string> names;
     QList<Scene_item*> result;
     std::vector<std::vector<CGAL::Color> > all_colors;
-    int nb_polylines =
-        CGAL::read_polylines_from_3mf(fileinfo.filePath().toUtf8().toStdString(),
-                                      all_points, all_colors, names);
-    if(nb_polylines < 0 )
-    {
-      ok = false;
-      std::cerr << "Error in reading of meshes."<<std::endl;
-      return result;
-    }
-
-    for(int i=0; i< nb_polylines; ++i)
-    {
-      Scene_polylines_item* pol_item = new Scene_polylines_item();
-      PolylineRange& polylines = pol_item->polylines;
-      polylines.push_back(all_points[i]);
-      pol_item->setName(names[i].data());
-      pol_item->invalidateOpenGLBuffers();
-      CGAL::Color c = all_colors[i].front();
-      pol_item->setColor(QColor(c.red(), c.green(), c.blue()));
-      pol_item->setProperty("already_colord", true);
-      result << pol_item;
-      if(add_to_scene)
-        CGAL::Three::Three::scene()->addItem(pol_item);
-    }
-    all_points.clear();
-    all_colors.clear();
-    names.clear();
-    int nb_point_sets =
-        CGAL::read_point_clouds_from_3mf(fileinfo.filePath().toUtf8().toStdString(),
-                                         all_points, all_colors, names);
-    if(nb_point_sets < 0 )
-    {
-      ok = false;
-      std::cerr << "Error in reading of meshes."<<std::endl;
-      return result;
-    }
-    for(int i=0; i< nb_point_sets; ++i)
-    {
-      Scene_points_with_normal_item* pts_item = new Scene_points_with_normal_item();
-      for(std::size_t j = 0; j < all_points[i].size(); ++j)
-      {
-        pts_item->point_set()->insert(all_points[i][j]);
-      }
-      pts_item->setName(names[i].data());
-      pts_item->invalidateOpenGLBuffers();
-      CGAL::Color c = all_colors[i].front();
-      pts_item->setColor(QColor(c.red(), c.green(), c.blue()));
-      pts_item->setProperty("already_colord", true);
-      result << pts_item;
-      if(add_to_scene)
-        CGAL::Three::Three::scene()->addItem(pts_item);
-    }
-    all_points.clear();
-    names.clear();
-    all_colors.clear();
     int nb_meshes =
         CGAL::read_triangle_soups_from_3mf(fileinfo.filePath().toUtf8().toStdString(),
                                   all_points, all_polygons, all_colors, names);
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/IO/CMakeLists.txt
index 01a48c330b8..c4487f3b768 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/CMakeLists.txt
@@ -71,8 +71,9 @@ else()
   
   if (LASLIB_FOUND)
     polyhedron_demo_plugin(las_plugin LAS_io_plugin KEYWORDS IO PointSetProcessing Classification)
-    target_link_libraries(las_plugin PUBLIC scene_points_with_normal_item ${LASLIB_LIBRARIES})
+    target_link_libraries(las_plugin PUBLIC scene_points_with_normal_item)
     target_compile_features(las_plugin PRIVATE ${needed_cxx_features})
+    CGAL_target_use_LASLIB(las_plugin)
   else()
     message(STATUS "NOTICE : the LAS IO plugin needs LAS libraries and will not be compiled.")
   endif()
@@ -85,10 +86,10 @@ find_path(3MF_INCLUDE_DIR
   )
 find_library(3MF_LIBRARIES NAMES 3MF DOC "Path to the lib3MF library")
 
-if(3MF_LIBRARIES AND 3MF_INCLUDE_DIR)
+if(3MF_LIBRARIES AND 3MF_INCLUDE_DIR AND EXISTS "${3MF_INCLUDE_DIR}/Model/COM/NMR_DLLInterfaces.h")
   include_directories(${3MF_INCLUDE_DIR})
   polyhedron_demo_plugin(3mf_io_plugin 3mf_io_plugin KEYWORDS IO PMP)
   target_link_libraries(3mf_io_plugin PRIVATE scene_surface_mesh_item scene_points_with_normal_item scene_polylines_item ${3MF_LIBRARIES})
 else()
-  message(STATUS "NOTICE : The 3mf_io_plugin requires the lib3MF library, and will not be compiled.")
+  message(STATUS "NOTICE : The 3mf_io_plugin requires the lib3MF library in a version < 2.0, and will not be compiled.")
 endif()
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/Nef_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/Nef_io_plugin.cpp
index 4aab33b4e0a..22b2ed695d4 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/Nef_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/Nef_io_plugin.cpp
@@ -15,13 +15,18 @@ class Polyhedron_demo_io_nef_plugin :
   Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.PluginInterface/1.0" FILE "nef_io_plugin.json")
 
 public:
-  QString nameFilters() const;
-  QString name() const { return "io_nef_plugin"; }
-  bool canLoad(QFileInfo) const;
-  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true);
+  QString nameFilters() const override;
+  QString name() const override { return "io_nef_plugin"; }
+  bool canLoad(QFileInfo) const override;
+  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true) override;
 
-  bool canSave(const CGAL::Three::Scene_item*);
-  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& items);
+  bool canSave(const CGAL::Three::Scene_item*) override;
+  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& items) override;
+  bool isDefaultLoader(const Scene_item* item) const override{
+    if(qobject_cast<const Scene_nef_polyhedron_item*>(item))
+      return true;
+    return false;
+  }
 };
 
 QString Polyhedron_demo_io_nef_plugin::nameFilters() const {
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/OFF_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/OFF_io_plugin.cpp
index e62593c9b89..6b195e276c4 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/OFF_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/OFF_io_plugin.cpp
@@ -29,28 +29,28 @@ class Polyhedron_demo_off_plugin :
   Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.IOPluginInterface/1.90" FILE "off_io_plugin.json")
 
 public:
-  bool isDefaultLoader(const Scene_item *item) const
+  bool isDefaultLoader(const Scene_item *item) const override
   {
     if(qobject_cast<const Scene_surface_mesh_item*>(item)
        || qobject_cast<const Scene_polygon_soup_item*>(item))
       return true;
     return false;
   }
-  bool isDefaultLoader(const QString& name) const
+  bool isDefaultLoader(const QString& name) const override
   {
     if(name == QString("off"))
       return true;
     return false;
   }
-  QString name() const { return "off_plugin"; }
-  QString nameFilters() const { return "OFF files (*.off);;Wavefront OBJ (*.obj)"; }
-  bool canLoad(QFileInfo fileinfo) const;
-  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true);
+  QString name() const override{ return "off_plugin"; }
+  QString nameFilters() const override { return "OFF files (*.off);;Wavefront OBJ (*.obj)"; }
+  bool canLoad(QFileInfo fileinfo) const override;
+  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true) override;
   CGAL::Three::Scene_item* load_off(QFileInfo fileinfo);
   CGAL::Three::Scene_item* load_obj(QFileInfo fileinfo);
 
-  bool canSave(const CGAL::Three::Scene_item*);
-  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& );
+  bool canSave(const CGAL::Three::Scene_item*) override;
+  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& ) override;
 };
 
 bool Polyhedron_demo_off_plugin::canLoad(QFileInfo) const {
@@ -136,7 +136,10 @@ Polyhedron_demo_off_plugin::load_off(QFileInfo fileinfo) {
   // Try to read .off in a surface_mesh
   SMesh *surface_mesh = new SMesh();
   try{
-    in >> *surface_mesh;
+    if(!(in >> *surface_mesh))
+    {
+      surface_mesh->clear();
+    }
   } catch(...)
   {
     surface_mesh->clear();
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/PLY_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/PLY_io_plugin.cpp
index 6ce2fdeb793..75c2e1d9845 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/PLY_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/PLY_io_plugin.cpp
@@ -23,19 +23,19 @@ class Polyhedron_demo_ply_plugin :
   Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.IOPluginInterface/1.90" FILE "ply_io_plugin.json")
 
 public:
-  bool isDefaultLoader(const CGAL::Three::Scene_item *item) const 
+  bool isDefaultLoader(const CGAL::Three::Scene_item *item) const override
   { 
     if(qobject_cast<const Scene_points_with_normal_item*>(item)) 
       return true; 
     return false;
   }
-  QString name() const { return "ply_plugin"; }
-  QString nameFilters() const { return "PLY files (*.ply)"; }
-  bool canLoad(QFileInfo fileinfo) const;
-  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true);
+  QString name() const override{ return "ply_plugin"; }
+  QString nameFilters() const override{ return "PLY files (*.ply)"; }
+  bool canLoad(QFileInfo fileinfo) const override;
+  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true)override;
 
-  bool canSave(const CGAL::Three::Scene_item*);
-  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>&);
+  bool canSave(const CGAL::Three::Scene_item*)override;
+  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>&)override;
 
 };
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/Polylines_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/Polylines_io_plugin.cpp
index d86309749f8..d9fe0b44e0d 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/Polylines_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/Polylines_io_plugin.cpp
@@ -75,6 +75,12 @@ public:
     return QList<QAction*>()<<actionSplit_polylines
                             <<actionJoin_polylines;
   }
+  
+  bool isDefaultLoader(const Scene_item* item) const override{
+    if(qobject_cast<const Scene_polylines_item*>(item))
+      return true;
+    return false;
+  }
   protected Q_SLOTS:
   //!Splits the selected Scene_polylines_item in multiple items all containing a single polyline.
   void split();
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
index 1c340b8f2ad..362709853c6 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
@@ -290,10 +290,11 @@ public:
 
 
   QString nameFilters() const {
-    return "VTK PolyData files (*.vtk);; VTK XML PolyData (*.vtp);; VTK XML UnstructuredGrid (*.vtu)"; }
+    return "VTK XML UnstructuredGrid (*.vtu);;VTK PolyData files (*.vtk);; VTK XML PolyData (*.vtp)"; }
   QString name() const { return "vtk_plugin"; }
   bool canSave(const CGAL::Three::Scene_item* item)
   {
+
     return (qobject_cast<const Scene_facegraph_item*>(item)
             || qobject_cast<const Scene_c3t3_item*>(item));
   }
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/lcc_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/lcc_io_plugin.cpp
index 71c47452676..55a3a7e1b14 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/lcc_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/lcc_io_plugin.cpp
@@ -17,24 +17,24 @@ class LCC_io_plugin :
   Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.IOPluginInterface/1.90" FILE "lcc_io_plugin.json")
   
 public:
-  bool isDefaultLoader(const CGAL::Three::Scene_item *item) const 
+  bool isDefaultLoader(const CGAL::Three::Scene_item *item) const override
   { 
     if(qobject_cast<const Scene_lcc_item*>(item)) 
       return true; 
     return false;
   }
-  QString name() const { return "lcc_plugin"; }
-  QString nameFilters() const { return 
+  QString name() const override{ return "lcc_plugin"; }
+  QString nameFilters() const override{ return 
         "OFF files (*.off);;"
         "3-map files (*.3map)"; }
   
-  QString saveNameFilters() const {
+  QString saveNameFilters() const override{
     return 
         "3-map files (*.3map)"; 
   }
   
-  bool canLoad(QFileInfo) const { return true; }
-  QList<CGAL::Three::Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true){
+  bool canLoad(QFileInfo) const override{ return true; }
+  QList<CGAL::Three::Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true) override{
     // Open file
     std::ifstream ifs(fileinfo.filePath().toUtf8());
     if(!ifs) {
@@ -67,8 +67,8 @@ public:
   }
   
   
-  bool canSave(const CGAL::Three::Scene_item*){return false;}
-  bool save(QFileInfo, QList<CGAL::Three::Scene_item*>& ){
+  bool canSave(const CGAL::Three::Scene_item*)override{return false;}
+  bool save(QFileInfo, QList<CGAL::Three::Scene_item*>& )override{
     return false;
   }
   
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp
index 4a7c004be2b..21a0d5c6207 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp
@@ -18,15 +18,20 @@ class Polyhedron_demo_c3t3_binary_io_plugin :
     Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.IOPluginInterface/1.90" FILE "c3t3_io_plugin.json")
 
 public:
-  QString name() const { return "C3t3_io_plugin"; }
-  QString nameFilters() const { return "binary files (*.cgal);;ascii (*.mesh);;maya (*.ma)"; }
-  QString saveNameFilters() const { return "binary files (*.cgal);;ascii (*.mesh);;maya (*.ma);;avizo (*.am);;OFF files (*.off)"; }
-  QString loadNameFilters() const { return "binary files (*.cgal);;ascii (*.mesh)"; }
-  bool canLoad(QFileInfo) const;
-  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true);
+  QString name() const override { return "C3t3_io_plugin"; }
+  QString nameFilters() const override { return "binary files (*.cgal);;ascii (*.mesh);;maya (*.ma)"; }
+  QString saveNameFilters() const override { return "binary files (*.cgal);;ascii (*.mesh);;maya (*.ma);;avizo (*.am);;OFF files (*.off)"; }
+  QString loadNameFilters() const override { return "binary files (*.cgal);;ascii (*.mesh)"; }
+  bool canLoad(QFileInfo) const override;
+  QList<Scene_item*> load(QFileInfo fileinfo, bool& ok, bool add_to_scene=true) override;
 
-  bool canSave(const CGAL::Three::Scene_item*);
-  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& );
+  bool canSave(const CGAL::Three::Scene_item*) override;
+  bool save(QFileInfo fileinfo,QList<CGAL::Three::Scene_item*>& ) override;
+  bool isDefaultLoader(const Scene_item* item) const override{
+    if(qobject_cast<const Scene_c3t3_item*>(item))
+      return true;
+    return false;
+  }
 
 private:
   bool try_load_other_binary_format(std::istream& in, C3t3& c3t3);
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/CMakeLists.txt
index 9db4d61b2e1..7dd9fbd4fce 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/CMakeLists.txt
@@ -51,7 +51,14 @@ polyhedron_demo_plugin(mesh_3_optimization_plugin Optimization_plugin
   ${meshingUI_FILES} KEYWORDS IO Mesh_3)
 target_link_libraries(mesh_3_optimization_plugin PUBLIC scene_c3t3_item scene_surface_mesh_item scene_image_item scene_implicit_function_item )
 
-
+# Use Eigen
+ find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+ 
+ if (EIGEN3_FOUND)
+   CGAL_target_use_Eigen(mesh_3_optimization_plugin)
+ else() #eigen
+   message(STATUS "The Mesh_3_optimization_plugin requires Eigen, which was not found, and will use a deprecated class to replace it. Warnings are to be expected.")
+ endif()#eigen
 
 polyhedron_demo_plugin(c3t3_io_plugin C3t3_io_plugin KEYWORDS IO Mesh_3)
 target_link_libraries(c3t3_io_plugin PUBLIC scene_c3t3_item)
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Io_image_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Io_image_plugin.cpp
index 286642446a0..d9b4fff0ef8 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Io_image_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Io_image_plugin.cpp
@@ -296,6 +296,11 @@ public:
       items.pop_front();
     return ok;
   }
+  bool isDefaultLoader(const Scene_item* item) const override{
+    if(qobject_cast<const Scene_image_item*>(item))
+      return true;
+    return false;
+  }
   QString name() const override{ return "segmented images"; }
 
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Meshing_dialog.ui b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Meshing_dialog.ui
index a29054048fa..cc9a9b224bd 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Meshing_dialog.ui
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Meshing_dialog.ui
@@ -100,9 +100,23 @@
      <property name="title">
       <string>Sharp features</string>
      </property>
-     <layout class="QGridLayout" name="gridLayout" columnstretch="0,1,0">
-      <item row="1" column="1">
-       <widget class="QComboBox" name="protectEdges"/>
+     <layout class="QGridLayout" name="gridLayout" columnstretch="0,0,0">
+      <item row="3" column="1">
+       <widget class="DoubleEdit" name="sharpEdgesAngle">
+        <property name="text">
+         <string>60.00</string>
+        </property>
+       </widget>
+      </item>
+      <item row="1" column="2">
+       <widget class="QCheckBox" name="protect">
+        <property name="text">
+         <string/>
+        </property>
+        <property name="checked">
+         <bool>true</bool>
+        </property>
+       </widget>
       </item>
       <item row="3" column="0">
        <widget class="QLabel" name="sharpEdgesAngleLabel">
@@ -115,15 +129,8 @@
         <property name="alignment">
          <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
         </property>
-       </widget>
-      </item>
-      <item row="7" column="0">
-       <widget class="QLabel" name="edgeLabel">
-        <property name="text">
-         <string>Edge &amp;size</string>
-        </property>
-        <property name="alignment">
-         <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+        <property name="buddy">
+         <cstring>sharpEdgesAngle</cstring>
         </property>
        </widget>
       </item>
@@ -134,6 +141,9 @@
         </property>
        </widget>
       </item>
+      <item row="1" column="1">
+       <widget class="QComboBox" name="protectEdges"/>
+      </item>
       <item row="1" column="0">
        <widget class="QLabel" name="protectLabel">
         <property name="text">
@@ -147,23 +157,6 @@
         </property>
        </widget>
       </item>
-      <item row="1" column="2">
-       <widget class="QCheckBox" name="protect">
-        <property name="text">
-         <string/>
-        </property>
-        <property name="checked">
-         <bool>true</bool>
-        </property>
-       </widget>
-      </item>
-      <item row="3" column="1">
-       <widget class="DoubleEdit" name="sharpEdgesAngle">
-        <property name="text">
-         <string>60.00</string>
-        </property>
-       </widget>
-      </item>
       <item row="7" column="1">
        <widget class="DoubleEdit" name="edgeSizing">
         <property name="text">
@@ -171,6 +164,19 @@
         </property>
        </widget>
       </item>
+      <item row="7" column="0">
+       <widget class="QLabel" name="edgeLabel">
+        <property name="text">
+         <string>Edge &amp;size</string>
+        </property>
+        <property name="alignment">
+         <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+        </property>
+        <property name="buddy">
+         <cstring>edgeSizing</cstring>
+        </property>
+       </widget>
+      </item>
      </layout>
     </widget>
    </item>
@@ -201,6 +207,9 @@
         <property name="alignment">
          <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
         </property>
+        <property name="buddy">
+         <cstring>approx</cstring>
+        </property>
        </widget>
       </item>
       <item row="1" column="2">
@@ -224,6 +233,9 @@
         <property name="alignment">
          <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
         </property>
+        <property name="buddy">
+         <cstring>facetAngle</cstring>
+        </property>
        </widget>
       </item>
       <item row="9" column="0" colspan="3">
@@ -315,17 +327,17 @@
         <property name="alignment">
          <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
         </property>
-       </widget>
-      </item>
-      <item row="1" column="1">
-       <widget class="DoubleEdit" name="approx">
-        <property name="text">
-         <string>0.00</string>
+        <property name="buddy">
+         <cstring>facetSizing</cstring>
         </property>
        </widget>
       </item>
       <item row="2" column="1">
-       <widget class="DoubleEdit" name="facetSizing"/>
+       <widget class="DoubleEdit" name="facetSizing">
+        <property name="text">
+         <string>0.065</string>
+        </property>
+       </widget>
       </item>
       <item row="3" column="1">
        <widget class="DoubleEdit" name="facetAngle">
@@ -337,6 +349,13 @@
         </property>
        </widget>
       </item>
+      <item row="1" column="1">
+       <widget class="DoubleEdit" name="approx">
+        <property name="text">
+         <string>0.0017</string>
+        </property>
+       </widget>
+      </item>
      </layout>
     </widget>
    </item>
@@ -390,6 +409,9 @@
         <property name="alignment">
          <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
         </property>
+        <property name="buddy">
+         <cstring>tetSizing</cstring>
+        </property>
        </widget>
       </item>
       <item row="0" column="1">
@@ -532,7 +554,7 @@
   <customwidget>
    <class>DoubleEdit</class>
    <extends>QLineEdit</extends>
-   <header>CGAL_double_edit.h</header>
+   <header location="global">CGAL_double_edit.h</header>
   </customwidget>
  </customwidgets>
  <tabstops>
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PCA/Basic_generator_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PCA/Basic_generator_plugin.cpp
index 269eb121ae4..4d92aeb7867 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PCA/Basic_generator_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PCA/Basic_generator_plugin.cpp
@@ -766,7 +766,7 @@ struct Point_generator
   {
     return Point(bl.x() + i*(ur.x()-bl.x())/(w-1),
                  bl.y() + j*(ur.y()-bl.y())/(h-1),
-                 0);
+                 bl.z() + j*(ur.z()-bl.z())/(h-1));
   }
 };
 template<class Facegraph_item>
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/PMP/CMakeLists.txt
index b97c86f9879..3dc0a808de7 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/CMakeLists.txt
@@ -3,24 +3,31 @@ if(EIGEN3_FOUND)
 
   polyhedron_demo_plugin(jet_fitting_plugin Jet_fitting_plugin)
   target_link_libraries(jet_fitting_plugin PUBLIC scene_surface_mesh_item scene_polylines_item)
+  CGAL_target_use_Eigen(jet_fitting_plugin)
 
 else(EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Jet fitting plugin will not be available.")
 endif(EIGEN3_FOUND)
 
+polyhedron_demo_plugin(extrude_plugin Extrude_plugin KEYWORDS PMP)
+target_link_libraries(extrude_plugin PUBLIC scene_surface_mesh_item scene_selection_item)
+
 if(EIGEN3_FOUND)
   if("${EIGEN3_VERSION}" VERSION_GREATER "3.1.90")
 
     qt5_wrap_ui( hole_fillingUI_FILES Hole_filling_widget.ui)
     polyhedron_demo_plugin(hole_filling_plugin Hole_filling_plugin ${hole_fillingUI_FILES} KEYWORDS PMP)
     target_link_libraries(hole_filling_plugin PUBLIC scene_surface_mesh_item scene_polylines_item scene_selection_item)
+    CGAL_target_use_Eigen(hole_filling_plugin)
 
     qt5_wrap_ui( fairingUI_FILES Fairing_widget.ui)
     polyhedron_demo_plugin(fairing_plugin Fairing_plugin ${fairingUI_FILES} KEYWORDS PMP)
     target_link_libraries(fairing_plugin PUBLIC scene_selection_item)
+    CGAL_target_use_Eigen(fairing_plugin)
 
     polyhedron_demo_plugin(hole_filling_polyline_plugin Hole_filling_polyline_plugin )
     target_link_libraries(hole_filling_polyline_plugin PUBLIC scene_surface_mesh_item scene_polylines_item)
+    CGAL_target_use_Eigen(hole_filling_polyline_plugin)
     
     qt5_wrap_ui( Mean_curvature_flow_skeleton_pluginUI_FILES  Mean_curvature_flow_skeleton_plugin.ui)
     polyhedron_demo_plugin(mean_curvature_flow_skeleton_plugin Mean_curvature_flow_skeleton_plugin ${Mean_curvature_flow_skeleton_pluginUI_FILES})
@@ -31,6 +38,19 @@ if(EIGEN3_FOUND)
         scene_polylines_item
         scene_mcf_item
         demo_framework)
+      CGAL_target_use_Eigen(mean_curvature_flow_skeleton_plugin)
+      # The smoothing plugin can still do some things, even if Ceres is not found
+      qt5_wrap_ui( smoothingUI_FILES Smoothing_plugin.ui)
+      polyhedron_demo_plugin(smoothing_plugin Smoothing_plugin ${smoothingUI_FILES})
+      target_link_libraries(smoothing_plugin PUBLIC scene_surface_mesh_item scene_selection_item)
+      CGAL_target_use_Eigen(smoothing_plugin)
+      find_package(Ceres QUIET)
+      if(TARGET ceres)
+        target_compile_definitions( smoothing_plugin PRIVATE CGAL_PMP_USE_CERES_SOLVER )
+        target_link_libraries(smoothing_plugin PUBLIC ceres)
+      endif()
+      
+      CGAL_target_use_Eigen(extrude_plugin)
   else()
     message(STATUS "NOTICE: The hole filling and fairing plugins require Eigen 3.2 (or higher) and will not be available.")
   endif()
@@ -111,16 +131,3 @@ qt5_wrap_ui( engravUI_FILES Engrave_dock_widget.ui )
 polyhedron_demo_plugin(engrave_text_plugin Engrave_text_plugin ${engravUI_FILES})
 target_link_libraries(engrave_text_plugin PUBLIC scene_surface_mesh_item scene_selection_item scene_polylines_item)
 
-polyhedron_demo_plugin(extrude_plugin Extrude_plugin KEYWORDS PMP)
-target_link_libraries(extrude_plugin PUBLIC scene_surface_mesh_item scene_selection_item)
-
-# The smoothing plugin can still do some things, even if Ceres is not found
-qt5_wrap_ui( smoothingUI_FILES Smoothing_plugin.ui)
-polyhedron_demo_plugin(smoothing_plugin Smoothing_plugin ${smoothingUI_FILES})
-target_link_libraries(smoothing_plugin PUBLIC scene_surface_mesh_item scene_selection_item)
-
-find_package(Ceres QUIET)
-if(TARGET ceres)
-  target_compile_definitions( smoothing_plugin PRIVATE CGAL_PMP_USE_CERES_SOLVER )
-  target_link_libraries(smoothing_plugin PUBLIC ceres)
-endif()
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Isotropic_remeshing_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PMP/Isotropic_remeshing_plugin.cpp
index bfb2bb520a7..2049f788572 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Isotropic_remeshing_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Isotropic_remeshing_plugin.cpp
@@ -612,7 +612,6 @@ public Q_SLOTS:
         }
         if (fpmap_valid)
         {
-          PMP::connected_components(pmesh, fpmap, PMP::parameters::edge_is_constrained_map(eif));
           poly_item->setItemIsMulticolor(true);
           poly_item->show_feature_edges(true);
         }
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Orient_soup_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PMP/Orient_soup_plugin.cpp
index 265507b8a9c..6d2d062e002 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Orient_soup_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Orient_soup_plugin.cpp
@@ -223,8 +223,8 @@ void Polyhedron_demo_orient_soup_plugin::apply_shuffle( Item* root_item,
   item->load(root_item);
   item->shuffle_orientations();
   item->setColor(root_item->color());
-  scene->replaceItem(index, item);
-  delete root_item;
+  scene->replaceItem(index, item, true);
+  root_item->deleteLater();
   QApplication::restoreOverrideCursor();
 }
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Selection_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PMP/Selection_plugin.cpp
index b4864357dd3..be80490894e 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Selection_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Selection_plugin.cpp
@@ -127,6 +127,12 @@ public:
       return res;
   }
   
+  bool isDefaultLoader(const Scene_item* item) const override{
+    if(qobject_cast<const Scene_polyhedron_selection_item*>(item))
+      return true;
+    return false;
+  }
+
   bool applicable(QAction* action) const override {
     if(action == actionSelfIntersection)
       return qobject_cast<Scene_face_graph_item*>(scene->item(scene->mainSelectionIndex()));
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Point_set/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/Point_set/CMakeLists.txt
index 12b2e9f9056..1d4bfdeb614 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Point_set/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/Point_set/CMakeLists.txt
@@ -1,20 +1,9 @@
 include( polyhedron_demo_macros )
 if(EIGEN3_FOUND)
 
-  set(polyfit_linked_libraries)
-  set(polyfit_compile_definitions)
-
   find_package(SCIP QUIET)
-  if(SCIP_FOUND)
-    include_directories(BEFORE ${SCIP_INCLUDE_DIRS})
-    set(polyfit_linked_libraries ${polyfit_linked_libraries} ${SCIP_LIBRARIES})
-    set(polyfit_compile_definitions ${polyfit_compile_definitions} "-DCGAL_USE_SCIP")
-  endif()
-  find_package(GLPK QUIET)
-  if(GLPK_FOUND)
-    include_directories(BEFORE ${GLPK_INCLUDE_DIR})
-    set(polyfit_linked_libraries ${polyfit_linked_libraries} ${GLPK_LIBRARIES})
-    set(polyfit_compile_definitions ${polyfit_compile_definitions} "-DCGAL_USE_GLPK")
+  if(NOT SCIP_FOUND)
+    find_package(GLPK QUIET)
   endif()
 
   if(NOT SCIP_FOUND AND NOT GLPK_FOUND)
@@ -23,26 +12,37 @@ if(EIGEN3_FOUND)
 
   qt5_wrap_ui( surface_reconstructionUI_FILES Surface_reconstruction_plugin.ui)
   polyhedron_demo_plugin(surface_reconstruction_plugin Surface_reconstruction_plugin Surface_reconstruction_poisson_impl Surface_reconstruction_advancing_front_impl Surface_reconstruction_scale_space_impl Surface_reconstruction_polygonal_impl ${surface_reconstructionUI_FILES} KEYWORDS PointSetProcessing)
-  target_link_libraries(surface_reconstruction_plugin PUBLIC scene_polygon_soup_item scene_surface_mesh_item scene_points_with_normal_item ${polyfit_linked_libraries})
-  target_compile_definitions(surface_reconstruction_plugin PRIVATE ${polyfit_compile_definitions})
+  target_link_libraries(surface_reconstruction_plugin PUBLIC scene_polygon_soup_item scene_surface_mesh_item scene_points_with_normal_item)
+  CGAL_target_use_Eigen(surface_reconstruction_plugin)
+
+  if (SCIP_FOUND)
+    CGAL_target_use_SCIP(surface_reconstruction_plugin)
+  elseif(GLPK_FOUND)
+    CGAL_target_use_GLPK(surface_reconstruction_plugin)
+  endif()
 
   qt5_wrap_ui( point_set_normal_estimationUI_FILES Point_set_normal_estimation_plugin.ui)
   polyhedron_demo_plugin(point_set_normal_estimation_plugin Point_set_normal_estimation_plugin ${point_set_normal_estimationUI_FILES} KEYWORDS PointSetProcessing Classification)
   target_link_libraries(point_set_normal_estimation_plugin PUBLIC scene_points_with_normal_item scene_callback_signaler)
+  CGAL_target_use_Eigen(point_set_normal_estimation_plugin)
 
   qt5_wrap_ui( features_detection_pluginUI_FILES Features_detection_plugin.ui)
   polyhedron_demo_plugin(features_detection_plugin Features_detection_plugin ${features_detection_pluginUI_FILES} KEYWORDS PointSetProcessing)
   target_link_libraries(features_detection_plugin PUBLIC scene_points_with_normal_item)
+  CGAL_target_use_Eigen(features_detection_plugin)
 
   polyhedron_demo_plugin(point_set_smoothing_plugin Point_set_smoothing_plugin KEYWORDS PointSetProcessing)
   target_link_libraries(point_set_smoothing_plugin PUBLIC scene_points_with_normal_item scene_callback_signaler)
+  CGAL_target_use_Eigen(point_set_smoothing_plugin)
 
   polyhedron_demo_plugin(point_set_average_spacing_plugin Point_set_average_spacing_plugin KEYWORDS PointSetProcessing Classification)
   target_link_libraries(point_set_average_spacing_plugin PUBLIC scene_points_with_normal_item scene_callback_signaler)
+  CGAL_target_use_Eigen(point_set_average_spacing_plugin)
 
   qt5_wrap_ui(point_set_shape_detectionUI_FILES Point_set_shape_detection_plugin.ui)
   polyhedron_demo_plugin(point_set_shape_detection_plugin Point_set_shape_detection_plugin ${point_set_shape_detectionUI_FILES} KEYWORDS PointSetProcessing Classification)
   target_link_libraries(point_set_shape_detection_plugin PUBLIC scene_surface_mesh_item scene_points_with_normal_item scene_polygon_soup_item scene_callback_signaler)
+  CGAL_target_use_Eigen(point_set_shape_detection_plugin)
 
 else(EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Surface reconstruction plugin will not be available.")
@@ -50,7 +50,6 @@ else(EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Smoothing plugin will not be available.")
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Average spacing plugin will not be available.")
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. Feature detection plugin will not be available.")
-
 endif()
 
   qt5_wrap_ui(point_set_bilateral_smoothingUI_FILES Point_set_bilateral_smoothing_plugin.ui)
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Surface_mesh/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/Surface_mesh/CMakeLists.txt
index 8ab1462de67..99c7d6e618b 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Surface_mesh/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/Surface_mesh/CMakeLists.txt
@@ -12,6 +12,7 @@ if(EIGEN3_FOUND)
   qt5_wrap_ui(parameterizationUI_FILES Parameterization_widget.ui OTE_dialog.ui)
   polyhedron_demo_plugin(parameterization_plugin Parameterization_plugin ${parameterizationUI_FILES})
   target_link_libraries(parameterization_plugin PUBLIC scene_surface_mesh_item scene_textured_item scene_selection_item)
+  CGAL_target_use_Eigen(parameterization_plugin)
 else(EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.1 (or greater) was not found. The Parameterization plugin will not be available.")
 endif(EIGEN3_FOUND)
@@ -31,7 +32,9 @@ target_link_libraries(mesh_simplification_plugin PUBLIC scene_surface_mesh_item
 qt5_wrap_ui( remeshingUI_FILES  Remeshing_dialog.ui)
 polyhedron_demo_plugin(offset_meshing_plugin Offset_meshing_plugin ${remeshingUI_FILES})
 target_link_libraries(offset_meshing_plugin PUBLIC scene_surface_mesh_item scene_polygon_soup_item)
-
+if(EIGEN3_FOUND)
+  CGAL_target_use_Eigen(offset_meshing_plugin)
+endif()
 if(TBB_FOUND)
   CGAL_target_use_TBB(offset_meshing_plugin)
 endif()
diff --git a/Polyhedron/demo/Polyhedron/Preferences.ui b/Polyhedron/demo/Polyhedron/Preferences.ui
index 10a7f773f85..358bf1ffbb8 100644
--- a/Polyhedron/demo/Polyhedron/Preferences.ui
+++ b/Polyhedron/demo/Polyhedron/Preferences.ui
@@ -7,7 +7,7 @@
     <x>0</x>
     <y>0</y>
     <width>631</width>
-    <height>526</height>
+    <height>628</height>
    </rect>
   </property>
   <property name="sizePolicy">
@@ -58,9 +58,9 @@
            <property name="geometry">
             <rect>
              <x>0</x>
-             <y>-96</y>
+             <y>0</y>
              <width>275</width>
-             <height>528</height>
+             <height>534</height>
             </rect>
            </property>
            <layout class="QVBoxLayout" name="verticalLayout_3">
@@ -285,6 +285,16 @@
               </property>
              </widget>
             </item>
+            <item>
+             <widget class="QPushButton" name="sshButton">
+              <property name="enabled">
+               <bool>true</bool>
+              </property>
+              <property name="text">
+               <string>Network Settings</string>
+              </property>
+             </widget>
+            </item>
             <item>
              <widget class="QPushButton" name="backFrontColor_pushButton">
               <property name="text">
diff --git a/Polyhedron/demo/Polyhedron/SSH_dialog.ui b/Polyhedron/demo/Polyhedron/SSH_dialog.ui
new file mode 100644
index 00000000000..0f18f927cb8
--- /dev/null
+++ b/Polyhedron/demo/Polyhedron/SSH_dialog.ui
@@ -0,0 +1,151 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<ui version="4.0">
+ <class>SSHDialog</class>
+ <widget class="QDialog" name="SSHDialog">
+  <property name="geometry">
+   <rect>
+    <x>0</x>
+    <y>0</y>
+    <width>415</width>
+    <height>441</height>
+   </rect>
+  </property>
+  <property name="windowTitle">
+   <string>SSH Settings</string>
+  </property>
+  <layout class="QVBoxLayout" name="verticalLayout_2">
+   <item>
+    <layout class="QVBoxLayout" name="verticalLayout">
+     <item>
+      <widget class="QGroupBox" name="groupBox_2">
+       <property name="title">
+        <string>SSH Preferences</string>
+       </property>
+       <layout class="QVBoxLayout" name="verticalLayout_3">
+        <item>
+         <widget class="QGroupBox" name="userBox">
+          <property name="title">
+           <string>User</string>
+          </property>
+          <layout class="QHBoxLayout" name="horizontalLayout">
+           <item>
+            <widget class="QLineEdit" name="userEdit"/>
+           </item>
+          </layout>
+         </widget>
+        </item>
+        <item>
+         <widget class="QGroupBox" name="serverBox">
+          <property name="title">
+           <string>Server</string>
+          </property>
+          <layout class="QHBoxLayout" name="horizontalLayout_2">
+           <item>
+            <widget class="QLineEdit" name="serverEdit"/>
+           </item>
+          </layout>
+         </widget>
+        </item>
+        <item>
+         <widget class="QGroupBox" name="pkBox">
+          <property name="title">
+           <string>Public Key </string>
+          </property>
+          <layout class="QHBoxLayout" name="horizontalLayout_3">
+           <item>
+            <widget class="QLineEdit" name="publicEdit"/>
+           </item>
+           <item>
+            <widget class="QPushButton" name="pubButton">
+             <property name="text">
+              <string>Browse...</string>
+             </property>
+            </widget>
+           </item>
+          </layout>
+         </widget>
+        </item>
+        <item>
+         <widget class="QGroupBox" name="privkBox">
+          <property name="title">
+           <string>Private Key</string>
+          </property>
+          <layout class="QHBoxLayout" name="horizontalLayout_4">
+           <item>
+            <widget class="QLineEdit" name="privkEdit"/>
+           </item>
+           <item>
+            <widget class="QPushButton" name="privButton">
+             <property name="text">
+              <string>Browse...</string>
+             </property>
+            </widget>
+           </item>
+          </layout>
+         </widget>
+        </item>
+       </layout>
+      </widget>
+     </item>
+     <item>
+      <widget class="QGroupBox" name="groupBox">
+       <property name="title">
+        <string>Camera Synchronization Server</string>
+       </property>
+       <layout class="QVBoxLayout" name="verticalLayout_4">
+        <item>
+         <widget class="QLineEdit" name="wsEdit"/>
+        </item>
+       </layout>
+      </widget>
+     </item>
+    </layout>
+   </item>
+   <item>
+    <widget class="QDialogButtonBox" name="buttonBox">
+     <property name="orientation">
+      <enum>Qt::Horizontal</enum>
+     </property>
+     <property name="standardButtons">
+      <set>QDialogButtonBox::Cancel|QDialogButtonBox::Ok</set>
+     </property>
+    </widget>
+   </item>
+  </layout>
+ </widget>
+ <resources/>
+ <connections>
+  <connection>
+   <sender>buttonBox</sender>
+   <signal>accepted()</signal>
+   <receiver>SSHDialog</receiver>
+   <slot>accept()</slot>
+   <hints>
+    <hint type="sourcelabel">
+     <x>248</x>
+     <y>254</y>
+    </hint>
+    <hint type="destinationlabel">
+     <x>157</x>
+     <y>274</y>
+    </hint>
+   </hints>
+  </connection>
+  <connection>
+   <sender>buttonBox</sender>
+   <signal>rejected()</signal>
+   <receiver>SSHDialog</receiver>
+   <slot>reject()</slot>
+   <hints>
+    <hint type="sourcelabel">
+     <x>316</x>
+     <y>260</y>
+    </hint>
+    <hint type="destinationlabel">
+     <x>286</x>
+     <y>274</y>
+    </hint>
+   </hints>
+  </connection>
+ </connections>
+</ui>
diff --git a/Polyhedron/demo/Polyhedron/Scene.cpp b/Polyhedron/demo/Polyhedron/Scene.cpp
index 5425285d9ed..4730d595adb 100644
--- a/Polyhedron/demo/Polyhedron/Scene.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene.cpp
@@ -143,6 +143,7 @@ Scene::replaceItem(Scene::Item_id index, CGAL::Three::Scene_item* item, bool emi
 
     if(emit_item_about_to_be_destroyed) {
       Q_EMIT itemAboutToBeDestroyed(item);
+      item->aboutToBeDestroyed();
     }
 
     Q_EMIT updated();
diff --git a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
index 685893acac1..0b98891d35c 100644
--- a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
@@ -1456,6 +1456,7 @@ void Scene_c3t3_item_priv::computeElements()
    }
   
   positions_poly.clear();
+  positions_grid.clear();
   normals.clear();
   f_colors.clear();
   positions_lines.clear();
diff --git a/Polyhedron/demo/Polyhedron/Scene_item_rendering_helper.cpp b/Polyhedron/demo/Polyhedron/Scene_item_rendering_helper.cpp
index 5413cd0616f..bffe5e847b5 100644
--- a/Polyhedron/demo/Polyhedron/Scene_item_rendering_helper.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_item_rendering_helper.cpp
@@ -78,9 +78,9 @@ void PRIV::compute_diag_bbox()
 {
   const Scene_item::Bbox& b_box = item->bbox();
   _diag_bbox = CGAL::approximate_sqrt(
-          (b_box.xmax() - b_box.xmin())*(b_box.xmax() - b_box.xmin())
-        + (b_box.ymax() - b_box.ymin())*(b_box.ymax() - b_box.ymin())
-        + (b_box.zmax() - b_box.zmin())*(b_box.zmax() - b_box.zmin())
+          CGAL::square(b_box.xmax() - b_box.xmin())
+        + CGAL::square(b_box.ymax() - b_box.ymin())
+        + CGAL::square(b_box.zmax() - b_box.zmin())
         );
 }
 
diff --git a/Polyhedron/demo/Polyhedron/Scene_spheres_item.cpp b/Polyhedron/demo/Polyhedron/Scene_spheres_item.cpp
index dbdb9e4dd9d..c26dfd45bec 100644
--- a/Polyhedron/demo/Polyhedron/Scene_spheres_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_spheres_item.cpp
@@ -241,7 +241,7 @@ void Scene_spheres_item::drawEdges(Viewer_interface *viewer) const
 }
 void Scene_spheres_item::add_sphere(const Sphere &sphere, std::size_t index,  CGAL::Color color)
 {
-  if(index > d->spheres.size()-1)
+  if((int)index > (int)d->spheres.size() - 1)
     d->spheres.resize(index+1);
 
   d->spheres[index].push_back(std::make_pair(sphere, color));
diff --git a/Polyhedron/demo/Polyhedron/Use_ssh.cpp b/Polyhedron/demo/Polyhedron/Use_ssh.cpp
new file mode 100644
index 00000000000..a1b342eda69
--- /dev/null
+++ b/Polyhedron/demo/Polyhedron/Use_ssh.cpp
@@ -0,0 +1,286 @@
+// Copyright (c) 2020  GeometryFactory (France).  All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org)
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
+// 
+//
+// Author(s)     : Maxime Gimeno
+
+#ifdef CGAL_USE_SSH
+
+#include <CGAL/Three/Three.h>
+
+#include "CGAL/Use_ssh.h"
+#include <iostream>
+#include <fstream>
+#include <cstring>
+#include <vector>
+#include <chrono>
+#include <thread>
+
+#include <QMessageBox>
+
+bool test_result(int res)
+{
+  switch(res){
+
+  case SSH_AUTH_ERROR:
+  {
+    std::cerr<<"Auth failed with error: "<<std::endl;
+    return false;
+  }
+  case SSH_AUTH_DENIED:
+  {
+    std::cerr<<"The server doesn't accept that public key as an authentication token. Try another key or another method."<<std::endl;
+    return false;
+  }
+  case SSH_AUTH_PARTIAL :
+  {
+    std::cerr<<"You've been partially authenticated, you still have to use another method."<<std::endl;
+    return false;
+  }
+  case SSH_OK:
+    return true;
+  case SSH_EOF:
+    std::cerr<<"key doesn't exist."<<std::endl;
+    return false;
+  default:
+    return false;
+  }
+  return true;
+}
+namespace CGAL{
+namespace ssh_internal{
+
+bool establish_ssh_session(ssh_session &session,
+                           const char* user,
+                           const char* server,
+                           const char* pub_key_path,
+                           const char* priv_key_path,
+                           const char* priv_key_password)
+{
+  int port = 22;
+
+  //Can use SSH_LOG_PROTOCOL here for verbose output
+  int verbosity = SSH_LOG_NOLOG;
+  int res;
+  //retry 4 times max each time the connection asks to be retried.
+  for(int k = 0; k < 4; ++k)
+  {
+    session = ssh_new();
+    ssh_options_set( session, SSH_OPTIONS_LOG_VERBOSITY, &verbosity );
+    ssh_options_set( session, SSH_OPTIONS_PORT, &port );
+    ssh_options_set( session, SSH_OPTIONS_USER, user );
+    ssh_options_set( session, SSH_OPTIONS_HOST, server);
+    
+    ssh_connect(session);
+#if LIBSSH_VERSION_MAJOR <1 && LIBSSH_VERSION_MINOR < 8
+    if( ssh_is_server_known(session) != SSH_SERVER_KNOWN_OK )
+#else
+      if( ssh_session_is_known_server(session) != SSH_KNOWN_HOSTS_OK )
+#endif
+    {
+      if(QMessageBox::warning(CGAL::Three::Three::mainWindow(), QString("Unknown Server"),
+                              QString ("The server you are trying to join is not known.\n"
+                                       "Do you wish to add it to the known servers list and continue?"),
+                              QMessageBox::Yes | QMessageBox::No) != QMessageBox::Yes)
+      {
+        return false;
+      }
+#if LIBSSH_VERSION_MAJOR <1 && LIBSSH_VERSION_MINOR < 8
+      if( ssh_write_knownhost(session) != SSH_OK )
+#else
+      if( ssh_session_update_known_hosts(session) != SSH_OK )
+#endif
+      {
+        std::cerr << "writeKnownHost failed" << std::endl;
+        return false;
+      }
+      else
+      {
+        ssh_connect(session);
+      }
+    }
+    ssh_key pubkey = ssh_key_new();
+    ssh_pki_import_pubkey_file(pub_key_path, &pubkey);
+    res = ssh_userauth_try_publickey(session, NULL, pubkey);
+    if(res == SSH_AUTH_AGAIN)
+      ssh_disconnect(session);
+    else
+      break;
+  }
+  
+  if(!test_result(res))
+  {
+    ssh_disconnect(session);
+    return false;
+  }
+
+  ssh_key privkey = ssh_key_new();
+  res = ssh_pki_import_privkey_file(priv_key_path, priv_key_password, NULL, NULL, &privkey);
+  if (!test_result(res))
+  {
+    ssh_disconnect(session);
+    return false;
+  }
+  res = ssh_userauth_publickey(session, NULL, privkey);
+  if(!test_result(res))
+  {
+    ssh_disconnect(session);
+    return false;
+  }
+  return true;
+}
+
+void close_connection(ssh_session &session)
+{
+  ssh_disconnect(session);
+}
+
+bool push_file(ssh_session &session,
+               const char* dest_path,
+               const char* filepath)
+{
+  //copy a file
+  ssh_scp scp = ssh_scp_new(
+        session, SSH_SCP_WRITE | SSH_SCP_RECURSIVE, "/tmp");
+  if (scp == NULL)
+  {
+    std::cerr<<"Error allocating scp session: %s\n"
+            << ssh_get_error(session)<<std::endl;
+    return false;
+  }
+  int res = ssh_scp_init(scp);
+  if(res != SSH_OK)
+  {
+    std::cerr<< "Error initializing scp session: %s\n"
+             << ssh_get_error(session)<<std::endl;
+    ssh_scp_free(scp);
+    ssh_disconnect(session);
+    return false;
+  }
+  //read a file into a buffer
+  std::ifstream file(filepath, std::ios::binary | std::ios::ate);
+  if(!file)
+  {
+    std::cerr<<"File not found."<<std::endl;
+    ssh_scp_free(scp);
+    ssh_disconnect(session);
+    return false;
+  }
+  std::streamsize size = file.tellg();
+  file.seekg(0, std::ios::beg);
+
+  std::vector<char> buffer(size);
+  if (!file.read(buffer.data(), size))
+  {
+    std::cerr<<"error while reading file."<<std::endl;
+    ssh_disconnect(session);
+    return false;
+  }
+  //push a file to /tmp
+  res = ssh_scp_push_directory(scp, ".", 0707);
+  if (res != SSH_OK)
+  {
+    std::cerr<<"Can't create remote directory: %s\n"
+            <<ssh_get_error(session)<<std::endl;
+    ssh_disconnect(session);
+    return false;
+  }
+  res = ssh_scp_push_file
+      (scp, dest_path, size, 0707);
+  if (res != SSH_OK)
+  {
+    std::cerr<< "Can't open remote file: %s\n"
+             << ssh_get_error(session)<<std::endl;
+    ssh_disconnect(session);
+    return false;
+  }
+  res = ssh_scp_write(scp, buffer.data(), size);
+  //some versions of libssh don't copy everything without this.
+  //This is the case for the official version on Ubuntu 18.04
+  std::chrono::duration<int, std::micro> timespan(size);
+  std::this_thread::sleep_for(timespan);
+  if (res != SSH_OK)
+  {
+    std::cerr<< "Can't write to remote file: %s\n"
+             << ssh_get_error(session)<<std::endl;
+    ssh_disconnect(session);
+    return false;
+  }
+  return true;
+}
+
+bool pull_file(ssh_session &session,
+               const char* from_path,
+               const char* to_path)
+{
+  int rc;
+  std::size_t size;
+  std::size_t processed = 0;
+  std::vector<char> buffer;
+
+  ssh_scp scp = ssh_scp_new(
+        session, SSH_SCP_READ | SSH_SCP_RECURSIVE, from_path);
+  if (scp == NULL)
+  {
+    std::cerr<<"Error allocating scp session: %s\n"
+            << ssh_get_error(session)<<std::endl;
+    return false;
+  }
+  int res = ssh_scp_init(scp);
+  if(res != SSH_OK)
+  {
+    std::cerr<< "Error initializing scp session: %s\n"
+             << ssh_get_error(session)<<std::endl;
+    ssh_scp_free(scp);
+    ssh_disconnect(session);
+    return false;
+  }
+  rc = ssh_scp_pull_request(scp);
+  if (rc != SSH_SCP_REQUEST_NEWFILE)
+  {
+    std::cerr<< "Error receiving information about file: %s\n"
+             << ssh_get_error(session)<<std::endl;
+    ssh_scp_free(scp);
+    ssh_disconnect(session);
+    return false;
+  }
+  size = ssh_scp_request_get_size64(scp);
+  buffer.resize(size);
+  if(ssh_scp_accept_request(scp) != SSH_OK)
+  {
+    std::cerr<< "Could not accept request."<<std::endl;
+    ssh_scp_free(scp);
+    ssh_disconnect(session);
+    return false;
+  }
+
+  do{
+    rc = ssh_scp_read(scp, buffer.data() + processed, size-processed);
+    if (rc == SSH_ERROR)
+    {
+      std::cerr<< "Error receiving file data: %s\n"<< ssh_get_error(session)<<std::endl;
+      //free(buffer);
+      ssh_scp_free(scp);
+      ssh_disconnect(session);
+      return false;
+    }
+    else
+      processed += rc;
+  }while(processed != size);
+  std::ofstream file(to_path, std::ios::binary |std::ios::trunc);
+  if(!file.write(buffer.data(), size))
+  {
+    std::cerr<<"Error while writing file."<<std::endl;
+  }
+  file.close();
+  ssh_scp_free(scp);
+  return true;
+}
+
+}}
+#endif
diff --git a/Polyhedron/demo/Polyhedron/Viewer.cpp b/Polyhedron/demo/Polyhedron/Viewer.cpp
index bfb1a2331ad..ec6f374323c 100644
--- a/Polyhedron/demo/Polyhedron/Viewer.cpp
+++ b/Polyhedron/demo/Polyhedron/Viewer.cpp
@@ -16,6 +16,11 @@
 #include <QApplication>
 #include <QOpenGLDebugLogger>
 #include <QStyleFactory>
+#include <QAction>
+#include <QRegularExpressionMatch>
+#ifdef CGAL_USE_WEBSOCKETS
+#include <QtWebSockets/QWebSocket>
+#endif
 
 #include <CGAL/Three/Three.h>
 
@@ -40,6 +45,7 @@ public:
   bool inDrawWithNames;
   bool clipping;
   bool projection_is_ortho;
+  bool cam_sharing;
   GLfloat gl_point_size;
   QVector4D clipbox[6];
   QPainter *painter;
@@ -111,6 +117,12 @@ public:
   {
     return shader_programs;
   }
+#ifdef CGAL_USE_WEBSOCKETS
+  QWebSocket m_webSocket;
+#endif
+  bool is_connected;
+  QString session;
+  QUrl m_url;
 };
 
 class LightingDialog :
@@ -268,6 +280,7 @@ void Viewer::doBindings()
   d->spec_power = viewer_settings.value("spec_power", 51.8).toFloat();
   d->scene = 0;
   d->projection_is_ortho = false;
+  d->cam_sharing = false;
   d->twosides = false;
   this->setProperty("draw_two_sides", false);
   this->setProperty("back_front_shading", false);
@@ -278,6 +291,7 @@ void Viewer::doBindings()
   d->shader_programs.resize(NB_OF_PROGRAMS);
   d->textRenderer = new TextRenderer();
   d->is_2d_selection_mode = false;
+  d->is_connected = false;
   
   connect( d->textRenderer, SIGNAL(sendMessage(QString,int)),
            this, SLOT(printMessage(QString,int)) );
@@ -623,7 +637,7 @@ void Viewer::mousePressEvent(QMouseEvent* event)
       d->showDistance(event->pos());
       event->accept();
   }
-  else {
+  else{
     makeCurrent();
     CGAL::QGLViewer::mousePressEvent(event);
   }
@@ -1931,6 +1945,79 @@ bool Viewer::isClipping() const
 {
   return d->clipping;
 }
+#ifdef CGAL_USE_WEBSOCKETS
+void Viewer::setShareCam(bool b, QString session)
+{
+  static bool init = false;
+  if(b)
+  {
+    d->cam_sharing = b;
+    d->session = session;
+    QString ws_url
+        = CGAL::Three::Three::mainWindow()->property("ws_url").toString();
+    if(ws_url.isEmpty())
+    {
+      QMessageBox::warning(this, "Error", "No Server configured. Please go to Edit->Preferences->Network Settings and fill the \"Camera Synchronization Server\" Field.");
+    }
+    else{
+      if(!init)
+      {
+        connect(&d->m_webSocket, &QWebSocket::connected, this, &Viewer::onSocketConnected);
+        connect(&d->m_webSocket, &QWebSocket::disconnected, this,[this]()
+        {
+          d->is_connected = false;
+          Viewer::socketClosed();
+        });
+        init = true;
+      }
+      d->m_webSocket.open(QUrl(ws_url));
+      QApplication::setOverrideCursor(Qt::WaitCursor);
+      QTimer::singleShot(1000, this, [this](){
+        QApplication::restoreOverrideCursor();
+        if(!d->is_connected){
+          QMessageBox::warning(CGAL::Three::Three::mainWindow(),
+                               "Connection failure",
+                               "The requested server was not found.");
+          setShareCam(false, "");
+        }
+      });
+    }
+  }
+  else
+  {
+    QAction* action = findChild<QAction*>("actionShareCamera");
+    action->setChecked(false);
+    d->m_webSocket.close();
+  }
+}
 
+void Viewer::onSocketConnected()
+{
+  connect(&d->m_webSocket, &QWebSocket::textMessageReceived,
+          this, &Viewer::onTextMessageSocketReceived);
+  connect(camera()->frame(), &CGAL::qglviewer::ManipulatedCameraFrame::manipulated,
+          this, [this](){
+    if(d->cam_sharing){
+      QString cam_state = QString("[%1] %2").arg(d->session).arg(dumpCameraCoordinates());
+      //send to server
+      d->m_webSocket.sendTextMessage(cam_state);
+    }
+  });
+  d->is_connected = true;
+}
+
+void Viewer::onTextMessageSocketReceived(QString message)
+{
+  QString session;
+  QString position;
+  QRegularExpression re("\\[(.*)\\] (.*)");
+  QRegularExpressionMatch match = re.match(message);
+  session = match.captured(1);
+  position = match.captured(2);
+  if(session != d->session){
+    return;
+  }
+  moveCameraToCoordinates(position, 0.05f);
+}
+#endif
 #include "Viewer.moc"
-
diff --git a/Polyhedron/demo/Polyhedron/Viewer.h b/Polyhedron/demo/Polyhedron/Viewer.h
index 600b9a6f041..f4fdf522abe 100644
--- a/Polyhedron/demo/Polyhedron/Viewer.h
+++ b/Polyhedron/demo/Polyhedron/Viewer.h
@@ -95,6 +95,7 @@ public:
 Q_SIGNALS:
   void sendMessage(QString);
   void doneInitGL(CGAL::Three::Viewer_interface*);
+  void socketClosed();
 public Q_SLOTS:
   //! Sets the antialiasing to true or false.
   void setAntiAliasing(bool b) Q_DECL_OVERRIDE;
@@ -131,6 +132,11 @@ public Q_SLOTS:
   void setBackFrontColors();
 
   void messageLogged(QOpenGLDebugMessage);
+#ifdef CGAL_USE_WEBSOCKETS
+  void setShareCam(bool, QString);
+  void onSocketConnected();
+  void onTextMessageSocketReceived(QString message);
+#endif
 
 protected:
   void paintEvent(QPaintEvent *)Q_DECL_OVERRIDE;
diff --git a/Polyhedron/demo/Polyhedron/include/CGAL/Use_ssh.h b/Polyhedron/demo/Polyhedron/include/CGAL/Use_ssh.h
new file mode 100644
index 00000000000..2cdca27452b
--- /dev/null
+++ b/Polyhedron/demo/Polyhedron/include/CGAL/Use_ssh.h
@@ -0,0 +1,25 @@
+#ifndef USE_SSH_H
+#define USE_SSH_H
+#include <libssh/libsshpp.hpp>
+namespace CGAL{
+namespace ssh_internal{
+//should be used inside a try/catch(ssh::SshException e)
+
+//give an unitialized session.
+bool establish_ssh_session(ssh_session& session,
+                           const char *user,
+                           const char *server,
+                           const char *pub_key_path,
+                           const char *priv_key_path,
+                           const char *priv_key_password);
+void close_connection(ssh_session& session);
+
+bool push_file(ssh_session& session,
+               const char* dest_path,
+               const char* filepath);
+bool pull_file(ssh_session &session,
+               const char *from_path,
+               const char *to_path);
+
+}}
+#endif
diff --git a/Polyhedron_IO/include/CGAL/IO/OFF_reader.h b/Polyhedron_IO/include/CGAL/IO/OFF_reader.h
index c1a79eda546..db5c46781e6 100644
--- a/Polyhedron_IO/include/CGAL/IO/OFF_reader.h
+++ b/Polyhedron_IO/include/CGAL/IO/OFF_reader.h
@@ -76,19 +76,35 @@ namespace CGAL {
     polygons.resize(scanner.size_of_facets());
     if(scanner.has_colors())
       vcolors.resize(scanner.size_of_vertices());
+    bool vcolored = false;
     for (std::size_t i = 0; i < scanner.size_of_vertices(); ++i) {
         double x, y, z, w;
         scanner.scan_vertex( x, y, z, w);
         CGAL_assertion(w!=0);
         IO::internal::fill_point( x/w, y/w, z/w, points[i] );
-        if(scanner.has_colors())
+        if(i == 0)
         {
-            unsigned char r=0, g=0, b=0;
-            scanner.scan_color( r, g, b);
-            vcolors[i] = Color_rgb(r,g,b);
+          std::string col;
+          char ci;
+          std::getline(in, col);
+          std::istringstream iss(col);
+          if(iss >> ci){
+            std::istringstream iss2(col);
+            vcolors[i] = scanner.get_color_from_line(iss2);
+            vcolored = true;
+          }
         }
         else
-            scanner.skip_to_next_vertex(i);
+        {
+          if(vcolored){
+            //stores the RGB value
+            std::string col;
+            std::getline(in, col);
+            std::istringstream iss(col);
+            vcolors[i] = scanner.get_color_from_line(iss);
+          }
+        }
+        
         if(!in)
           return false;
     }
diff --git a/Principal_component_analysis/demo/Principal_component_analysis/CMakeLists.txt b/Principal_component_analysis/demo/Principal_component_analysis/CMakeLists.txt
index 128b250b8f1..af76de02587 100644
--- a/Principal_component_analysis/demo/Principal_component_analysis/CMakeLists.txt
+++ b/Principal_component_analysis/demo/Principal_component_analysis/CMakeLists.txt
@@ -19,9 +19,7 @@ include_directories( ./ )
 find_package(CGAL COMPONENTS Qt5)
 
 find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-else()
+if (NOT EIGEN3_FOUND)
   message(STATUS "NOTICE: This project requires the Eigen library, and will not be compiled.")
   return()
 endif()
@@ -47,6 +45,7 @@ if(CGAL_Qt5_FOUND AND Qt5_FOUND )
   add_file_dependencies( PCA_demo.cpp "${CMAKE_CURRENT_BINARY_DIR}/MainWindow_moc.cpp"
     "${CMAKE_CURRENT_BINARY_DIR}/Viewer_moc.cpp" )
   add_executable  ( PCA_demo PCA_demo.cpp ${UI_FILES} ${CGAL_Qt5_RESOURCE_FILES} ${CGAL_Qt5_MOC_FILES})
+  CGAL_target_use_Eigen(PCA_demo)
 
   target_link_libraries( PCA_demo PRIVATE
     CGAL::CGAL CGAL::CGAL_Qt5 Qt5::Gui)
diff --git a/Principal_component_analysis/examples/Principal_component_analysis/CMakeLists.txt b/Principal_component_analysis/examples/Principal_component_analysis/CMakeLists.txt
index 0518b6ea3cd..ae1c1e63325 100644
--- a/Principal_component_analysis/examples/Principal_component_analysis/CMakeLists.txt
+++ b/Principal_component_analysis/examples/Principal_component_analysis/CMakeLists.txt
@@ -12,14 +12,15 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
 
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     create_single_source_cgal_program( "${cppfile}" )
+    if (EIGEN3_FOUND)
+      get_filename_component(target ${cppfile} NAME_WE)
+      CGAL_target_use_Eigen(${target})
+    endif()
   endforeach()
 
 else()
diff --git a/Principal_component_analysis/include/CGAL/PCA_util.h b/Principal_component_analysis/include/CGAL/PCA_util.h
index 0f8c0ab8307..689786cc5df 100644
--- a/Principal_component_analysis/include/CGAL/PCA_util.h
+++ b/Principal_component_analysis/include/CGAL/PCA_util.h
@@ -648,7 +648,8 @@ assemble_covariance_matrix_3(InputIterator first,
        t[0].y(), t[1].y(), 0.0,
                    t[0].z(), t[1].z(), 1.0};
     Matrix transformation = init_matrix<FT>(3,delta);
-    FT length = std::sqrt(t.squared_length());
+    using std::sqrt;
+    FT length = sqrt(t.squared_length());
 
 		// skip zero measure primitives
     if(length == (FT)0.0)
diff --git a/Principal_component_analysis/include/CGAL/PCA_util_Eigen.h b/Principal_component_analysis/include/CGAL/PCA_util_Eigen.h
index 81759d878ee..a79526fca11 100644
--- a/Principal_component_analysis/include/CGAL/PCA_util_Eigen.h
+++ b/Principal_component_analysis/include/CGAL/PCA_util_Eigen.h
@@ -566,7 +566,8 @@ assemble_covariance_matrix_3(InputIterator first,
     transformation << t[0].x(), t[1].x(), 0.0, 
                       t[0].y(), t[1].y(), 0.0,
                       t[0].z(), t[1].z(), 1.0;
-    FT length = std::sqrt(t.squared_length());
+    using std::sqrt;
+    FT length = sqrt(t.squared_length());
 
     // skip zero measure primitives
     if(length == (FT)0.0)
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
index bd4b8ebd9c6..8edd3203486 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
@@ -82,7 +82,8 @@ linear_least_squares_fitting_2(InputIterator first,
     FT delta[4] = {t[0].x(), t[1].x(), 
 		   t[0].y(), t[1].y()};
     Matrix transformation = init_matrix<FT>(2,delta);
-    FT length = std::sqrt(t.squared_length());
+    using std::sqrt;
+    FT length = sqrt(t.squared_length());
     CGAL_assertion(length != 0.0);
 
     // Find the 2nd order moment for the segment wrt to the origin by an affine transformation.
diff --git a/Principal_component_analysis/test/Principal_component_analysis/CMakeLists.txt b/Principal_component_analysis/test/Principal_component_analysis/CMakeLists.txt
index 93abc4b5e32..994d7529744 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/CMakeLists.txt
+++ b/Principal_component_analysis/test/Principal_component_analysis/CMakeLists.txt
@@ -12,14 +12,15 @@ if ( CGAL_FOUND )
 
   # Use Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
-  if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-  endif()
 
   # create a target per cppfile
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     create_single_source_cgal_program( "${cppfile}" )
+    if (EIGEN3_FOUND)
+      get_filename_component(target ${cppfile} NAME_WE)
+      CGAL_target_use_Eigen(${target})
+    endif()
   endforeach()
 
 else()
diff --git a/Principal_component_analysis_LGPL/include/CGAL/centroid.h b/Principal_component_analysis_LGPL/include/CGAL/centroid.h
index 0d5061ebd6b..dc3b46266b9 100644
--- a/Principal_component_analysis_LGPL/include/CGAL/centroid.h
+++ b/Principal_component_analysis_LGPL/include/CGAL/centroid.h
@@ -120,7 +120,9 @@ centroid(InputIterator begin,
       it++)
   {
     const Segment& s = *it;
-    FT length = std::sqrt(std::abs(s.squared_length()));
+    using std::abs;
+    using std::sqrt;
+    FT length = sqrt(abs(s.squared_length()));
     Point c = K().construct_midpoint_2_object()(s[0],s[1]);
     v = v + length * (c - ORIGIN);
     sum_lengths += length;
@@ -440,7 +442,8 @@ centroid(InputIterator begin,
       it++)
   {
     const Segment& s = *it;
-    FT length = std::sqrt(s.squared_length());
+    using std::sqrt;
+    FT length = sqrt(s.squared_length());
     Point c = CGAL::midpoint(s.source(),s.target());
     // Point c = K().construct_midpoint_3_object()(s[0],s[1]);
     //Point c = Point((s[0][0] + s[1][0])/2.0, (s[0][1] + s[1][1])/2.0, (s[0][2] + s[1][2])/2.0);
diff --git a/Property_map/include/CGAL/Dynamic_property_map.h b/Property_map/include/CGAL/Dynamic_property_map.h
index 35cdcd5f4db..2300b4b5efe 100644
--- a/Property_map/include/CGAL/Dynamic_property_map.h
+++ b/Property_map/include/CGAL/Dynamic_property_map.h
@@ -13,11 +13,13 @@
 #define CGAL_DYNAMIC_PROPERTY_MAP_H
 
 #include <boost/graph/graph_traits.hpp>
+#include <boost/graph/properties.hpp>
+
 #include <CGAL/boost/graph/properties.h>
 #include <CGAL/property_map.h>
+
 #include <boost/shared_ptr.hpp>
 #include <boost/unordered_map.hpp>
-
 #include <boost/type_traits/is_same.hpp>
 #include <boost/mpl/if.hpp>
 
diff --git a/Ridges_3/examples/Ridges_3/CMakeLists.txt b/Ridges_3/examples/Ridges_3/CMakeLists.txt
index c6409270728..09a60dbb011 100644
--- a/Ridges_3/examples/Ridges_3/CMakeLists.txt
+++ b/Ridges_3/examples/Ridges_3/CMakeLists.txt
@@ -11,7 +11,6 @@ if ( CGAL_FOUND )
   # use either Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     
     # Link with Boost.ProgramOptions (optional)
     find_package(Boost QUIET COMPONENTS program_options)
@@ -29,9 +28,12 @@ if ( CGAL_FOUND )
    endif()
 
    create_single_source_cgal_program( Compute_Ridges_Umbilics.cpp)
+   CGAL_target_use_Eigen(Compute_Ridges_Umbilics)
    create_single_source_cgal_program( Ridges_Umbilics_SM.cpp)
+   CGAL_target_use_Eigen(Ridges_Umbilics_SM)
    create_single_source_cgal_program( Ridges_Umbilics_LCC.cpp)
-
+   CGAL_target_use_Eigen(Ridges_Umbilics_LCC)
+   
   else()
 
     message(STATUS "NOTICE: This program requires Eigen 3.1 (or greater) and will not be compiled.")
diff --git a/Ridges_3/test/Ridges_3/CMakeLists.txt b/Ridges_3/test/Ridges_3/CMakeLists.txt
index 8ed993f8e6b..122000c9c68 100644
--- a/Ridges_3/test/Ridges_3/CMakeLists.txt
+++ b/Ridges_3/test/Ridges_3/CMakeLists.txt
@@ -14,9 +14,8 @@ if ( CGAL_FOUND )
   # use either Eigen
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "ridge_test.cpp" )
-
+    CGAL_target_use_Eigen(ridge_test)
   else()
   
     message(STATUS "NOTICE: This program requires Eigen 3.1 (or greater) and will not be compiled.")
diff --git a/STL_Extension/include/CGAL/Handle.h b/STL_Extension/include/CGAL/Handle.h
index 278232748a5..7e725eb67dc 100644
--- a/STL_Extension/include/CGAL/Handle.h
+++ b/STL_Extension/include/CGAL/Handle.h
@@ -39,13 +39,15 @@ class Handle
     
     typedef std::ptrdiff_t Id_type ;
     
-    Handle()
+    Handle() noexcept
 	: PTR(static_cast<Rep*>(0)) {}
 
-    Handle(const Handle& x)
+    // FIXME: if the precondition throws in a noexcept function, the program terminates
+    Handle(const Handle& x) noexcept
     {
       CGAL_precondition( x.PTR != static_cast<Rep*>(0) );
       PTR = x.PTR;
+      CGAL_assume (PTR->count > 0);
       PTR->count++;
     }
 
@@ -56,7 +58,7 @@ class Handle
     }
 
     Handle&
-    operator=(const Handle& x)
+    operator=(const Handle& x) noexcept
     {
       CGAL_precondition( x.PTR != static_cast<Rep*>(0) );
       x.PTR->count++;
@@ -66,6 +68,8 @@ class Handle
       return *this;
     }
 
+    friend void swap(Handle& a, Handle& b) noexcept { std::swap(a.PTR, b.PTR); }
+
     void reset()
     {
       if (PTR)
@@ -77,11 +81,11 @@ class Handle
     }
 
     int
-    refs()  const { return PTR->count; }
+    refs()  const noexcept { return PTR->count; }
 
-    Id_type id() const { return PTR - static_cast<Rep*>(0); }
+    Id_type id() const noexcept { return PTR - static_cast<Rep*>(0); }
 
-    bool identical(const Handle& h) const { return PTR == h.PTR; }
+    bool identical(const Handle& h) const noexcept { return PTR == h.PTR; }
 
   protected:
     Rep* PTR;
@@ -89,7 +93,7 @@ class Handle
 
 //inline Handle::Id_type id(const Handle& x) { return x.id() ; }
 
-inline bool identical(const Handle &h1, const Handle &h2) { return h1.identical(h2); }
+inline bool identical(const Handle &h1, const Handle &h2) noexcept { return h1.identical(h2); }
 
 } //namespace CGAL
 
diff --git a/STL_Extension/include/CGAL/Handle_for.h b/STL_Extension/include/CGAL/Handle_for.h
index 8bc097d7c02..b283f469003 100644
--- a/STL_Extension/include/CGAL/Handle_for.h
+++ b/STL_Extension/include/CGAL/Handle_for.h
@@ -102,7 +102,7 @@ public:
         ptr_ = p;
     }
 
-    Handle_for(const Handle_for& h)
+    Handle_for(const Handle_for& h) noexcept
       : ptr_(h.ptr_)
     {
 	CGAL_assume (ptr_->count > 0);
@@ -110,7 +110,7 @@ public:
     }
 
     Handle_for&
-    operator=(const Handle_for& h)
+    operator=(const Handle_for& h) noexcept
     {
         Handle_for tmp = h;
         swap(tmp);
@@ -132,7 +132,7 @@ public:
     //        from e.g. using nullptr as a ptr value, but this is drastic.
 
     Handle_for&
-    operator=(Handle_for && h)
+    operator=(Handle_for && h) noexcept
     {
         swap(h);
         return *this;
@@ -164,15 +164,15 @@ public:
         *this = t;
     }
 
-    Id_type id() const { return Ptr() - static_cast<T const*>(0); }
+    Id_type id() const noexcept { return Ptr() - static_cast<T const*>(0); }
     
-    bool identical(const Handle_for& h) const { return Ptr() == h.Ptr(); }
+    bool identical(const Handle_for& h) const noexcept { return Ptr() == h.Ptr(); }
 
 
     // Ptr() is the "public" access to the pointer to the object.
     // The non-const version asserts that the instance is not shared.
     const element_type *
-    Ptr() const
+    Ptr() const noexcept
     {
        return &(ptr_->t);
     }
@@ -188,25 +188,25 @@ public:
     */
 
     bool
-    is_shared() const
+    is_shared() const noexcept
     {
 	return ptr_->count > 1;
     }
 
     bool
-    unique() const
+    unique() const noexcept
     {
 	return !is_shared();
     }
 
     long
-    use_count() const
+    use_count() const noexcept
     {
 	return ptr_->count;
     }
 
     void
-    swap(Handle_for& h)
+    swap(Handle_for& h) noexcept
     {
       std::swap(ptr_, h.ptr_);
     }
@@ -222,11 +222,11 @@ protected:
     // ptr() is the protected access to the pointer.  Both const and non-const.
     // Redundant with Ptr().
     element_type *
-    ptr()
+    ptr() noexcept
     { return &(ptr_->t); }
 
     const element_type *
-    ptr() const
+    ptr() const noexcept
     { return &(ptr_->t); }
 };
 
diff --git a/Scale_space_reconstruction_3/examples/Scale_space_reconstruction_3/CMakeLists.txt b/Scale_space_reconstruction_3/examples/Scale_space_reconstruction_3/CMakeLists.txt
index bab0af3c5b1..7dd3f858f13 100644
--- a/Scale_space_reconstruction_3/examples/Scale_space_reconstruction_3/CMakeLists.txt
+++ b/Scale_space_reconstruction_3/examples/Scale_space_reconstruction_3/CMakeLists.txt
@@ -20,11 +20,14 @@ if ( CGAL_FOUND )
 
   find_package( Eigen3 3.1.0 )
   if( EIGEN3_FOUND )
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "scale_space.cpp" )
+    CGAL_target_use_Eigen(scale_space)
     create_single_source_cgal_program( "scale_space_incremental.cpp" )
+    CGAL_target_use_Eigen(scale_space_incremental)
     create_single_source_cgal_program( "scale_space_manifold.cpp" )
+    CGAL_target_use_Eigen(scale_space_manifold)
     create_single_source_cgal_program( "scale_space_advancing_front.cpp" )
+    CGAL_target_use_Eigen(scale_space_advancing_front)
     if(ACTIVATE_CONCURRENCY AND TBB_FOUND)
       CGAL_target_use_TBB(scale_space)
       CGAL_target_use_TBB(scale_space_incremental)
diff --git a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Segment_Delaunay_graph_2.txt b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Segment_Delaunay_graph_2.txt
index 93176e528b4..f10e3b43395 100644
--- a/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Segment_Delaunay_graph_2.txt
+++ b/Segment_Delaunay_graph_2/doc/Segment_Delaunay_graph_2/Segment_Delaunay_graph_2.txt
@@ -404,30 +404,17 @@ classes:
 
 As mentioned above, performing computations with exact arithmetic
 can be very costly. For this reason we have devoted considerable
-effort in implementing different kinds of arithmetic filtering
-mechanisms. Presently, there two ways of performing arithmetic
-filtering for the predicates involved in the computation of
-segment Delaunay graphs:
-<OL>
-<LI>The user can use a kernel with a filtered number type
-as the first template parameter in the `Segment_Delaunay_graph_traits_2<K,MTag>`.
-<LI>The user can define up to three different kernels `CK`,
+effort in implementing arithmetic filtering mechanisms
+through special traits classes, `Segment_Delaunay_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>`
+and `Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>`.
+These two traits class employ the `Filtered_predicate<EP,FP>` mechanism,
+and the user can define up to three different kernels `CK`,
 `FK` and `EK` (default values are provided for most
-parameters). The first kernel `CK` is used only for
+parameters): the first kernel `CK` is used only for
 constructions. The second kernel `FK` is the filtering kernel:
 the traits class will attempt to compute the predicates using this
 kernel. If the filtering kernel fails to successfully compute a
-predicate, the exact kernel `EK` will be used. These three
-kernels are then used in the 
-`Segment_Delaunay_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>` and
-`Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>`
-classes, which have been implemented using the
-`Filtered_predicate<EP,FP>` mechanism.
-</OL>
-Our experience so far has shown that for all reasonable and valid
-values of the template parameters, the second method for arithmetic
-filtering is more efficient among the two.
-This approach is also used in the examples.
+predicate, the exact kernel `EK` will be used.
 
 Let's consider once more the class
 `Segment_Delaunay_graph_traits_2<K,MTag>`.
@@ -506,7 +493,7 @@ for inputs consisting of more than about 1,000 sites.
 \subsection Segment_Delaunay_graph_2FirstExample First Example using the Filtered Traits
 
 The following example shows how to use the segment Delaunay graph traits
-in conjunction with the `Filtered_exact<CT,ET>` mechanism. In
+in conjunction with filtered traits mechanisms. In
 addition it shows how to use a few of the iterators provided by the
 `Segment_Delaunay_graph_2` class in order to count a few
 site-related quantities.
diff --git a/Shape_detection/benchmark/Shape_detection/CMakeLists.txt b/Shape_detection/benchmark/Shape_detection/CMakeLists.txt
index f2c7bf19d77..4bcb6bc9978 100644
--- a/Shape_detection/benchmark/Shape_detection/CMakeLists.txt
+++ b/Shape_detection/benchmark/Shape_detection/CMakeLists.txt
@@ -15,12 +15,12 @@ if(CGAL_FOUND)
   # Use Eigen.
   find_package(Eigen3 3.1.0 QUIET) # (3.1.0 or greater)
   if(EIGEN3_FOUND)
-    include(${EIGEN3_USE_FILE})
-
     create_single_source_cgal_program(
       "benchmark_region_growing_on_point_set_2.cpp")
+    CGAL_target_use_Eigen(benchmark_region_growing_on_point_set_2)
     create_single_source_cgal_program(
       "benchmark_region_growing_on_point_set_3.cpp")
+    CGAL_target_use_Eigen(benchmark_region_growing_on_point_set_3)
   endif()
 
 else()
diff --git a/Shape_detection/benchmark/Shape_detection/README.md b/Shape_detection/benchmark/Shape_detection/README.md
index da9a3b99a68..b7eab3675f9 100644
--- a/Shape_detection/benchmark/Shape_detection/README.md
+++ b/Shape_detection/benchmark/Shape_detection/README.md
@@ -1,11 +1,5 @@
 README:
 
-Data:
-To keep the size of this package small, all benchmark data are placed here:
-https://github.com/... /data
-
-You can download them and use to get the results below.
-
 Results (Point Set 2):
 
 ```
diff --git a/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_2.cpp b/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_2.cpp
index a1fe25bf58a..f45f4745dbb 100644
--- a/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_2.cpp
+++ b/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_2.cpp
@@ -92,6 +92,15 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_2.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return EXIT_FAILURE;
+  }
+
   Input_range input_range;
   FT a, b, c, d, e, f;
 
diff --git a/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_3.cpp b/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_3.cpp
index 0137b1f05fc..cb17dd6d858 100644
--- a/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_3.cpp
+++ b/Shape_detection/benchmark/Shape_detection/benchmark_region_growing_on_point_set_3.cpp
@@ -128,6 +128,15 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_3.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_3.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return EXIT_FAILURE;
+  }
+
   Input_range input;
   Point_3 p; Vector_3 n;
 
diff --git a/Shape_detection/doc/Shape_detection/Shape_detection.txt b/Shape_detection/doc/Shape_detection/Shape_detection.txt
index 835e08ae30b..26ad047e26d 100644
--- a/Shape_detection/doc/Shape_detection/Shape_detection.txt
+++ b/Shape_detection/doc/Shape_detection/Shape_detection.txt
@@ -306,9 +306,9 @@ The `RegionType` class defines the three necessary functions:
 - `RegionType::update()` - updates the internal flag from the default `false` to `true`.
 
 We also define a `SeedMap`, such that the second object is handled first, while the first object follows.
-Moreover, the last object is always skipped. Notice that in this example, the container with objects is `std::list`,
-which is not a random access. In general, it is much slower, but illustrates that the 
-generic region growing algorithm can be applied to any type of a container.
+Moreover, the last object is always skipped. Notice that in this example, the container with objects is `std::vector`,
+which is random access. However, the generic region growing algorithm can be applied 
+to any other type of container, e.g. `std::list`.
 
 The result of using these classes with the region growing main class is that the first two objects form the first region, 
 the third object forms the second region, and the last object is skipped.
diff --git a/Shape_detection/examples/Shape_detection/CMakeLists.txt b/Shape_detection/examples/Shape_detection/CMakeLists.txt
index d1c49d4986e..f8869233fbd 100644
--- a/Shape_detection/examples/Shape_detection/CMakeLists.txt
+++ b/Shape_detection/examples/Shape_detection/CMakeLists.txt
@@ -15,8 +15,6 @@ if(CGAL_FOUND)
   # Use Eigen.
   find_package(Eigen3 3.1.0 QUIET) # (3.1.0 or greater)
   if(EIGEN3_FOUND)
-    include(${EIGEN3_USE_FILE})
-
     create_single_source_cgal_program(
       "efficient_RANSAC_basic.cpp")
     create_single_source_cgal_program(
@@ -35,6 +33,19 @@ if(CGAL_FOUND)
 
     create_single_source_cgal_program(
       "shape_detection_basic_deprecated.cpp")
+    
+    foreach(target
+        efficient_RANSAC_basic
+        efficient_RANSAC_with_callback
+        efficient_RANSAC_and_plane_regularization
+        region_growing_on_point_set_2
+        region_growing_on_point_set_3
+        region_growing_on_polygon_mesh
+        region_growing_with_custom_classes
+        shape_detection_basic_deprecated)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
+    
   endif()
 
   create_single_source_cgal_program(
diff --git a/Shape_detection/examples/Shape_detection/efficient_RANSAC_with_parameters.cpp b/Shape_detection/examples/Shape_detection/efficient_RANSAC_with_parameters.cpp
index b2425c2c514..e4d21ac5856 100644
--- a/Shape_detection/examples/Shape_detection/efficient_RANSAC_with_parameters.cpp
+++ b/Shape_detection/examples/Shape_detection/efficient_RANSAC_with_parameters.cpp
@@ -65,7 +65,7 @@ int main(int argc, char** argv) {
   // Set probability to miss the largest primitive at each iteration.
   parameters.probability = 0.05;
  
-  // Detect shapes with at least 500 points.
+  // Detect shapes with at least 200 points.
   parameters.min_points = 200;
 
   // Set maximum Euclidean distance between a point and a shape.
diff --git a/Shape_detection/examples/Shape_detection/region_growing_on_point_set_2.cpp b/Shape_detection/examples/Shape_detection/region_growing_on_point_set_2.cpp
index b8b350fcf33..ffd34a43e62 100644
--- a/Shape_detection/examples/Shape_detection/region_growing_on_point_set_2.cpp
+++ b/Shape_detection/examples/Shape_detection/region_growing_on_point_set_2.cpp
@@ -80,6 +80,15 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_2.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return EXIT_FAILURE;
+  }
+
   Input_range input_range;
   FT a, b, c, d, e, f;
 
diff --git a/Shape_detection/examples/Shape_detection/region_growing_on_point_set_3.cpp b/Shape_detection/examples/Shape_detection/region_growing_on_point_set_3.cpp
index 5a8561d37bb..abb522a20af 100644
--- a/Shape_detection/examples/Shape_detection/region_growing_on_point_set_3.cpp
+++ b/Shape_detection/examples/Shape_detection/region_growing_on_point_set_3.cpp
@@ -111,6 +111,15 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_3.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_3.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return EXIT_FAILURE;
+  }
+
   const bool with_normal_map = true;
   Input_range input_range(with_normal_map);
 
diff --git a/Shape_detection/examples/Shape_detection/region_growing_on_polygon_mesh.cpp b/Shape_detection/examples/Shape_detection/region_growing_on_polygon_mesh.cpp
index e49cee21325..98d2f794cc2 100644
--- a/Shape_detection/examples/Shape_detection/region_growing_on_polygon_mesh.cpp
+++ b/Shape_detection/examples/Shape_detection/region_growing_on_polygon_mesh.cpp
@@ -67,6 +67,15 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/polygon_mesh.off");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file polygon_mesh.off!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return EXIT_FAILURE;
+  }
+
   Polygon_mesh polygon_mesh;
   in >> polygon_mesh;
     
diff --git a/Shape_detection/include/CGAL/Shape_detection/Efficient_RANSAC/Efficient_RANSAC.h b/Shape_detection/include/CGAL/Shape_detection/Efficient_RANSAC/Efficient_RANSAC.h
index 3708c3cfaab..cbc376969ae 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Efficient_RANSAC/Efficient_RANSAC.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Efficient_RANSAC/Efficient_RANSAC.h
@@ -161,11 +161,49 @@ namespace CGAL {
         , cluster_epsilon(-1)
       {}
 
-      FT probability;         ///< Probability to control search endurance. %Default value: 5%.
-      std::size_t min_points; ///< Minimum number of points of a shape. %Default value: 1% of total number of input points.
-      FT epsilon;             ///< Maximum tolerance Euclidean distance from a point and a shape. %Default value: 1% of bounding box diagonal.
-      FT normal_threshold;	  ///< Maximum tolerance normal deviation from a point's normal to the normal on a shape at the projected point. %Default value: 0.9 (around 25 degrees).
-      FT cluster_epsilon;	    ///< Maximum distance between points to be considered connected. %Default value: 1% of bounding box diagonal.
+      /*! 
+        Probability to control search endurance. 
+        %Default value is 0.05.
+
+        A lower probability provides a higher reliability and determinism at the cost 
+        of longer running time due to a higher search endurance.
+
+        It must belong to the interval [0, 1].
+      */
+      FT probability;
+
+      /*! 
+        Minimum number of points in a shape. 
+        %Default value is 1% of total number of input points.
+
+        It must belong to the interval [0, +inf).
+      */
+      std::size_t min_points;
+
+      /*! 
+        Maximum acceptable Euclidean distance between a point and a shape.
+        %Default value is 1% of the bounding box diagonal.
+
+        It must belong to the interval [0, +inf).
+      */
+      FT epsilon;
+
+      /*! 
+        Maximum threshold on the dot product between the estimated 
+        shape's normal and the point's normal, that is the cosine of the angle (cos(25°) = 0.9).
+        %Default value is 0.9 (around 25 degrees).
+
+        It must belong to the interval [0, 1].
+      */
+      FT normal_threshold;
+
+      /*! 
+        Maximum acceptable Euclidean distance between points, which are assumed to be neighbors.
+        %Default value is 1% of the bounding box diagonal.
+
+        It must belong to the interval [0, +inf).
+      */
+      FT cluster_epsilon;
     };
     /// @}
 
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
index 00e1ea9e80d..b71b71800bc 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
@@ -40,9 +40,10 @@ namespace Point_set {
     \brief Region type based on the quality of the least squares line 
     fit applied to 2D points.
 
-    This class fits a line to chunks of points in a 2D point set and controls 
-    the quality of this fit. If all quality conditions are satisfied, the chunk
-    is accepted as a valid region, otherwise rejected.
+    This class fits a line, using \ref PkgPrincipalComponentAnalysisDRef "PCA", 
+    to chunks of points in a 2D point set and controls the quality of this fit. 
+    If all quality conditions are satisfied, the chunk is accepted as a valid region, 
+    otherwise rejected.
 
     \tparam GeomTraits 
     must be a model of `Kernel`.
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
index dbd98cb1b3c..842c4420277 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
@@ -40,9 +40,10 @@ namespace Point_set {
     \brief Region type based on the quality of the least squares plane 
     fit applied to 3D points.
 
-    This class fits a plane to chunks of points in a 3D point set and controls 
-    the quality of this fit. If all quality conditions are satisfied, the chunk
-    is accepted as a valid region, otherwise rejected.
+    This class fits a plane, using \ref PkgPrincipalComponentAnalysisDRef "PCA", 
+    to chunks of points in a 3D point set and controls the quality of this fit. 
+    If all quality conditions are satisfied, the chunk is accepted as a valid region, 
+    otherwise rejected.
 
     \tparam GeomTraits 
     must be a model of `Kernel`.
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
index 7b552249f44..499e23c956c 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
@@ -49,9 +49,10 @@ namespace Polygon_mesh {
     \brief Region type based on the quality of the least squares plane 
     fit applied to faces of a polygon mesh.
 
-    This class fits a plane to chunks of faces in a polygon mesh and controls 
-    the quality of this fit. If all quality conditions are satisfied, the chunk
-    is accepted as a valid region, otherwise rejected.
+    This class fits a plane, using \ref PkgPrincipalComponentAnalysisDRef "PCA", 
+    to chunks of faces in a polygon mesh and controls the quality of this fit. 
+    If all quality conditions are satisfied, the chunk is accepted as a valid region, 
+    otherwise rejected.
 
     \tparam GeomTraits 
     must be a model of `Kernel`.
@@ -97,6 +98,7 @@ namespace Polygon_mesh {
     using Squared_length_3 = typename Traits::Compute_squared_length_3;
     using Squared_distance_3 = typename Traits::Compute_squared_distance_3;
     using Scalar_product_3 = typename Traits::Compute_scalar_product_3;
+    using Cross_product_3 = typename Traits::Construct_cross_product_vector_3;
 
     using Get_sqrt = internal::Get_sqrt<Traits>;
     using Sqrt = typename Get_sqrt::Sqrt;
@@ -160,6 +162,7 @@ namespace Polygon_mesh {
     m_squared_length_3(traits.compute_squared_length_3_object()),
     m_squared_distance_3(traits.compute_squared_distance_3_object()),
     m_scalar_product_3(traits.compute_scalar_product_3_object()),
+    m_cross_product_3(traits.construct_cross_product_vector_3_object()),
     m_sqrt(Get_sqrt::sqrt_object(traits)),
     m_to_local_converter() {
 
@@ -207,9 +210,13 @@ namespace Polygon_mesh {
 
       const FT distance_to_fitted_plane = 
       get_max_face_distance(face);
+      if (distance_to_fitted_plane < FT(0))
+        return false;
       
+      // The sign of this scalar product is important, as it indicates
+      // into which side of the plane the face's normal points.
       const FT cos_value = 
-      CGAL::abs(m_scalar_product_3(face_normal, m_normal_of_best_fit));
+      m_scalar_product_3(face_normal, m_normal_of_best_fit);
 
       return (( distance_to_fitted_plane <= m_distance_threshold ) && 
         ( cos_value >= m_normal_threshold ));
@@ -284,6 +291,13 @@ namespace Polygon_mesh {
 
         // The best fit plane will be a plane fitted to all vertices of all
         // region faces with its normal being perpendicular to the plane.
+        // Given that the points, and no normals, are used in estimating
+        // the plane, the estimated normal will point into an arbitray
+        // one of the two possible directions.
+        // We flip it into the correct direction (the one that the majority
+        // of faces agree with) below.
+        // This fix is proposed by nh2: 
+        // https://github.com/CGAL/cgal/pull/4563
         CGAL::linear_least_squares_fitting_3(
           points.begin(), points.end(), 
           fitted_plane, fitted_centroid, 
@@ -291,18 +305,49 @@ namespace Polygon_mesh {
           Local_traits(), 
           CGAL::Eigen_diagonalize_traits<Local_FT, 3>());
 
-        m_plane_of_best_fit = 
+        const Plane_3 unoriented_plane_of_best_fit =
         Plane_3(
           static_cast<FT>(fitted_plane.a()), 
           static_cast<FT>(fitted_plane.b()), 
           static_cast<FT>(fitted_plane.c()), 
           static_cast<FT>(fitted_plane.d()));
 
-        const Vector_3 normal = m_plane_of_best_fit.orthogonal_vector();
-        const FT normal_length = m_sqrt(m_squared_length_3(normal));
+        Vector_3 unoriented_plane_normal =
+        unoriented_plane_of_best_fit.orthogonal_vector();
 
-        CGAL_precondition(normal_length > FT(0));
-        m_normal_of_best_fit = normal / normal_length;
+        const FT squared_length = m_squared_length_3(unoriented_plane_normal);
+        if (squared_length != FT(0)) {
+          const FT normal_length = m_sqrt(squared_length);
+          CGAL_precondition(normal_length > FT(0));
+          unoriented_plane_normal /= normal_length;
+        }
+
+        // Compute actual direction of plane's normal sign
+        // based on faces belonging to that region.
+        // Approach:
+        // Each face gets one vote to keep or flip the current plane normal.
+        Vector_3 face_normal;
+        long votes_to_keep_normal = 0;
+
+        for (const std::size_t face_index : region) {
+          const auto face = *(m_face_range.begin() + face_index);
+
+          get_face_normal(face, face_normal);
+          const bool agrees = 
+          m_scalar_product_3(face_normal, unoriented_plane_normal) > FT(0);
+          votes_to_keep_normal += (agrees ? 1 : -1);
+        }
+        const bool flip_normal = (votes_to_keep_normal < 0);
+
+        m_plane_of_best_fit =
+        flip_normal
+          ? unoriented_plane_of_best_fit.opposite()
+          : unoriented_plane_of_best_fit;
+
+        m_normal_of_best_fit =
+        flip_normal
+          ? (-1 * unoriented_plane_normal)
+          : unoriented_plane_normal;
       }
     }
 
@@ -359,17 +404,30 @@ namespace Polygon_mesh {
       const Point_3& point2 = get(m_vertex_to_point_map, *vertex); ++vertex;
       const Point_3& point3 = get(m_vertex_to_point_map, *vertex);
 
-      const Vector_3 tmp_normal = CGAL::normal(point1, point2, point3);
-      const FT tmp_normal_length = m_sqrt(m_squared_length_3(tmp_normal));
+      const Vector_3 u = point2 - point1;
+      const Vector_3 v = point3 - point1; 
+      face_normal = m_cross_product_3(u, v);
+      const FT squared_length = m_squared_length_3(face_normal);
+      if (squared_length == FT(0))
+        return;
 
-      CGAL_precondition(tmp_normal_length > FT(0));
-      face_normal = tmp_normal / tmp_normal_length;
+      const FT normal_length = m_sqrt(squared_length);
+      CGAL_precondition(normal_length > FT(0));
+      face_normal /= normal_length;
     }
 
     // The maximum distance from the vertices of the face to the best fit plane.
     template<typename Face>
     FT get_max_face_distance(const Face& face) const {
 
+      const FT a = CGAL::abs(m_plane_of_best_fit.a());
+      const FT b = CGAL::abs(m_plane_of_best_fit.b());
+      const FT c = CGAL::abs(m_plane_of_best_fit.c());
+      const FT d = CGAL::abs(m_plane_of_best_fit.d());
+
+      if (a == FT(0) && b == FT(0) && c == FT(0) && d == FT(0))
+        return -FT(1);
+
       const auto hedge = halfedge(face, m_face_graph);
       const auto vertices = vertices_around_face(hedge, m_face_graph);
 
@@ -403,6 +461,7 @@ namespace Polygon_mesh {
     const Squared_length_3 m_squared_length_3;
     const Squared_distance_3 m_squared_distance_3;
     const Scalar_product_3 m_scalar_product_3;
+    const Cross_product_3 m_cross_product_3;
     const Sqrt m_sqrt;
 
     const To_local_converter m_to_local_converter;
diff --git a/Shape_detection/package_info/Shape_detection/maintainer b/Shape_detection/package_info/Shape_detection/maintainer
index 08648392ab4..15b87b3289e 100644
--- a/Shape_detection/package_info/Shape_detection/maintainer
+++ b/Shape_detection/package_info/Shape_detection/maintainer
@@ -2,4 +2,4 @@ Clément Jamin <clement.jamin.pro@gmail.com>
 Sven Oesau <sven.oesau@inria.fr>
 Simon Giraudot <simon.giraudot@geometryfactory.com>
 Thien Hoang <thienvhoang99@gmail.com>
-Dmitry Anisimov <dmitry.anisimov@inria.fr>
+Dmitry Anisimov <rudanston@gmail.com>
diff --git a/Shape_detection/test/Shape_detection/CMakeLists.txt b/Shape_detection/test/Shape_detection/CMakeLists.txt
index 67551a95348..d8f7c9c9ba0 100644
--- a/Shape_detection/test/Shape_detection/CMakeLists.txt
+++ b/Shape_detection/test/Shape_detection/CMakeLists.txt
@@ -15,8 +15,6 @@ if(CGAL_FOUND)
   # Use Eigen.
   find_package(Eigen3 3.1.0 QUIET) # (3.1.0 or greater)
   if(EIGEN3_FOUND)
-    include(${EIGEN3_USE_FILE})
-
     create_single_source_cgal_program(
       "test_region_growing_basic.cpp")
     create_single_source_cgal_program(
@@ -33,6 +31,21 @@ if(CGAL_FOUND)
       "test_region_growing_on_point_set_3_with_sorting.cpp")
     create_single_source_cgal_program(
       "test_region_growing_on_polygon_mesh_with_sorting.cpp")
+    create_single_source_cgal_program(
+      "test_region_growing_on_degenerated_mesh.cpp")
+    foreach(target
+        test_region_growing_basic
+        test_region_growing_on_cube
+        test_region_growing_on_point_set_2
+        test_region_growing_on_point_set_3
+        test_region_growing_on_polygon_mesh
+        test_region_growing_on_point_set_2_with_sorting
+        test_region_growing_on_point_set_3_with_sorting
+        test_region_growing_on_polygon_mesh_with_sorting
+        test_region_growing_on_degenerated_mesh)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
+    
   endif()
 
   create_single_source_cgal_program(
diff --git a/Shape_detection/test/Shape_detection/data/degenerated.off b/Shape_detection/test/Shape_detection/data/degenerated.off
new file mode 100644
index 00000000000..aa7c69eb5e1
--- /dev/null
+++ b/Shape_detection/test/Shape_detection/data/degenerated.off
@@ -0,0 +1,20547 @@
+OFF
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+3 1621 1550 1480
+3 5431 1481 1641
+3 5431 1641 1480
+3 1481 5495 1641
+3 1481 5431 1613
+3 1613 1614 1481
+3 1636 5495 1481
+3 1636 1481 1614
+3 1401 1614 1400
+3 1635 5501 5500
+3 5502 1641 5501
+3 1635 5502 5501
+3 1641 5502 5920
+3 1549 5416 1550
+3 1400 1608 1616
+3 1400 1616 1401
+3 1608 1577 1616
+3 1608 1549 1577
+3 5429 1549 1608
+3 5416 5429 1634
+3 5416 1549 5429
+3 1400 1634 5429
+3 1608 1400 5429
+3 1634 5431 1480
+3 1634 1480 5416
+3 1550 5416 1480
+3 1400 1613 5431
+3 5431 1634 1400
+3 1876 5464 1874
+3 1358 1876 1874
+3 1358 1355 1876
+3 1878 5464 5465
+3 1876 5465 5464
+3 1878 6686 5464
+3 1874 5464 6686
+3 1876 6740 5465
+3 1824 5465 6740
+3 949 2865 985
+3 4416 4424 2714
+3 950 4651 4416
+3 4416 4651 2893
+3 2893 6087 4416
+3 4424 4416 6087
+3 4393 5153 4416
+3 4416 2714 4393
+3 949 5153 4393
+3 6773 4654 4640
+3 2887 4640 4654
+3 4640 2887 4653
+3 1938 1849 1850
+3 1918 5484 1850
+3 1849 5485 1847
+3 1850 1849 1847
+3 1850 5484 1938
+3 1261 2035 2028
+3 1262 1261 2028
+3 1465 1557 2040
+3 1465 2040 1995
+3 2040 1557 2050
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp b/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
index 791ac71a32f..14246ea65f4 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
@@ -37,6 +37,16 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_2.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    assert(false);
+    return EXIT_FAILURE;
+  }
+
   Input_range input_range;
   FT a, b, c, d, e, f;
 
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_cube.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_cube.cpp
index c2ce454ccb7..4b97bd2f01d 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_cube.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_cube.cpp
@@ -42,6 +42,15 @@ bool test_region_growing_on_cube(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/cube.off");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file cube.off!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return false;
+  }
+
   Polyhedron polyhedron;
   in >> polyhedron;
     
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_degenerated_mesh.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_degenerated_mesh.cpp
new file mode 100644
index 00000000000..c674749d4a1
--- /dev/null
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_degenerated_mesh.cpp
@@ -0,0 +1,132 @@
+// STL includes.
+#include <vector>
+#include <string>
+#include <fstream>
+#include <iostream>
+#include <iterator>
+#include <cassert>
+
+// CGAL includes.
+#include <CGAL/assertions.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <CGAL/Shape_detection/Region_growing/Region_growing.h>
+#include <CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh.h>
+
+namespace SD = CGAL::Shape_detection;
+
+template<class Kernel>
+bool test_region_growing_on_degenerated_mesh(int argc, char *argv[]) {
+
+  using FT      = typename Kernel::FT;
+  using Point_3 = typename Kernel::Point_3;
+
+  using Surface_mesh = CGAL::Surface_mesh<Point_3>;
+  using Face_range   = typename Surface_mesh::Face_range;
+
+  using Neighbor_query = SD::Polygon_mesh::One_ring_neighbor_query<Surface_mesh>;
+  using Region_type    = SD::Polygon_mesh::Least_squares_plane_fit_region<Kernel, Surface_mesh>;
+  using Region_growing = SD::Region_growing<Face_range, Neighbor_query, Region_type>;
+
+  // Default parameter values for the data file degenerated.off.
+  const FT          distance_threshold = FT(1);
+  const FT          angle_threshold    = FT(45);
+  const std::size_t min_region_size    = 5;
+
+  // Load data.
+  std::ifstream in(argc > 1 ? argv[1] : "data/degenerated.off");
+  CGAL::set_ascii_mode(in);
+
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file degenerated.off!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return false;
+  }
+
+  Surface_mesh surface_mesh;
+  in >> surface_mesh;
+    
+  in.close();
+  const Face_range face_range = faces(surface_mesh);
+
+  assert(face_range.size() == 13477);
+  if (face_range.size() != 13477) 
+    return false;
+
+  // Create parameter classes.
+  Neighbor_query neighbor_query(surface_mesh);
+
+  using Vertex_to_point_map = typename Region_type::Vertex_to_point_map;
+  const Vertex_to_point_map vertex_to_point_map(
+    get(CGAL::vertex_point, surface_mesh));
+
+  Region_type region_type(
+    surface_mesh, 
+    distance_threshold, angle_threshold, min_region_size, 
+    vertex_to_point_map);
+
+  // Run region growing.
+  Region_growing region_growing(
+    face_range, neighbor_query, region_type);
+  
+  std::vector< std::vector<std::size_t> > regions;
+  region_growing.detect(std::back_inserter(regions));
+
+  // Test data.
+  assert(regions.size() >= 265 && regions.size() <= 269);
+  if (regions.size() < 265 || regions.size() > 269) 
+    return false;
+
+  for (const auto& region : regions)
+    if (!region_type.is_valid_region(region)) 
+      return false;
+
+  std::vector<std::size_t> unassigned_faces;
+  region_growing.unassigned_items(std::back_inserter(unassigned_faces));
+
+  assert(unassigned_faces.size() >= 501 && unassigned_faces.size() <= 521);
+  if (unassigned_faces.size() < 501 || unassigned_faces.size() > 521) 
+    return false;
+
+  return true;
+}
+
+int main(int argc, char *argv[]) {
+
+  // ------>
+
+  bool cartesian_double_test_success = true;
+  if (!test_region_growing_on_degenerated_mesh< CGAL::Simple_cartesian<double> >(argc, argv)) 
+    cartesian_double_test_success = false;
+    
+  std::cout << "cartesian_double_test_success: " << cartesian_double_test_success << std::endl;
+  assert(cartesian_double_test_success);
+
+  // ------>
+
+  bool exact_inexact_test_success = true;
+  if (!test_region_growing_on_degenerated_mesh<CGAL::Exact_predicates_inexact_constructions_kernel>(argc, argv)) 
+    exact_inexact_test_success = false;
+    
+  std::cout << "exact_inexact_test_success: " << exact_inexact_test_success << std::endl;
+  assert(exact_inexact_test_success);
+
+  // ------>
+
+  bool exact_exact_test_success = true;
+  if (!test_region_growing_on_degenerated_mesh<CGAL::Exact_predicates_exact_constructions_kernel>(argc, argv)) 
+    exact_exact_test_success = false;
+    
+  std::cout << "exact_exact_test_success: " << exact_exact_test_success << std::endl;
+  assert(exact_exact_test_success);
+
+  const bool success = cartesian_double_test_success && exact_inexact_test_success && exact_exact_test_success;
+  return (success) ? EXIT_SUCCESS : EXIT_FAILURE;
+}
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2.cpp
index 5814d7294c6..39efcd97799 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2.cpp
@@ -46,6 +46,15 @@ bool test_region_growing_on_point_set_2(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_2.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return false;
+  }
+
   Input_range input_range;
   FT a, b, c, d, e, f;
 
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
index 9ab1943d3a5..c3b2c40eebd 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
@@ -41,6 +41,16 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_2.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    assert(false);
+    return EXIT_FAILURE;
+  }
+
   Input_range input_range;
   FT a, b, c, d, e, f;
 
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3.cpp
index 5667c32c5ad..f758f508ae5 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3.cpp
@@ -45,6 +45,15 @@ bool test_region_growing_on_point_set_3(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_3.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_3.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return false;
+  }
+
   const bool with_normal_map = true;
   Input_range input_range(with_normal_map);
 
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
index 4869de2b0b0..198e7031ff3 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
@@ -41,6 +41,16 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_3.xyz");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file point_set_3.xyz!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    assert(false);
+    return EXIT_FAILURE;
+  }
+
   const bool with_normal_map = true;
   Input_range input_range(with_normal_map);
 
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh.cpp
index 9b161f1d1b2..80a3a6264d8 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh.cpp
@@ -40,6 +40,15 @@ bool test_region_growing_on_polygon_mesh(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/polygon_mesh.off");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file polygon_mesh.off!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    return false;
+  }
+
   Surface_mesh surface_mesh;
   in >> surface_mesh;
     
@@ -70,8 +79,8 @@ bool test_region_growing_on_polygon_mesh(int argc, char *argv[]) {
   region_growing.detect(std::back_inserter(regions));
 
   // Test data.
-  assert(regions.size() >= 327 && regions.size() <= 331);
-  if (regions.size() < 327 || regions.size() > 331) 
+  assert(regions.size() >= 324 && regions.size() <= 328);
+  if (regions.size() < 324 || regions.size() > 328) 
     return false;
 
   for (const auto& region : regions)
@@ -81,8 +90,8 @@ bool test_region_growing_on_polygon_mesh(int argc, char *argv[]) {
   std::vector<std::size_t> unassigned_faces;
   region_growing.unassigned_items(std::back_inserter(unassigned_faces));
 
-  assert(unassigned_faces.size() >= 908 && unassigned_faces.size() <= 928);
-  if (unassigned_faces.size() < 908 || unassigned_faces.size() > 928) 
+  assert(unassigned_faces.size() >= 904 && unassigned_faces.size() <= 924);
+  if (unassigned_faces.size() < 904 || unassigned_faces.size() > 924) 
     return false;
 
   return true;
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh_with_sorting.cpp
index 6cfe0900a82..244f73d0e79 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_polygon_mesh_with_sorting.cpp
@@ -38,6 +38,16 @@ int main(int argc, char *argv[]) {
   std::ifstream in(argc > 1 ? argv[1] : "data/polygon_mesh.off");
   CGAL::set_ascii_mode(in);
 
+  if (!in) {
+    std::cout << 
+    "Error: cannot read the file polygon_mesh.off!" << std::endl;
+    std::cout << 
+    "You can either create a symlink to the data folder or provide this file by hand." 
+    << std::endl << std::endl;
+    assert(false);
+    return EXIT_FAILURE;
+  }
+
   Polygon_mesh polygon_mesh;
   in >> polygon_mesh;
     
@@ -79,7 +89,7 @@ int main(int argc, char *argv[]) {
   region_growing.release_memory();
   assert(regions.size() >= 324 && regions.size() <= 328);
 
-  const bool exact_exact_test_success = (regions.size() >= 323 && regions.size() <= 327);
+  const bool exact_exact_test_success = (regions.size() >= 324 && regions.size() <= 328);
   std::cout << "exact_exact_test_success: " << exact_exact_test_success << std::endl;
 
   const bool success = exact_exact_test_success;
diff --git a/Solver_interface/examples/Solver_interface/CMakeLists.txt b/Solver_interface/examples/Solver_interface/CMakeLists.txt
index e8cc264ec88..13ad3314c8e 100644
--- a/Solver_interface/examples/Solver_interface/CMakeLists.txt
+++ b/Solver_interface/examples/Solver_interface/CMakeLists.txt
@@ -14,24 +14,21 @@ if ( CGAL_FOUND )
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
 
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "singular_value_decomposition.cpp" )
+    CGAL_target_use_Eigen(singular_value_decomposition)
     create_single_source_cgal_program( "sparse_solvers.cpp" )
+    CGAL_target_use_Eigen(sparse_solvers)
+    create_single_source_cgal_program( "diagonalize_matrix.cpp" )
+    CGAL_target_use_Eigen(diagonalize_matrix)
   endif()
 
-  create_single_source_cgal_program( "diagonalize_matrix.cpp" )
   create_single_source_cgal_program( "mixed_integer_program.cpp" )
 
   find_package( SCIP QUIET)
 
   if (SCIP_FOUND)
 
-    include_directories( BEFORE ${SCIP_INCLUDE_DIRS} )
-
-    target_link_libraries( mixed_integer_program PRIVATE ${SCIP_LIBRARIES} )
-
-    target_compile_definitions(mixed_integer_program PRIVATE -DCGAL_USE_SCIP)
-
+    CGAL_target_use_SCIP(mixed_integer_program)
     message("SCIP found and used")
 
   else()
@@ -39,13 +36,8 @@ if ( CGAL_FOUND )
       find_package( GLPK QUIET)
 
       if (GLPK_FOUND)
-
-        include_directories( BEFORE ${GLPK_INCLUDE_DIR} )
-
-        target_link_libraries( mixed_integer_program PRIVATE ${GLPK_LIBRARIES} )
-
-        target_compile_definitions(mixed_integer_program PRIVATE -DCGAL_USE_GLPK)
-
+        
+        CGAL_target_use_GLPK(mixed_integer_program)
         message("GLPK found and used")
 
       else()
diff --git a/Spatial_searching/benchmark/Spatial_searching/CMakeLists.txt b/Spatial_searching/benchmark/Spatial_searching/CMakeLists.txt
index ca8157f8a8e..adb47481272 100644
--- a/Spatial_searching/benchmark/Spatial_searching/CMakeLists.txt
+++ b/Spatial_searching/benchmark/Spatial_searching/CMakeLists.txt
@@ -13,9 +13,6 @@ if ( CGAL_FOUND )
 include(${CGAL_USE_FILE})
 
 find_package(Eigen3 3.1.91) #(requires 3.2.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-endif()
 
   include_directories (BEFORE "include")
 
@@ -33,6 +30,23 @@ endif()
   create_single_source_cgal_program( "nn3nanoflan.cpp" )
   create_single_source_cgal_program( "sizeof.cpp" )
   create_single_source_cgal_program( "deque.cpp" )
+  foreach(target
+      Compare_ANN_STANN_CGAL
+      nanoflan
+      binary
+      nearest_neighbor_searching_50
+      nearest_neighbor_searching_inplace_50
+      Nearest_neighbor_searching
+      Nearest_neighbor_searching_2D
+      Nearest_neighbor_searching_2D_user_defined
+      Split_data
+      nn3cgal
+      nn4cgal
+      nn3nanoflan
+      sizeof
+      deque)
+    CGAL_target_use_Eigen(${target})
+  endforeach()
 
 else()
   
diff --git a/Spatial_searching/examples/Spatial_searching/CMakeLists.txt b/Spatial_searching/examples/Spatial_searching/CMakeLists.txt
index c4a335960b5..f60f06a9bc6 100644
--- a/Spatial_searching/examples/Spatial_searching/CMakeLists.txt
+++ b/Spatial_searching/examples/Spatial_searching/CMakeLists.txt
@@ -18,9 +18,6 @@ if ( NOT CGAL_FOUND )
 endif()
             
 find_package(Eigen3 3.1.91) #(requires 3.2.0 or greater)
-if (EIGEN3_FOUND)
-  include( ${EIGEN3_USE_FILE} )
-endif()
 
 if (MSVC)
     # Turn off VC++ warning
@@ -68,8 +65,10 @@ create_single_source_cgal_program( "weighted_Minkowski_distance.cpp" )
 if (EIGEN3_FOUND)
 
   create_single_source_cgal_program( "fuzzy_range_query.cpp" )
+  CGAL_target_use_Eigen(fuzzy_range_query)
 
   create_single_source_cgal_program( "general_neighbor_searching.cpp" )
+  CGAL_target_use_Eigen(general_neighbor_searching)
 
 else()
 
diff --git a/Spatial_searching/examples/Spatial_searching/searching_polyhedron_vertices_with_fuzzy_sphere.cpp b/Spatial_searching/examples/Spatial_searching/searching_polyhedron_vertices_with_fuzzy_sphere.cpp
index 05481a615dd..70a53e948ec 100644
--- a/Spatial_searching/examples/Spatial_searching/searching_polyhedron_vertices_with_fuzzy_sphere.cpp
+++ b/Spatial_searching/examples/Spatial_searching/searching_polyhedron_vertices_with_fuzzy_sphere.cpp
@@ -30,19 +30,15 @@ int main(int argc, char* argv[])
   in  >> mesh;
 
   Vertex_point_pmap vppmap = get(CGAL::vertex_point,mesh);
+  Traits traits(vppmap);
+  Tree tree(vertices(mesh).begin(), vertices(mesh).end(), Splitter(), traits);
 
-  // Insert number_of_data_points in the tree
-  Tree tree(vertices(mesh).begin(),
-            vertices(mesh).end(),
-            Splitter(),
-            Traits(vppmap)
-  );
   Point_3 query(0.0, 0.0, 0.0);
   double radius = 0.5;
   double epsilon = 0.01;
 
   // search vertices
-  CGAL::Fuzzy_sphere<Traits> fz(query, radius, epsilon);
+  CGAL::Fuzzy_sphere<Traits> fz(query, radius, epsilon, traits);
   
   //collect vertices that are inside the sphere
   std::list<vertex_descriptor> result;
diff --git a/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_builder_traits_2_aux.h b/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_builder_traits_2_aux.h
index f96399f697c..e38aa809e1f 100644
--- a/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_builder_traits_2_aux.h
+++ b/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_builder_traits_2_aux.h
@@ -106,98 +106,23 @@ public:
 
   Exceptionless_filtered_construction() {}
 
-  template <class A1>
+  template <class ... A>
   result_type
-  operator()(const A1 &a1) const
+  operator()(A&& ... a) const
   {
     try
     {
       Protect_FPU_rounding<Protection> P;
-      FC_result_type fr = Filter_construction(To_Filtered(a1));
+      FC_result_type fr = Filter_construction(To_Filtered(std::forward<A>(a))...);
       if ( fr )
         return From_Filtered(fr);
     }
     catch (Uncertain_conversion_exception&) {}
 
     Protect_FPU_rounding<!Protection> P(CGAL_FE_TONEAREST);
-    EC_result_type er = Exact_construction(To_Exact(a1)) ;
+    EC_result_type er = Exact_construction(To_Exact(std::forward<A>(a))...) ;
     return From_Exact(er);
   }
-  
-  template <class A1, class A2>
-  result_type
-  operator()(const A1 &a1, const A2 &a2) const
-  {
-    try
-    {
-      Protect_FPU_rounding<Protection> P;
-      FC_result_type fr = Filter_construction(To_Filtered(a1),To_Filtered(a2));
-      if ( fr )
-        return From_Filtered(fr);
-    }
-    catch (Uncertain_conversion_exception&) {}
-    
-    Protect_FPU_rounding<!Protection> P(CGAL_FE_TONEAREST);
-    EC_result_type er = Exact_construction(To_Exact(a1), To_Exact(a2)) ;
-    return From_Exact(er);
-  }
-  
-  template <class A1, class A2, class A3>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3) const
-  {
-    try
-    {
-      Protect_FPU_rounding<Protection> P;
-      FC_result_type fr = Filter_construction(To_Filtered(a1),To_Filtered(a2),To_Filtered(a3));
-      if ( fr )
-        return From_Filtered(fr);
-    }
-    catch (Uncertain_conversion_exception&) {}
-    
-    Protect_FPU_rounding<!Protection> P(CGAL_FE_TONEAREST);
-    EC_result_type er = Exact_construction(To_Exact(a1), To_Exact(a2), To_Exact(a3)) ;
-    return From_Exact(er);
-
-  }
-  
-  template <class A1, class A2, class A3, class A4>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4) const
-  {
-    try
-    {
-      Protect_FPU_rounding<Protection> P;
-      FC_result_type fr = Filter_construction(To_Filtered(a1),To_Filtered(a2),To_Filtered(a3),To_Filtered(a4));
-      if ( fr )
-        return From_Filtered(fr);
-    }
-    catch (Uncertain_conversion_exception&) {}
-    
-    Protect_FPU_rounding<!Protection> P(CGAL_FE_TONEAREST);
-    EC_result_type er = Exact_construction(To_Exact(a1), To_Exact(a2), To_Exact(a3), To_Exact(a4)) ;
-    return From_Exact(er);
-
-  }
-  
-  template <class A1, class A2, class A3, class A4, class A5>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4, const A5 &a5) const
-  {
-    try
-    {
-      Protect_FPU_rounding<Protection> P;
-      FC_result_type fr = Filter_construction(To_Filtered(a1),To_Filtered(a2),To_Filtered(a3),To_Filtered(a4),To_Filtered(a5));
-      if ( fr )
-        return From_Filtered(fr);
-    }
-    catch (Uncertain_conversion_exception&) {}
-    
-    Protect_FPU_rounding<!Protection> P(CGAL_FE_TONEAREST);
-    EC_result_type er = Exact_construction(To_Exact(a1), To_Exact(a2), To_Exact(a3), To_Exact(a4), To_Exact(a5)) ;
-    return From_Exact(er);
-
-  }
 };
 
 
diff --git a/Straight_skeleton_2/include/CGAL/Unfiltered_predicate_adaptor.h b/Straight_skeleton_2/include/CGAL/Unfiltered_predicate_adaptor.h
index 73311ab7aeb..16f2714a06e 100644
--- a/Straight_skeleton_2/include/CGAL/Unfiltered_predicate_adaptor.h
+++ b/Straight_skeleton_2/include/CGAL/Unfiltered_predicate_adaptor.h
@@ -45,111 +45,14 @@ public:
     : Certified_approx_predicate(o1, o2)
   {}
 
-  template <class A1>
+  template <class ... A>
   result_type
-  operator()(const A1 &a1) const
+  operator()(A&& ... a) const
 #ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
   ;
 #else
   {
-    return static_cast<result_type>(Certified_approx_predicate(a1));
-  }
-#endif
-
-  template <class A1, class A2>
-  result_type
-  operator()(const A1 &a1, const A2 &a2) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2));
-  }
-#endif
-
-  template <class A1, class A2, class A3>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3,a4));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4, class A5>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	     const A5 &a5) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4, class A5, class A6>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	     const A5 &a5, const A6 &a6) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4, class A5, class A6,
-            class A7>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	     const A5 &a5, const A6 &a6, const A7 &a7) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4, class A5, class A6,
-            class A7, class A8>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-             const A5 &a5, const A6 &a6, const A7 &a7, const A8 &a8) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7, a8));
-  }
-#endif
-
-  template <class A1, class A2, class A3, class A4, class A5, class A6,
-            class A7, class A8, class A9>
-  result_type
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-             const A5 &a5, const A6 &a6, const A7 &a7, const A8 &a8,
-             const A9 &a9 ) const
-#ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
-  ;
-#else
-  {
-    return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7, a8, a9));
+    return static_cast<result_type>(Certified_approx_predicate(std::forward<A>(a)...));
   }
 #endif
 
@@ -158,90 +61,12 @@ public:
 
 #ifndef CGAL_CFG_OUTOFLINE_TEMPLATE_MEMBER_DEFINITION_BUG
 template <class CAP>
-  template <class A1>
+  template <class ... A>
 typename Unfiltered_predicate_adaptor<CAP>::result_type
 Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1) const
+  operator()(A&& ... a) const
 {
-  return static_cast<result_type>(Certified_approx_predicate(a1));
-}
-
-template <class CAP>
-  template <class A1, class A2>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4, class A5>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	     const A5 &a5) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4, class A5, class A6>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-	     const A5 &a5, const A6 &a6) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4, class A5, class A6, class A7>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-             const A5 &a5, const A6 &a6, const A7 &a7 ) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4, class A5, class A6, class A7, class A8>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-             const A5 &a5, const A6 &a6, const A7 &a7, const A8 &a8 ) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7, a8));
-}
-
-template <class CAP>
-  template <class A1, class A2, class A3, class A4, class A5, class A6, class A7, class A8, class A9>
-typename Unfiltered_predicate_adaptor<CAP>::result_type
-Unfiltered_predicate_adaptor<CAP>::
-  operator()(const A1 &a1, const A2 &a2, const A3 &a3, const A4 &a4,
-             const A5 &a5, const A6 &a6, const A7 &a7, const A8 &a8, 
-             const A9 &a9 ) const
-{
-  return static_cast<result_type>(Certified_approx_predicate(a1, a2, a3, a4, a5, a6, a7, a8, a9));
+  return static_cast<result_type>(Certified_approx_predicate(std::forward<A>(a)...));
 }
 #endif
 
diff --git a/Stream_support/include/CGAL/IO/read_3mf.h b/Stream_support/include/CGAL/IO/read_3mf.h
index ac1b48459a8..7a6def1f2fe 100644
--- a/Stream_support/include/CGAL/IO/read_3mf.h
+++ b/Stream_support/include/CGAL/IO/read_3mf.h
@@ -65,12 +65,6 @@ bool extract_soups (NMR::PLib3MFModelMeshObject *pMeshObject,
     pBuffer.resize(nNeededChars + 1);
     hResult = NMR::lib3mf_object_getnameutf8(pMeshObject, &pBuffer[0], nNeededChars + 1, NULL);
     pBuffer[nNeededChars] = 0;
-    std::string temp(&pBuffer[0]);
-    if(temp.find("_cgal_pc") != std::string::npos
-       || temp.find("_cgal_pl")!= std::string::npos) //ignore point clouds and polylines
-    {
-      return false;
-    }
     name = std::string(&pBuffer[0]);
   }
   else
@@ -120,151 +114,6 @@ bool extract_soups (NMR::PLib3MFModelMeshObject *pMeshObject,
   return true;
 }
 
-template<typename PointRange,
-         typename PolygonRange,
-         typename ColorRange>
-bool extract_polylines (NMR::PLib3MFModelMeshObject *pMeshObject,
-                        const NMR::MODELTRANSFORM& ,
-                        PointRange& points,
-                        PolygonRange&,
-                        ColorRange& colors,
-                        std::string& name) {
-  typedef typename PointRange::value_type Point_3;
-
-  HRESULT hResult;
-  DWORD nNeededChars;
-  std::vector<char> pBuffer;
-  // Retrieve Mesh Name Length
-  hResult = NMR::lib3mf_object_getnameutf8(pMeshObject, NULL, 0, &nNeededChars);
-  if (hResult != LIB3MF_OK)
-  {
-    points.resize(0);
-    std::cerr<<"Error during name extraction.";
-    return false;
-  }
-
-  // Retrieve Mesh Name
-  if (nNeededChars > 0) {
-    pBuffer.resize(nNeededChars + 1);
-    hResult = NMR::lib3mf_object_getnameutf8(pMeshObject, &pBuffer[0], nNeededChars + 1, NULL);
-    pBuffer[nNeededChars] = 0;
-    std::string temp(&pBuffer[0]);
-    if(temp.find("_cgal_pl")== std::string::npos) //ignore not polylines
-    {
-      points.resize(0);
-      return false;
-    }
-    name = std::string(&pBuffer[0]);
-  }
-  else
-  {
-    points.resize(0);
-    return false;
-  }
-
-  NMR::PLib3MFPropertyHandler * pPropertyHandler;
-  hResult = NMR::lib3mf_meshobject_createpropertyhandler(pMeshObject, &pPropertyHandler);
-  if (hResult != LIB3MF_OK) {
-    DWORD nErrorMessage;
-    LPCSTR pszErrorMessage;
-    std::cerr << "could not create property handler: " << std::hex << hResult << std::endl;
-    NMR::lib3mf_getlasterror(pMeshObject, &nErrorMessage, &pszErrorMessage);
-    std::cerr << "error #" << std::hex << nErrorMessage << ": " << pszErrorMessage << std::endl;
-    NMR::lib3mf_release(pMeshObject);
-    return false;
-  }
-
-  points.resize(points.size()-3);//ignore dummy_vertices
-  for(DWORD vid = 0; vid < points.size(); ++vid)
-  {
-    NMR::MODELMESHVERTEX pVertex;
-    NMR::lib3mf_meshobject_getvertex(pMeshObject, vid+3, &pVertex);
-    points[vid] =
-        Point_3(pVertex.m_fPosition[0],
-        pVertex.m_fPosition[1],
-        pVertex.m_fPosition[2]);
-  }
-
-  NMR::MODELMESH_TRIANGLECOLOR_SRGB pColor;
-  NMR::lib3mf_propertyhandler_getcolor(pPropertyHandler, 0, &pColor);//get color of the dummy triangle
-  NMR::MODELMESHCOLOR_SRGB mColor = pColor.m_Colors[0];
-  colors[0]=CGAL::Color(mColor.m_Red, mColor.m_Green,
-                        mColor.m_Blue, mColor.m_Alpha);
-  return true;
-}
-
-template<typename PointRange,
-         typename PolygonRange,
-         typename ColorRange>
-bool extract_point_clouds (NMR::PLib3MFModelMeshObject *pMeshObject,
-                           const NMR::MODELTRANSFORM&,
-                           PointRange& points,
-                           PolygonRange&,
-                           ColorRange& colors,
-                           std::string& name) {
-  typedef typename PointRange::value_type Point_3;
-
-  HRESULT hResult;
-  DWORD nNeededChars;
-  std::vector<char> pBuffer;
-  // Retrieve Mesh Name Length
-  hResult = NMR::lib3mf_object_getnameutf8(pMeshObject, NULL, 0, &nNeededChars);
-  if (hResult != LIB3MF_OK)
-  {
-    std::cerr<<"Error during name extraction.";
-    points.resize(0);
-    return false;
-  }
-
-  // Retrieve Mesh Name
-  if (nNeededChars > 0) {
-    pBuffer.resize(nNeededChars + 1);
-    hResult = NMR::lib3mf_object_getnameutf8(pMeshObject, &pBuffer[0], nNeededChars + 1, NULL);
-    pBuffer[nNeededChars] = 0;
-    std::string temp(&pBuffer[0]);
-    if(temp.find("_cgal_pc")== std::string::npos) //ignore not point_cloud
-    {
-      points.resize(0);
-      return false;
-    }
-    name = std::string(&pBuffer[0]);
-  }
-  else{
-    points.resize(0);
-    return false;
-  }
-
-  NMR::PLib3MFPropertyHandler * pPropertyHandler;
-  hResult = NMR::lib3mf_meshobject_createpropertyhandler(pMeshObject, &pPropertyHandler);
-  if (hResult != LIB3MF_OK) {
-    DWORD nErrorMessage;
-    LPCSTR pszErrorMessage;
-    std::cerr << "could not create property handler: " << std::hex << hResult << std::endl;
-    NMR::lib3mf_getlasterror(pMeshObject, &nErrorMessage, &pszErrorMessage);
-    std::cerr << "error #" << std::hex << nErrorMessage << ": " << pszErrorMessage << std::endl;
-    NMR::lib3mf_release(pMeshObject);
-    return -1;
-  }
-
-  points.resize(points.size()-3);//ignore dummy_vertices
-  for(DWORD vid = 0; vid < points.size(); ++vid)
-  {
-    NMR::MODELMESHVERTEX pVertex;
-    NMR::lib3mf_meshobject_getvertex(pMeshObject, vid+3, &pVertex);
-    points[vid] =
-        Point_3(pVertex.m_fPosition[0],
-        pVertex.m_fPosition[1],
-        pVertex.m_fPosition[2]);
-  }
-
-  NMR::MODELMESH_TRIANGLECOLOR_SRGB pColor;
-  NMR::lib3mf_propertyhandler_getcolor(pPropertyHandler, 0, &pColor);//get color of the dummy triangle
-  NMR::MODELMESHCOLOR_SRGB mColor = pColor.m_Colors[0];
-  colors[0]=CGAL::Color(mColor.m_Red, mColor.m_Green,
-                        mColor.m_Blue, mColor.m_Alpha);
-  return true;
-}
-
 
 template<typename PointRanges, typename PolygonRanges, typename ColorRanges,
          typename PointRange, typename PolygonRange, typename ColorRange>
@@ -589,6 +438,8 @@ int read_from_3mf(const std::string& file_name, PointRanges& all_points,
  * \param names will contain the name of each mesh in `file_name` if any.
  *  If the i'th mesh has no name, it will be called "Unknown Mesh" in names.
  * \return the number of soups read.
+ * 
+ * \attention Only versions inferior to 2.0 of lib3mf are supported.
  */
 template<typename PointRanges, typename PolygonRanges, typename ColorRanges>
 int read_triangle_soups_from_3mf(const std::string& file_name, PointRanges& all_points,
@@ -605,43 +456,6 @@ int read_triangle_soups_from_3mf(const std::string& file_name, PointRanges& all_
        all_colors, names, extract_soups<PointRange, PolygonRange, ColorRange>);
 }
 
-
-template<typename PointRanges, typename ColorRanges>
-int read_polylines_from_3mf(const std::string& file_name,
-                            PointRanges& all_points,
-                            ColorRanges& all_colors,
-                            std::vector<std::string>& names
-                            )
-{
-  typedef typename PointRanges::value_type PointRange;
-  typedef std::vector<std::size_t> Polygon;
-  typedef std::vector<Polygon> PolygonRange;
-  typedef std::vector<CGAL::Color> ColorRange;
-  std::vector<PolygonRange> all_polygons;
-  return read_from_3mf<PointRanges,std::vector<PolygonRange>,
-      std::vector<ColorRange>, PointRange, PolygonRange, ColorRange>
-      (file_name, all_points, all_polygons, all_colors, names,
-       extract_polylines<PointRange, PolygonRange, ColorRange>);
-}
-
-
-template<typename PointRanges, typename ColorRanges>
-int read_point_clouds_from_3mf(const std::string& file_name,
-                               PointRanges& all_points,
-                               ColorRanges& all_colors,
-                               std::vector<std::string>& names
-                               )
-{
-  typedef typename PointRanges::value_type PointRange;
-  typedef std::vector<std::size_t> Polygon;
-  typedef std::vector<Polygon> PolygonRange;
-  typedef std::vector<CGAL::Color> ColorRange;
-  std::vector<PolygonRange> all_polygons;
-  return read_from_3mf<PointRanges,std::vector<PolygonRange>,
-      std::vector<ColorRange>, PointRange, PolygonRange, ColorRange>
-      (file_name, all_points, all_polygons, all_colors, names,
-       extract_point_clouds<PointRange, PolygonRange, ColorRange>);
-}
 }//end CGAL
 
 #endif // CGAL_IO_READ_3MF_H
diff --git a/Stream_support/include/CGAL/IO/write_3mf.h b/Stream_support/include/CGAL/IO/write_3mf.h
index f6c2a73689e..4aa6ecbf866 100644
--- a/Stream_support/include/CGAL/IO/write_3mf.h
+++ b/Stream_support/include/CGAL/IO/write_3mf.h
@@ -359,6 +359,8 @@ bool write_polyline_to_model(const PointRange& points,
  *  soups in `file_name`.
  * \param names will contains the name of each mesh in `file_name`.
  * \return `true` if the writing is successful, `false` otherwise.
+ * 
+ * \attention Only versions inferior to 2.0 of lib3mf are supported.
  */
 template<typename PointRanges, typename PolygonRanges>
 bool write_triangle_soups_to_3mf(const std::string& file_name,
@@ -406,6 +408,8 @@ bool write_triangle_soups_to_3mf(const std::string& file_name,
  * must be available for each mesh.
  * \param names will contains the name of each mesh in `file_name`.
  * \return `true` if the writing is successful, `false` otherwise.
+ *
+ * \attention Only versions inferior to 2.0 of lib3mf are supported.
  */
 template<typename TriangleMeshRange>
 bool write_triangle_meshes_to_3mf(const std::string& file_name,
diff --git a/Stream_support/test/Stream_support/CMakeLists.txt b/Stream_support/test/Stream_support/CMakeLists.txt
index d97144f1b86..93787ca49f6 100644
--- a/Stream_support/test/Stream_support/CMakeLists.txt
+++ b/Stream_support/test/Stream_support/CMakeLists.txt
@@ -18,7 +18,7 @@ if ( CGAL_FOUND )
   file(GLOB cppfiles RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
   foreach(cppfile ${cppfiles})
     if ( "${cppfile}" STREQUAL "test_3mf_to_sm.cpp" )
-      if(3MF_LIBRARIES AND 3MF_INCLUDE_DIR)
+      if(3MF_LIBRARIES AND 3MF_INCLUDE_DIR  AND EXISTS "${3MF_INCLUDE_DIR}/Model/COM/NMR_DLLInterfaces.h")
         include_directories(${3MF_INCLUDE_DIR})
         create_single_source_cgal_program( "${cppfile}" )
           target_link_libraries(test_3mf_to_sm PRIVATE ${3MF_LIBRARIES})
diff --git a/Stream_support/test/Stream_support/test_3mf_to_sm.cpp b/Stream_support/test/Stream_support/test_3mf_to_sm.cpp
index 654cae33bb0..4f4e94feb7e 100644
--- a/Stream_support/test/Stream_support/test_3mf_to_sm.cpp
+++ b/Stream_support/test/Stream_support/test_3mf_to_sm.cpp
@@ -51,33 +51,6 @@ int main(int argc, char** argv)
     ofs << mesh;
     ofs.close();
   }
-  int nb_polylines =
-      CGAL::read_polylines_from_3mf(file_name, all_points, all_colors, names);
-
-  if(nb_polylines == 0)
-    std::cout<<"No polyline found."<<std::endl;
-  else
-  {
-    std::cout<<nb_polylines<<" polylines found, of ";
-    for(int i = 0; i< nb_polylines-1; ++i){
-      std::cout<<all_points[i].size()<<", ";
-    }
-    std::cout<<all_points.back().size()<<" points."<<std::endl;
-  }
-  all_points.clear();
-  all_colors.clear();
-  int nb_point_sets =
-      CGAL::read_point_clouds_from_3mf(file_name, all_points, all_colors, names);
-  if(nb_point_sets == 0)
-    std::cout<<"No point cloud found."<<std::endl;
-  else
-  {
-    std::cout<<nb_point_sets<<" point clouds found, of ";
-    for(int i = 0; i< nb_point_sets-1; ++i){
-      std::cout<<all_points[i].size()<<", ";
-    }
-    std::cout<<all_points.back().size()<<" points."<<std::endl;
-  }
 
   // testing writing functions
   Mesh sphere, tube;
@@ -147,31 +120,6 @@ int main(int argc, char** argv)
   meshes[1] = tube;
   CGAL::write_triangle_meshes_to_3mf("meshes.3mf", meshes, names);
 
-
-  //testing of point clouds
-
-  HRESULT hResult;
-  NMR::PLib3MFModel * pModel;
-  hResult = NMR::lib3mf_createmodel(&pModel);
-  NMR::PLib3MFModelMeshObject* pMeshObject;
-  if (hResult != LIB3MF_OK) {
-    std::cout << "could not create model: " << std::hex << hResult << std::endl;
-    return 1;
-  }
-  for(std::size_t i=0; i< names.size(); ++i)
-  {
-    CGAL::write_mesh_to_model(all_points[i], all_polygons[i],
-                              all_colors[i], names[i], &pMeshObject, pModel);
-  }
-  CGAL::Color color(255,0,0);
-  CGAL::write_point_cloud_to_model(all_points.front(),
-                                   color, names.front(), &pMeshObject, pModel);
-  CGAL::export_model_to_file("micro.3mf", pModel);
-  //testing of polylines
-  CGAL::write_polyline_to_model(all_points.back(),
-                                color, names.back(), &pMeshObject, pModel);
-  CGAL::export_model_to_file("micro.3mf", pModel);
-
   std::cout<<"OK."<<std::endl;
   return 0;
 }
diff --git a/Surface_mesh/include/CGAL/Surface_mesh/Surface_mesh.h b/Surface_mesh/include/CGAL/Surface_mesh/Surface_mesh.h
index e6a397f9941..22c65544df2 100644
--- a/Surface_mesh/include/CGAL/Surface_mesh/Surface_mesh.h
+++ b/Surface_mesh/include/CGAL/Surface_mesh/Surface_mesh.h
@@ -2287,6 +2287,9 @@ private: //------------------------------------------------------- private data
 
     os << "end_header" << std::endl;  
 
+    std::vector<int> reindex;
+    reindex.resize (sm.num_vertices());
+    int n = 0;
     for(VIndex vi : sm.vertices())
     {
       for (std::size_t i = 0; i < vprinters.size(); ++ i)
@@ -2297,22 +2300,23 @@ private: //------------------------------------------------------- private data
       }
       if (get_mode (os) == IO::ASCII)
         os << std::endl;
+      reindex[std::size_t(vi)] = n ++;
     }
 
-    std::vector<VIndex> polygon;
+    std::vector<int> polygon;
     
     for(FIndex fi : sm.faces())
     {
       // Get list of vertex indices
       polygon.clear();
-      for(HIndex hi : halfedges_around_face(halfedge(fi, sm), sm))
-        polygon.push_back (sm.target(hi));
+      for(VIndex vi : CGAL::vertices_around_face(sm.halfedge(fi),sm))
+        polygon.push_back (reindex[std::size_t(vi)]);
 
       if (get_mode (os) == IO::ASCII)
       {
         os << polygon.size() << " ";
         for (std::size_t i = 0; i < polygon.size(); ++ i)
-          os << int(polygon[i]) << " ";
+          os << polygon[i] << " ";
       }
       else
       {
@@ -2320,7 +2324,7 @@ private: //------------------------------------------------------- private data
         os.write (reinterpret_cast<char*>(&size), sizeof(size));
         for (std::size_t i = 0; i < polygon.size(); ++ i)
         {
-          int idx = int(polygon[i]);
+          int idx = polygon[i];
           os.write (reinterpret_cast<char*>(&idx), sizeof(idx));
         }
       }
@@ -2340,12 +2344,12 @@ private: //------------------------------------------------------- private data
     {
       for(EIndex ei : sm.edges())
       {
+        int v0 = reindex[std::size_t(sm.vertex(ei,0))];
+        int v1 = reindex[std::size_t(sm.vertex(ei,1))];
         if (get_mode (os) == IO::ASCII)
-          os << int(sm.vertex(ei,0)) << " " << int(sm.vertex(ei,1)) << " ";
+          os << v0 << " " << v1 << " ";
         else
         {
-          int v0 = int(sm.vertex(ei,0));
-          int v1 = int(sm.vertex(ei,1));
           os.write (reinterpret_cast<char*>(&v0), sizeof(v0));
           os.write (reinterpret_cast<char*>(&v1), sizeof(v1));
         }
@@ -2366,12 +2370,12 @@ private: //------------------------------------------------------- private data
     {
       for(HIndex hi : sm.halfedges())
       {
+        int source = reindex[std::size_t(sm.source(hi))];
+        int target = reindex[std::size_t(sm.target(hi))];
         if (get_mode (os) == IO::ASCII)
-          os << int(sm.source(hi)) << " " << int(sm.target(hi)) << " ";
+          os << source << " " << target << " ";
         else
         {
-          int source = int(sm.source(hi));
-          int target = int(sm.target(hi));
           os.write (reinterpret_cast<char*>(&source), sizeof(source));
           os.write (reinterpret_cast<char*>(&target), sizeof(target));
         }
@@ -2457,6 +2461,7 @@ private: //------------------------------------------------------- private data
       is.setstate(std::ios::failbit);
       return false;
     }
+    is >> sm_skip_comments;
     is >> n >> f >> e;
     if(!is){
       return false;
@@ -2474,12 +2479,14 @@ private: //------------------------------------------------------- private data
       boost::tie(vnormal, created) = sm.template add_property_map<Vertex_index,Vector_3>("v:normal",Vector_3(0,0,0));
       v_has_normals = true;
     }
+    std::string line;
     char ci;
-
     for(int i=0; i < n; i++){
       is >> sm_skip_comments;
+      std::getline(is, line);
+      std::istringstream iss(line);
       double x, y, z;
-      is >> iformat(x) >> iformat(y) >> iformat(z);
+      iss >> iformat(x) >> iformat(y) >> iformat(z);
       
       Vertex_index vi = sm.add_vertex();
       put(vpm, vi, P(x, y, z));
@@ -2487,26 +2494,37 @@ private: //------------------------------------------------------- private data
       
       vertexmap[i] = vi;
       if(v_has_normals){
-        is >> v;
+        if(!(iss >> v))
+        {
+          std::cerr<<"This doesn't seem to be a correct NOFF file. Aborting."<<std::endl;
+          is.setstate(std::ios::failbit);          
+          return false;
+        }
         vnormal[vi] = v;
       }
 
 
       if(i == 0 && ((off == "COFF") || (off == "CNOFF"))){
         std::string col;
-        std::getline(is, col);
-        std::istringstream iss(col);
-        if(iss >> ci){
+        std::getline(iss, col);
+        std::istringstream iss2(col);
+        if(iss2 >> ci){
          bool created;
          boost::tie(vcolor, created) = sm.template add_property_map<Vertex_index,CGAL::Color>("v:color",CGAL::Color(0,0,0));
-         std::istringstream iss2(col);
-         vcolor[vi] = File_scanner_OFF::get_color_from_line(iss2);
+         std::istringstream iss3(col);
+         vcolor[vi] = File_scanner_OFF::get_color_from_line(iss3);
          vcolored = true;
         }
+        else
+        {
+          std::cerr<<"This doesn't seem to be a correct COFF file. Aborting."<<std::endl;
+          is.setstate(std::ios::failbit);
+          return false;
+        }
       }else{
          if(vcolored){
            //stores the RGB value
-           vcolor[vi] = File_scanner_OFF::get_color_from_line(is);
+           vcolor[vi] = File_scanner_OFF::get_color_from_line(iss);
          }
        }
     }
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/CMakeLists.txt b/Surface_mesh_approximation/examples/Surface_mesh_approximation/CMakeLists.txt
index e3b19a50cad..aa73bcd3807 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/CMakeLists.txt
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/CMakeLists.txt
@@ -31,8 +31,6 @@ find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
 if (NOT EIGEN3_FOUND)
   message(STATUS "This project requires the Eigen library, and will not be compiled.")
   return()
-else()
-  include( ${EIGEN3_USE_FILE} )
 endif()
 
 # Creating entries for all C++ files with "main" routine
@@ -41,14 +39,20 @@ endif()
 include( CGAL_CreateSingleSourceCGALProgram )
 
 create_single_source_cgal_program( "vsa_approximation_2_example.cpp" )
+CGAL_target_use_Eigen(vsa_approximation_2_example)
 
 create_single_source_cgal_program( "vsa_approximation_example.cpp" )
+CGAL_target_use_Eigen(vsa_approximation_example)
 
 create_single_source_cgal_program( "vsa_class_interface_example.cpp" )
+CGAL_target_use_Eigen(vsa_class_interface_example)
 
 create_single_source_cgal_program( "vsa_isotropic_metric_example.cpp" )
+CGAL_target_use_Eigen(vsa_isotropic_metric_example)
 
 create_single_source_cgal_program( "vsa_segmentation_example.cpp" )
+CGAL_target_use_Eigen(vsa_segmentation_example)
 
 create_single_source_cgal_program( "vsa_simple_approximation_example.cpp" )
+CGAL_target_use_Eigen(vsa_simple_approximation_example)
 
diff --git a/Surface_mesh_approximation/test/Surface_mesh_approximation/CMakeLists.txt b/Surface_mesh_approximation/test/Surface_mesh_approximation/CMakeLists.txt
index caac2a6f132..a41a41f1996 100644
--- a/Surface_mesh_approximation/test/Surface_mesh_approximation/CMakeLists.txt
+++ b/Surface_mesh_approximation/test/Surface_mesh_approximation/CMakeLists.txt
@@ -32,8 +32,6 @@ find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
 if (NOT EIGEN3_FOUND)
   message(STATUS "This project requires the Eigen library, and will not be compiled.")
   return()
-else()
-  include( ${EIGEN3_USE_FILE} )
 endif()
 
 
@@ -43,21 +41,30 @@ endif()
 include( CGAL_CreateSingleSourceCGALProgram )
 
 create_single_source_cgal_program( "vsa_class_interface_test.cpp" )
+CGAL_target_use_Eigen(vsa_class_interface_test)
 
 create_single_source_cgal_program( "vsa_correctness_test.cpp" )
+CGAL_target_use_Eigen(vsa_correctness_test)
 
 create_single_source_cgal_program( "vsa_error_decrease_test.cpp" )
+CGAL_target_use_Eigen(vsa_error_decrease_test)
 
 create_single_source_cgal_program( "vsa_kernel_test.cpp" )
+CGAL_target_use_Eigen(vsa_kernel_test)
 
 create_single_source_cgal_program( "vsa_approximation_test.cpp" )
+CGAL_target_use_Eigen(vsa_approximation_test)
 
 create_single_source_cgal_program( "vsa_segmentation_test.cpp" )
+CGAL_target_use_Eigen(vsa_segmentation_test)
 
 create_single_source_cgal_program( "vsa_meshing_manifold_test.cpp" )
+CGAL_target_use_Eigen(vsa_meshing_manifold_test)
 
 create_single_source_cgal_program( "vsa_metric_test.cpp" )
+CGAL_target_use_Eigen(vsa_metric_test)
 
 create_single_source_cgal_program( "vsa_teleportation_test.cpp" )
+CGAL_target_use_Eigen(vsa_teleportation_test)
 
 
diff --git a/Surface_mesh_deformation/benchmark/Surface_mesh_deformation/optimal_rotation/CMakeLists.txt b/Surface_mesh_deformation/benchmark/Surface_mesh_deformation/optimal_rotation/CMakeLists.txt
index 67a2731cdc5..4d24c1d593c 100644
--- a/Surface_mesh_deformation/benchmark/Surface_mesh_deformation/optimal_rotation/CMakeLists.txt
+++ b/Surface_mesh_deformation/benchmark/Surface_mesh_deformation/optimal_rotation/CMakeLists.txt
@@ -11,10 +11,8 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "benchmark_for_concept_models.cpp" )
-
+    CGAL_target_use_Eigen(benchmark_for_concept_models)
   else()
     message(STATUS "This program requires the Eigen library, version 3.1 or later and will not be compiled.")
   endif()
diff --git a/Surface_mesh_deformation/demo/Surface_mesh_deformation/CMakeLists.txt b/Surface_mesh_deformation/demo/Surface_mesh_deformation/CMakeLists.txt
index b90af134997..0955eda3677 100644
--- a/Surface_mesh_deformation/demo/Surface_mesh_deformation/CMakeLists.txt
+++ b/Surface_mesh_deformation/demo/Surface_mesh_deformation/CMakeLists.txt
@@ -18,10 +18,8 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.91) #(requires 3.2.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "deform_mesh_for_botsch08_format.cpp" )
-
+    CGAL_target_use_Eigen(deform_mesh_for_botsch08_format)
   else()
     message(STATUS "NOTICE: This program requires the Eigen library, version 3.2 or later and will not be compiled.")
   endif()
diff --git a/Surface_mesh_deformation/examples/Surface_mesh_deformation/CMakeLists.txt b/Surface_mesh_deformation/examples/Surface_mesh_deformation/CMakeLists.txt
index aa90c5d271d..6e6d1782ce0 100644
--- a/Surface_mesh_deformation/examples/Surface_mesh_deformation/CMakeLists.txt
+++ b/Surface_mesh_deformation/examples/Surface_mesh_deformation/CMakeLists.txt
@@ -13,8 +13,6 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.91) #(requires 3.2.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "all_roi_assign_example.cpp" )
     create_single_source_cgal_program( "all_roi_assign_example_custom_polyhedron.cpp" )
     create_single_source_cgal_program( "all_roi_assign_example_Surface_mesh.cpp" )
@@ -24,11 +22,24 @@ if ( CGAL_FOUND )
     create_single_source_cgal_program( "k_ring_roi_translate_rotate_Surface_mesh.cpp" )
     create_single_source_cgal_program( "deform_mesh_for_botsch08_format_sre_arap.cpp" )
 
+    foreach(target
+        all_roi_assign_example
+        all_roi_assign_example_custom_polyhedron
+        all_roi_assign_example_Surface_mesh
+        custom_weight_for_edges_example
+        deform_polyhedron_with_custom_pmap_example
+        k_ring_roi_translate_rotate_example
+        k_ring_roi_translate_rotate_Surface_mesh
+        deform_mesh_for_botsch08_format_sre_arap)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
+    
     find_package( OpenMesh QUIET )
     if ( OpenMesh_FOUND )
     include( UseOpenMesh )
       create_single_source_cgal_program( "all_roi_assign_example_with_OpenMesh.cpp" )
       target_link_libraries( all_roi_assign_example_with_OpenMesh PRIVATE ${OPENMESH_LIBRARIES} )
+      CGAL_target_use_Eigen(all_roi_assign_example_with_OpenMesh)
     else()
       message(STATUS "Example that use OpenMesh will not be compiled.")
     endif()
diff --git a/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h b/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
index a3c6080dee3..06a8151e9b7 100644
--- a/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
+++ b/Surface_mesh_deformation/include/CGAL/Surface_mesh_deformation.h
@@ -16,10 +16,11 @@
 
 #include <CGAL/disable_warnings.h>
 
+#include <CGAL/assertions.h>
+#include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/config.h>
 #include <CGAL/Default.h>
 #include <CGAL/tuple.h>
-
 #include <CGAL/Polygon_mesh_processing/Weights.h>
 #include <CGAL/Simple_cartesian.h>
 
@@ -215,13 +216,9 @@ public:
 // Index maps
 #ifndef DOXYGEN_RUNNING
   typedef typename Default::Get<
-    VIM,
-    typename boost::property_map<Triangle_mesh, boost::vertex_index_t>::type
-  >::type Vertex_index_map;
+    VIM, typename CGAL::GetInitializedVertexIndexMap<Triangle_mesh>::type>::type Vertex_index_map;
   typedef typename Default::Get<
-    HIM,
-    typename boost::property_map<Triangle_mesh, boost::halfedge_index_t>::type
-  >::type Hedge_index_map;
+    HIM, typename CGAL::GetInitializedHalfedgeIndexMap<Triangle_mesh>::type>::type Hedge_index_map;
 #else
   /// vertex index map type
   typedef VIM Vertex_index_map;
@@ -356,9 +353,10 @@ public:
   //vertex_point_map set by default
   Surface_mesh_deformation(Triangle_mesh& triangle_mesh,
                            Vertex_index_map vertex_index_map,
-                           Hedge_index_map hedge_index_map
-                          )
-    : m_triangle_mesh(triangle_mesh), vertex_index_map(vertex_index_map), hedge_index_map(hedge_index_map),
+                           Hedge_index_map hedge_index_map)
+    : m_triangle_mesh(triangle_mesh),
+      vertex_index_map(vertex_index_map),
+      hedge_index_map(hedge_index_map),
       ros_id_map(std::vector<std::size_t>(num_vertices(triangle_mesh), (std::numeric_limits<std::size_t>::max)() )),
       is_roi_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
       is_ctrl_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
@@ -374,10 +372,10 @@ public:
 
   //vertex_point_map and hedge_index_map set by default
   Surface_mesh_deformation(Triangle_mesh& triangle_mesh,
-                           Vertex_index_map vertex_index_map
-                          )
-    : m_triangle_mesh(triangle_mesh), vertex_index_map(vertex_index_map),
-      hedge_index_map(get(boost::halfedge_index, triangle_mesh)),
+                           Vertex_index_map vertex_index_map)
+    : m_triangle_mesh(triangle_mesh),
+      vertex_index_map(vertex_index_map),
+      hedge_index_map(CGAL::get_initialized_halfedge_index_map(triangle_mesh)),
       ros_id_map(std::vector<std::size_t>(num_vertices(triangle_mesh), (std::numeric_limits<std::size_t>::max)() )),
       is_roi_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
       is_ctrl_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
@@ -393,8 +391,8 @@ public:
   //vertex_point_map, hedge_index_map and vertex_index_map set by default
   Surface_mesh_deformation(Triangle_mesh& triangle_mesh)
     : m_triangle_mesh(triangle_mesh),
-      vertex_index_map(get(boost::vertex_index, triangle_mesh)),
-      hedge_index_map(get(boost::halfedge_index, triangle_mesh)),
+      vertex_index_map(CGAL::get_initialized_vertex_index_map(triangle_mesh)),
+      hedge_index_map(CGAL::get_initialized_halfedge_index_map(triangle_mesh)),
       ros_id_map(std::vector<std::size_t>(num_vertices(triangle_mesh), (std::numeric_limits<std::size_t>::max)() )),
       is_roi_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
       is_ctrl_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
@@ -413,18 +411,19 @@ public:
                            Vertex_index_map vertex_index_map,
                            Hedge_index_map hedge_index_map,
                            Vertex_point_map vertex_point_map,
-                           Weight_calculator weight_calculator = Weight_calculator()
-                          )
-    : m_triangle_mesh(triangle_mesh), vertex_index_map(vertex_index_map), hedge_index_map(hedge_index_map),
-    ros_id_map(std::vector<std::size_t>(num_vertices(triangle_mesh), (std::numeric_limits<std::size_t>::max)() )),
-    is_roi_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
-    is_ctrl_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
-    m_iterations(5), m_tolerance(1e-4),
-    need_preprocess_factorization(true),
-    need_preprocess_region_of_solution(true),
-    last_preprocess_successful(false),
-    weight_calculator(weight_calculator),
-    vertex_point_map(vertex_point_map)
+                           Weight_calculator weight_calculator = Weight_calculator())
+    : m_triangle_mesh(triangle_mesh),
+      vertex_index_map(vertex_index_map),
+      hedge_index_map(hedge_index_map),
+      ros_id_map(std::vector<std::size_t>(num_vertices(triangle_mesh), (std::numeric_limits<std::size_t>::max)() )),
+      is_roi_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
+      is_ctrl_map(std::vector<bool>(num_vertices(triangle_mesh), false)),
+      m_iterations(5), m_tolerance(1e-4),
+      need_preprocess_factorization(true),
+      need_preprocess_region_of_solution(true),
+      last_preprocess_successful(false),
+      weight_calculator(weight_calculator),
+      vertex_point_map(vertex_point_map)
   {
     init();
   }
@@ -433,21 +432,23 @@ public:
 /// \name Construction
 /// @{
     /**
-   * The constructor of a deformation object
+   * The constructor of a deformation object.
    *
    * @pre `triangle_mesh` consists of only triangular facets
    * @param triangle_mesh triangulated surface mesh to deform
-   * @param vertex_index_map property map which associates an id to each vertex, from `0` to `num_vertices(triangle_mesh)-1`.
-   * @param hedge_index_map property map which associates an id to each halfedge, from `0` to `2*num_edges(triangle_mesh)-1`.
+   * @param vertex_index_map a property map which associates a unique id to each vertex,
+   *                         between `0` to `num_vertices(triangle_mesh)-1`.
+   * @param hedge_index_map property map which associates a unique id to each halfedge,
+   *                        between `0` to `2*num_edges(triangle_mesh)-1`.
    * @param vertex_point_map property map which associates a point to each vertex of the triangle mesh.
    * @param weight_calculator function object or pointer for weight calculation
+   *
    */
   Surface_mesh_deformation(Triangle_mesh& triangle_mesh,
-    Vertex_index_map vertex_index_map=get(boost::vertex_index, triangle_mesh),
-    Hedge_index_map hedge_index_map=get(boost::halfedge_index, triangle_mesh),
-    Vertex_point_map vertex_point_map=get(boost::vertex_point, triangle_mesh),
-    Weight_calculator weight_calculator = Weight_calculator()
-    );
+                           Vertex_index_map vertex_index_map = unspecified_internal_vertex_index_map,
+                           Hedge_index_map hedge_index_map = unspecified_internal_halfedge_index_map,
+                           Vertex_point_map vertex_point_map = get(boost::vertex_point, triangle_mesh),
+                           Weight_calculator weight_calculator = Weight_calculator());
 /// @}
   #endif
 
diff --git a/Surface_mesh_deformation/test/Surface_mesh_deformation/CMakeLists.txt b/Surface_mesh_deformation/test/Surface_mesh_deformation/CMakeLists.txt
index 54163d64df1..555174ccf92 100644
--- a/Surface_mesh_deformation/test/Surface_mesh_deformation/CMakeLists.txt
+++ b/Surface_mesh_deformation/test/Surface_mesh_deformation/CMakeLists.txt
@@ -13,15 +13,18 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.91) #(requires 3.2.0 or greater)
   if (EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "Cactus_deformation_session.cpp" )
+    CGAL_target_use_Eigen(Cactus_deformation_session)
     create_single_source_cgal_program( "Cactus_performance_test.cpp" )
+    CGAL_target_use_Eigen(Cactus_performance_test)
     create_single_source_cgal_program( "Symmetry_test.cpp" )
+    CGAL_target_use_Eigen(Symmetry_test)
 
     find_package( OpenMesh QUIET )
     if ( OpenMesh_FOUND )
     include( UseOpenMesh )
       create_single_source_cgal_program( "Cactus_deformation_session_OpenMesh.cpp" )
+      CGAL_target_use_Eigen(Cactus_deformation_session_OpenMesh)
       target_link_libraries( Cactus_deformation_session_OpenMesh PRIVATE ${OPENMESH_LIBRARIES} )
     else()
       message(STATUS "Example that use OpenMesh will not be compiled.")
diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
index 62640e3b6a9..3519d912b03 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
@@ -14,7 +14,6 @@ if ( CGAL_FOUND )
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if (EIGEN3_FOUND)
     # Executables that require Eigen 3.1
-    include( ${EIGEN3_USE_FILE} )
 
 # ------------------------------------------------------------------
 # Detect SuiteSparse libraries:
@@ -52,11 +51,17 @@ if ( CGAL_FOUND )
 # ------------------------------------------------------------------
 
     create_single_source_cgal_program( "discrete_authalic.cpp" )
+    CGAL_target_use_Eigen(discrete_authalic)
     create_single_source_cgal_program( "lscm.cpp" )
+    CGAL_target_use_Eigen(lscm)
     create_single_source_cgal_program( "orbifold.cpp" )
+    CGAL_target_use_Eigen(orbifold)
     create_single_source_cgal_program( "seam_Polyhedron_3.cpp" )
+    CGAL_target_use_Eigen(seam_Polyhedron_3)
     create_single_source_cgal_program( "simple_parameterization.cpp" )
+    CGAL_target_use_Eigen(simple_parameterization)
     create_single_source_cgal_program( "square_border_parameterizer.cpp" )
+    CGAL_target_use_Eigen(square_border_parameterizer)
     
     if(SuiteSparse_FOUND)
       target_link_libraries(orbifold PRIVATE ${SuiteSparse_LIBRARIES})
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
index 3d570311b53..068a882f0e1 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
@@ -25,6 +25,7 @@
 #include <CGAL/Surface_mesh_parameterization/Error_code.h>
 #include <CGAL/Surface_mesh_parameterization/orbifold_shortest_path.h>
 
+#include <CGAL/assertions.h>
 #include <CGAL/Polygon_mesh_processing/Weights.h>
 
 #include <CGAL/assertions.h>
diff --git a/Surface_mesh_parameterization/test/Surface_mesh_parameterization/CMakeLists.txt b/Surface_mesh_parameterization/test/Surface_mesh_parameterization/CMakeLists.txt
index 4021770c494..401f37978b4 100644
--- a/Surface_mesh_parameterization/test/Surface_mesh_parameterization/CMakeLists.txt
+++ b/Surface_mesh_parameterization/test/Surface_mesh_parameterization/CMakeLists.txt
@@ -14,8 +14,8 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
   if(EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
     create_single_source_cgal_program( "extensive_parameterization_test.cpp" )
+    CGAL_target_use_Eigen(extensive_parameterization_test)
   else(EIGEN3_FOUND)
     message(STATUS "NOTICE: The tests require Eigen 3.1 (or greater) and will not be compiled.")
   endif(EIGEN3_FOUND)
diff --git a/Surface_mesh_segmentation/include/CGAL/mesh_segmentation.h b/Surface_mesh_segmentation/include/CGAL/mesh_segmentation.h
index 70b3dbb32f3..a96c08a1414 100644
--- a/Surface_mesh_segmentation/include/CGAL/mesh_segmentation.h
+++ b/Surface_mesh_segmentation/include/CGAL/mesh_segmentation.h
@@ -63,7 +63,7 @@ sdf_values( const TriangleMesh& triangle_mesh,
  * \ingroup PkgSurfaceMeshSegmentationRef
  * @brief Function computing the Shape Diameter Function over a surface mesh.
  *
- * This function implements the Shape Diameter Function (SDF) as described in \cgalCite{shapira2008consistent}.
+ * This function implements the Shape Diameter Function (SDF) as described in \cgalCite{Shapira2008Consistent}.
  * It is possible to compute raw SDF values (without post-processing). In such a case,
  * -1 is used to indicate when no SDF value could be computed for a facet.
  *
@@ -151,7 +151,7 @@ sdf_values_postprocessing(const TriangleMesh& triangle_mesh,
  * A segment is a set of connected facets which are placed under the same cluster (see \cgalFigureRef{Cluster_vs_segment}).
  *
  * \note Log-normalization is applied on `sdf_values_map` before segmentation.
- *       As described in the original paper \cgalCite{shapira2008consistent},
+ *       As described in the original paper \cgalCite{Shapira2008Consistent},
  *       this normalization is done to preserve thin parts of the mesh
  *       by increasing the distance between smaller SDF values and reducing
  *       it between larger ones.
diff --git a/Surface_mesh_shortest_path/include/CGAL/Surface_mesh_shortest_path/Surface_mesh_shortest_path.h b/Surface_mesh_shortest_path/include/CGAL/Surface_mesh_shortest_path/Surface_mesh_shortest_path.h
index a54781c1ae1..01057be54ca 100644
--- a/Surface_mesh_shortest_path/include/CGAL/Surface_mesh_shortest_path/Surface_mesh_shortest_path.h
+++ b/Surface_mesh_shortest_path/include/CGAL/Surface_mesh_shortest_path/Surface_mesh_shortest_path.h
@@ -67,7 +67,7 @@ Refer to those respective papers for the details of the implementation.
 If index property maps are not provided through the constructor of the class, internal property maps must
 be available and initialized.
 
-\sa \link PkgBGLHelper `CGAL::set_halfedgeds_items_id()`\endlink
+\sa \link BGLGraphExternalIndices `CGAL::set_halfedgeds_items_id()`\endlink
 */
 
 template<class Traits,
@@ -2199,7 +2199,7 @@ public:
 
   Internal property maps must be available and initialized.
 
-  \sa \link PkgBGLHelper `CGAL::set_halfedgeds_items_id()`\endlink
+  \sa \link BGLGraphExternalIndices `CGAL::set_halfedgeds_items_id()`\endlink
   */
   Surface_mesh_shortest_path(const Triangle_mesh& tm,
                              const Traits& traits = Traits())
diff --git a/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h b/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
index 6c7a573cde6..081c1d890c3 100644
--- a/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
+++ b/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
@@ -16,17 +16,16 @@ the number of edges effectively removed.
 @param np optional sequence of \ref sms_namedparameters "Named Parameters" among the ones listed below
 
 \cgalNamedParamsBegin
-  \cgalParamBegin{vertex_point_map} the property map with the points associated to the vertices of the mesh.
-     If this parameter is omitted, an internal property map for
-     `CGAL::vertex_point_t` should be available in `PolygonMesh`
+  \cgalParamBegin{vertex_point_map}
+    the property map with the points associated to the vertices of the mesh.
   \cgalParamEnd
 
   \cgalParamBegin{geom_traits} an instance of a geometric traits class, model of `Kernel`,
     compatible with the value type of the vertex point map.
   \cgalParamEnd
 
-  \cgalParamBegin{halfedge_index_map} the property map containing an index for each halfedge,
-    initialized 0 to `num_halfedges(graph)`
+  \cgalParamBegin{halfedge_index_map}
+    the property map containing for each halfedge of `surface_mesh` a unique index between `0` to `num_halfedges(graph)`.
   \cgalParamEnd
 
   \cgalParamBegin{get_cost}
@@ -38,7 +37,7 @@ the number of edges effectively removed.
   \cgalParamEnd
 
   \cgalParamBegin{edge_is_constrained_map}
-    The property map containing the constrained-or-not status of each edge of `pmesh`
+    The property map containing the constrained-or-not status of each edge of `pmesh`.
   \cgalParamEnd
 
   \cgalParamBegin{visitor}
diff --git a/Surface_mesh_simplification/examples/Surface_mesh_simplification/CMakeLists.txt b/Surface_mesh_simplification/examples/Surface_mesh_simplification/CMakeLists.txt
index 18f08c1db4e..cb06fb9d434 100644
--- a/Surface_mesh_simplification/examples/Surface_mesh_simplification/CMakeLists.txt
+++ b/Surface_mesh_simplification/examples/Surface_mesh_simplification/CMakeLists.txt
@@ -44,8 +44,8 @@ create_single_source_cgal_program( "edge_collapse_visitor_surface_mesh.cpp" )
 
 find_package(Eigen3 3.1.0 QUIET) #(3.1.0 or greater)
 if( Eigen3_FOUND )
-  include( ${EIGEN3_USE_FILE} )
   create_single_source_cgal_program( "edge_collapse_garland_heckbert.cpp" )
+  CGAL_target_use_Eigen(edge_collapse_garland_heckbert)
 else ()
   message(STATUS "Garland-Heckbert polices require the Eigen library, which has not been found; related examples will not be compiled.")
 endif()
diff --git a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_polyhedron.cpp b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_polyhedron.cpp
index 4287233a4c4..0549a04058f 100644
--- a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_polyhedron.cpp
+++ b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_polyhedron.cpp
@@ -42,7 +42,7 @@ int main(int argc, char** argv)
   // The surface mesh and stop conditions are mandatory arguments.
   // The index maps are needed because the vertices and edges
   // of this surface mesh lack an "id()" field.
-  std::cout << "Collapsing edges of LCC: " << filename << ", aiming for " << edge_count_treshold << " final edges..." << std::endl;
+  std::cout << "Collapsing edges of Polyhedron: " << filename << ", aiming for " << edge_count_treshold << " final edges..." << std::endl;
   int r = SMS::edge_collapse(surface_mesh, stop,
                              CGAL::parameters::vertex_index_map(get(CGAL::vertex_external_index, surface_mesh))
                                               .halfedge_index_map(get(CGAL::halfedge_external_index, surface_mesh)));
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/edge_collapse.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/edge_collapse.h
index 0602aa8a6ff..d83ef51cffb 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/edge_collapse.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/edge_collapse.h
@@ -92,12 +92,10 @@ int edge_collapse(TM& tmesh,
   return internal::edge_collapse(tmesh, should_stop,
                                  choose_parameter(get_parameter(np, internal_np::geom_traits),
                                                   Geom_traits()),
-                                 choose_parameter(get_parameter(np, internal_np::vertex_index),
-                                                  get_const_property_map(boost::vertex_index, tmesh)),
+                                 CGAL::get_initialized_vertex_index_map(tmesh, np),
                                  choose_parameter(get_parameter(np, internal_np::vertex_point),
                                                   get_property_map(vertex_point, tmesh)),
-                                 choose_parameter(get_parameter(np, internal_np::halfedge_index),
-                                                  get_const_property_map(boost::halfedge_index, tmesh)),
+                                 CGAL::get_initialized_halfedge_index_map(tmesh, np),
                                  choose_parameter(get_parameter(np, internal_np::edge_is_constrained),
                                                   No_constrained_edge_map<TM>()),
                                  choose_parameter(get_parameter(np, internal_np::get_cost_policy),
diff --git a/Surface_mesh_skeletonization/benchmark/Surface_mesh_skeletonization/CMakeLists.txt b/Surface_mesh_skeletonization/benchmark/Surface_mesh_skeletonization/CMakeLists.txt
index d73305b0549..4ee6bec3cc0 100644
--- a/Surface_mesh_skeletonization/benchmark/Surface_mesh_skeletonization/CMakeLists.txt
+++ b/Surface_mesh_skeletonization/benchmark/Surface_mesh_skeletonization/CMakeLists.txt
@@ -38,8 +38,6 @@ find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
 
 if(NOT EIGEN3_FOUND)
   message(STATUS "NOTICE: Eigen 3.2 (or greater) is not found.")
-else()
-  include( ${EIGEN3_USE_FILE} )
 endif(NOT EIGEN3_FOUND)
 
 
@@ -47,5 +45,7 @@ endif(NOT EIGEN3_FOUND)
 # ##########################################################
 
 create_single_source_cgal_program( "solver_benchmark.cpp" )
+CGAL_target_use_Eigen(solver_benchmark)
 create_single_source_cgal_program( "mcf_scale_invariance.cpp" )
+CGAL_target_use_Eigen(mcf_scale_invariance)
 
diff --git a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/CMakeLists.txt b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/CMakeLists.txt
index 7327aafc329..d3f29d30dc3 100644
--- a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/CMakeLists.txt
+++ b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/CMakeLists.txt
@@ -14,8 +14,6 @@ if ( CGAL_FOUND )
   find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
 
   if(EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "simple_mcfskel_example.cpp" )
     create_single_source_cgal_program( "simple_mcfskel_sm_example.cpp" )
     create_single_source_cgal_program( "simple_mcfskel_LCC_example.cpp" )
@@ -23,6 +21,16 @@ if ( CGAL_FOUND )
     create_single_source_cgal_program( "MCF_Skeleton_sm_example.cpp" )
     create_single_source_cgal_program( "MCF_Skeleton_LCC_example.cpp" )
     create_single_source_cgal_program( "segmentation_example.cpp" )
+    foreach(target
+        simple_mcfskel_example
+        simple_mcfskel_sm_example
+        simple_mcfskel_LCC_example
+        MCF_Skeleton_example
+        MCF_Skeleton_sm_example
+        MCF_Skeleton_LCC_example
+        segmentation_example)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
   else()
     message(STATUS "These programs require the Eigen library (3.2 or greater), and will not be compiled.")
   endif()
diff --git a/Surface_mesh_skeletonization/test/Surface_mesh_skeletonization/CMakeLists.txt b/Surface_mesh_skeletonization/test/Surface_mesh_skeletonization/CMakeLists.txt
index fdab781a1ca..fd313cbf499 100644
--- a/Surface_mesh_skeletonization/test/Surface_mesh_skeletonization/CMakeLists.txt
+++ b/Surface_mesh_skeletonization/test/Surface_mesh_skeletonization/CMakeLists.txt
@@ -14,10 +14,10 @@ if ( CGAL_FOUND )
   find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
 
   if(EIGEN3_FOUND)
-    include( ${EIGEN3_USE_FILE} )
-
     create_single_source_cgal_program( "MCF_Skeleton_test.cpp" )
+    CGAL_target_use_Eigen(MCF_Skeleton_test)
     create_single_source_cgal_program( "skeleton_connectivity_test.cpp" )
+    CGAL_target_use_Eigen(skeleton_connectivity_test)
   else()
     message(STATUS "These tests require the Eigen library (3.2 or greater), and will not be compiled.")
   endif()
diff --git a/Triangulation/applications/Triangulation/CMakeLists.txt b/Triangulation/applications/Triangulation/CMakeLists.txt
index f95f8c19f46..eb9a2aee481 100644
--- a/Triangulation/applications/Triangulation/CMakeLists.txt
+++ b/Triangulation/applications/Triangulation/CMakeLists.txt
@@ -26,9 +26,6 @@ if ( NOT Boost_FOUND )
 endif()
 
 find_package(Eigen3 3.1.0) 
-if (EIGEN3_FOUND) 
-  include( ${EIGEN3_USE_FILE} ) 
-endif()
 
 # include for local directory
 include_directories( BEFORE include )
@@ -39,6 +36,8 @@ include_directories( BEFORE include )
 # ##########################################################
 
 create_single_source_cgal_program( "points_to_RT_to_off.cpp" )
+CGAL_target_use_Eigen(points_to_RT_to_off)
 create_single_source_cgal_program( "points_to_DT_to_off.cpp" )
+CGAL_target_use_Eigen(points_to_DT_to_off)
 
 
diff --git a/Triangulation/benchmark/Triangulation/CMakeLists.txt b/Triangulation/benchmark/Triangulation/CMakeLists.txt
index f82e906db3d..aa2d0cf578c 100644
--- a/Triangulation/benchmark/Triangulation/CMakeLists.txt
+++ b/Triangulation/benchmark/Triangulation/CMakeLists.txt
@@ -15,10 +15,11 @@ if ( CGAL_FOUND )
 
   find_package(Eigen3 3.1.0) 
   if (EIGEN3_FOUND) 
-    include( ${EIGEN3_USE_FILE} ) 
     include_directories (BEFORE "include")
     create_single_source_cgal_program( "delaunay.cpp" )
+    CGAL_target_use_Eigen(delaunay)
     create_single_source_cgal_program( "Td_vs_T2_and_T3.cpp" )
+    CGAL_target_use_Eigen(Td_vs_T2_and_T3)
 
   else()
     message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
diff --git a/Triangulation/examples/Triangulation/CMakeLists.txt b/Triangulation/examples/Triangulation/CMakeLists.txt
index 69eacb3a05b..a528bd6a21c 100644
--- a/Triangulation/examples/Triangulation/CMakeLists.txt
+++ b/Triangulation/examples/Triangulation/CMakeLists.txt
@@ -18,8 +18,6 @@ if ( CGAL_FOUND )
   
   find_package(Eigen3 3.1.0) 
   if (EIGEN3_FOUND) 
-    include( ${EIGEN3_USE_FILE} ) 
-
     create_single_source_cgal_program( "barycentric_subdivision.cpp" )
     create_single_source_cgal_program( "delaunay_triangulation.cpp" )
     create_single_source_cgal_program( "convex_hull.cpp" )
@@ -28,6 +26,16 @@ if ( CGAL_FOUND )
     create_single_source_cgal_program( "triangulation_data_structure_dynamic.cpp" )
     create_single_source_cgal_program( "triangulation_data_structure_static.cpp" )
 
+    foreach(target
+        barycentric_subdivision
+        delaunay_triangulation
+        convex_hull
+        regular_triangulation
+        triangulation
+        triangulation_data_structure_dynamic
+        triangulation_data_structure_static)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
   else()
     message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
   endif()
diff --git a/Triangulation/test/Triangulation/CMakeLists.txt b/Triangulation/test/Triangulation/CMakeLists.txt
index 49054feffce..1a58eb9e81d 100644
--- a/Triangulation/test/Triangulation/CMakeLists.txt
+++ b/Triangulation/test/Triangulation/CMakeLists.txt
@@ -16,7 +16,6 @@ if ( CGAL_FOUND )
   
   find_package(Eigen3 3.1.0) 
   if (EIGEN3_FOUND) 
-    include( ${EIGEN3_USE_FILE} ) 
     include_directories (BEFORE "include")
 
     create_single_source_cgal_program( "test_triangulation.cpp" )
@@ -25,6 +24,15 @@ if ( CGAL_FOUND )
     create_single_source_cgal_program( "test_tds.cpp" )
     create_single_source_cgal_program( "test_torture.cpp" )
     create_single_source_cgal_program( "test_insert_if_in_star.cpp" )
+    foreach(target
+        test_triangulation
+        test_delaunay
+        test_regular
+        test_tds
+        test_torture
+        test_insert_if_in_star)
+      CGAL_target_use_Eigen(${target})
+    endforeach()
 
   else()
     message(STATUS "NOTICE: Some of the executables in this directory need Eigen 3.1 (or greater) and will not be compiled.")
diff --git a/Triangulation/test/Triangulation/test_delaunay.cpp b/Triangulation/test/Triangulation/test_delaunay.cpp
index bf6b38ff7ab..4c105df3d2f 100644
--- a/Triangulation/test/Triangulation/test_delaunay.cpp
+++ b/Triangulation/test/Triangulation/test_delaunay.cpp
@@ -10,6 +10,7 @@ int main()
 #else
 
 #include <CGAL/Epick_d.h>
+#include <CGAL/Epeck_d.h>
 #include <CGAL/point_generators_d.h>
 #include <CGAL/Delaunay_triangulation.h>
 #include <CGAL/algorithm.h>
@@ -112,13 +113,21 @@ void test(const int d, const string & type, const int N)
 template< int D >
 void go(const int N)
 {
-    typedef CGAL::Epick_d<CGAL::Dimension_tag<D> > FK;
-    typedef CGAL::Delaunay_triangulation<FK> Triangulation;
-    test<Triangulation>(D, "static", N);
+    typedef CGAL::Epick_d<CGAL::Dimension_tag<D> > KI;
+    typedef CGAL::Delaunay_triangulation<KI> Triangulation;
+    test<Triangulation>(D, "inexact static", N);
 
-    typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> FK_dyn;
-    typedef CGAL::Delaunay_triangulation<FK_dyn> Triangulation_dyn;
-    test<Triangulation_dyn>(D, "dynamic", N);
+    typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> KI_dyn;
+    typedef CGAL::Delaunay_triangulation<KI_dyn> Triangulation_dyn;
+    test<Triangulation_dyn>(D, "inexact dynamic", N);
+
+    typedef CGAL::Epeck_d<CGAL::Dimension_tag<D> > KE;
+    typedef CGAL::Delaunay_triangulation<KE> TriangulationE;
+    test<TriangulationE>(D, "exact static", N);
+
+    typedef CGAL::Epeck_d<CGAL::Dynamic_dimension_tag> KE_dyn;
+    typedef CGAL::Delaunay_triangulation<KE_dyn> TriangulationE_dyn;
+    test<TriangulationE_dyn>(D, "exact dynamic", N);
 }
 
 int main(int argc, char **argv)
diff --git a/Triangulation/test/Triangulation/test_regular.cpp b/Triangulation/test/Triangulation/test_regular.cpp
index f124b1ddabf..c044e663f0e 100644
--- a/Triangulation/test/Triangulation/test_regular.cpp
+++ b/Triangulation/test/Triangulation/test_regular.cpp
@@ -1,4 +1,5 @@
 #include <CGAL/Epick_d.h>
+#include <CGAL/Epeck_d.h>
 #include <CGAL/point_generators_d.h>
 #include <CGAL/Regular_triangulation.h>
 #include <CGAL/algorithm.h>
@@ -93,13 +94,21 @@ void test(const int d, const string & type, const int N)
 template< int D >
 void go(const int N)
 {
-  typedef CGAL::Epick_d<CGAL::Dimension_tag<D> > FK;
-  typedef CGAL::Regular_triangulation<FK> Triangulation;
-  test<FK, Triangulation>(D, "static", N);
+  typedef CGAL::Epick_d<CGAL::Dimension_tag<D> > KI;
+  typedef CGAL::Regular_triangulation<KI> Triangulation;
+  test<KI, Triangulation>(D, "inexact static", N);
 
-  typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> FK_dyn;
-  typedef CGAL::Regular_triangulation<FK_dyn> Triangulation_dyn;
-  test<FK_dyn, Triangulation_dyn>(D, "dynamic", N);
+  typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> KI_dyn;
+  typedef CGAL::Regular_triangulation<KI_dyn> Triangulation_dyn;
+  test<KI_dyn, Triangulation_dyn>(D, "inexact dynamic", N);
+
+  typedef CGAL::Epeck_d<CGAL::Dimension_tag<D> > KE;
+  typedef CGAL::Regular_triangulation<KE> TriangulationE;
+  test<KE, TriangulationE>(D, "exact static", N);
+
+  typedef CGAL::Epeck_d<CGAL::Dynamic_dimension_tag> KE_dyn;
+  typedef CGAL::Regular_triangulation<KE_dyn> TriangulationE_dyn;
+  test<KE_dyn, TriangulationE_dyn>(D, "exact dynamic", N);
 }
 
 void test_inserting_points_at_the_same_position()
diff --git a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
index a3d3af22911..6e04239a242 100644
--- a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
@@ -25,6 +25,7 @@
 #include <CGAL/internal/info_check.h>
 #include <CGAL/is_iterator.h>
 
+#include <boost/container/flat_set.hpp>
 #include <boost/iterator/zip_iterator.hpp>
 #include <boost/mpl/and.hpp>
 
@@ -45,10 +46,46 @@ struct Get_iterator_value_type<T,true>{
 } } //namespace CGAL::internal
 #endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
 
-
-
 namespace CGAL {
+namespace internal {
 
+// Compare geometry to ensure deterministic flips
+template <class Tr>
+class Cdt_2_less_edge
+  : public CGAL::cpp98::binary_function<typename Tr::Edge, typename Tr::Edge, bool>
+{
+  const Tr* tr_ptr;
+
+  typedef typename Tr::Point  Point;
+  typedef typename Tr::Edge   Edge;
+
+public:
+  Cdt_2_less_edge(const Tr* tr_ptr) : tr_ptr(tr_ptr) { }
+
+  // just a manual lexicographical_compare
+  bool operator() (const Edge& e1, const Edge& e2) const
+  {
+    const Point& e1p1 = tr_ptr->point(e1.first, Tr::ccw(e1.second));
+    const Point& e2p1 = tr_ptr->point(e2.first, Tr::ccw(e2.second));
+
+    CGAL::Comparison_result res1 = tr_ptr->compare_xy(e1p1, e2p1);
+    if(res1 == CGAL::SMALLER)
+      return true;
+    if(res1 == CGAL::LARGER)
+      return false;
+
+    const Point& e1p2 = tr_ptr->point(e1.first, Tr::cw(e1.second));
+    const Point& e2p2 = tr_ptr->point(e2.first, Tr::cw(e2.second));
+
+    CGAL::Comparison_result res2 = tr_ptr->compare_xy(e1p2, e2p2);
+    if(res2 == CGAL::SMALLER)
+      return true;
+
+    return false;
+  }
+};
+
+} // namespace internal
 
 template <class Gt,
           class Tds_ = Default ,
@@ -74,13 +111,14 @@ public:
   typedef typename Ctr::Face_circulator       Face_circulator;
   typedef typename Ctr::size_type             size_type;
   typedef typename Ctr::Locate_type           Locate_type;
- 
+
   typedef typename Ctr::List_edges List_edges;  
   typedef typename Ctr::List_faces List_faces;
   typedef typename Ctr::List_vertices  List_vertices;
   typedef typename Ctr::List_constraints List_constraints;
-  typedef typename Ctr::Less_edge less_edge;
-  typedef typename Ctr::Edge_set Edge_set;
+
+  typedef internal::Cdt_2_less_edge<CDt> Less_edge;
+  typedef boost::container::flat_set<Edge, Less_edge> Edge_set;
 
   //Tag to distinguish Delaunay from regular triangulations
   typedef Tag_false Weighted_tag;
@@ -530,8 +568,10 @@ public:
   int i, ii, indf, indn;
   Face_handle ni, f,ff;
   Edge ei,eni; 
-  typename Ctr::Edge_set edge_set;
-  typename Ctr::Less_edge less_edge;
+
+  Less_edge less_edge(this);
+  Edge_set edge_set(less_edge);
+
   Edge e[4];
   typename List_edges::iterator itedge=edges.begin();
 
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 4805a68e33e..48ab6cc3111 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -170,10 +170,6 @@ public:
   // Tag to distinguish periodic triangulations from others
   typedef Tag_false                          Periodic_tag;
 
-  class Less_edge;
-  typedef std::set<Edge,Less_edge> Edge_set;
-
-
   Constrained_triangulation_2(const Gt& gt = Gt()) : Triangulation(gt) { }
 
   Constrained_triangulation_2(std::list<Constraint>& lc, const Gt& gt=Gt())
@@ -435,21 +431,6 @@ insert_constraint(Vertex_handle  vaa, Vertex_handle vbb, OutputIterator out)
   // template<class OutputItEdges>
   // OutputItEdges incident_constraints(Vertex_handle v, 
   //                                     OutputItEdges out) const;
-  
-
-  class Less_edge 
-    :  public CGAL::cpp98::binary_function<Edge, Edge, bool>
-  {
-  public:
-    Less_edge() {}
-    bool operator() (const Edge& e1, const Edge& e2) const
-      {
-	int ind1=e1.second, ind2=e2.second;
- 	return( (&(*e1.first) < &(*e2.first))
- 		|| ( (&(*e1.first) == &(*e2.first)) && (ind1 < ind2)));
-      } 
-  };
-
 
   void file_output(std::ostream& os) const;
 
diff --git a/Triangulation_2/include/CGAL/Triangulation_face_base_with_id_2.h b/Triangulation_2/include/CGAL/Triangulation_face_base_with_id_2.h
index d47a256a245..8d5a54281e1 100644
--- a/Triangulation_2/include/CGAL/Triangulation_face_base_with_id_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_face_base_with_id_2.h
@@ -42,11 +42,15 @@ public:
     : Fb(v0, v1, v2, n0, n1, n2)
   { }
 
-  int& id() { return _id; }
-  int id() const { return _id; }
+  int& id() { return face_id; }
+  int id() const { return face_id; }
+
+  int& edge_id(const std::size_t i) { return edge_ids[i]; }
+  int edge_id(const std::size_t i) const { return edge_ids[i]; }
 
 private:
-  int _id;
+  int face_id;
+  std::array<int, 3> edge_ids;
 };
 
 } //namespace CGAL
diff --git a/Triangulation_2/include/CGAL/boost/graph/internal/properties_2D_triangulation.h b/Triangulation_2/include/CGAL/boost/graph/internal/properties_2D_triangulation.h
index 6bad3c9aa0c..16895ba78a8 100644
--- a/Triangulation_2/include/CGAL/boost/graph/internal/properties_2D_triangulation.h
+++ b/Triangulation_2/include/CGAL/boost/graph/internal/properties_2D_triangulation.h
@@ -111,7 +111,7 @@ public:
   T2_halfedge_id_map(const Tr& tr) : tr(tr) { }
 
   // Halfedge id is twice the edge id, and +0/+1 depending whether
-  // h.first is such that h.first < opposite(h).first --> different ids
+  // h.first is such that h.first < opposite(h).first
   value_type operator[](key_type h) const
   {
     const Face_handle f1 = h.first;
@@ -119,13 +119,13 @@ public:
     CGAL_assertion(!tr.is_infinite(f1) || !tr.is_infinite(f2));
 
     if(tr.is_infinite(f1))
-      return 2*(3 * f2->id() + f2->index(f1));
+      return 2*(f2->edge_id(f2->index(f1)));
     else if(tr.is_infinite(f2))
-      return 2*(3 * f1->id() + h.second) + 1;
+      return 2*(f1->edge_id(h.second)) + 1;
     else if(f1->id() < f2->id())
-      return 2*(3 * f1->id() + h.second);
+      return 2*(f1->edge_id(h.second));
     else
-      return 2*(3 * f2->id() + f2->index(f1)) + 1;
+      return 2*(f1->edge_id(h.second)) + 1;
   }
 
 private:
@@ -152,13 +152,9 @@ public:
     CGAL_assertion(!tr.is_infinite(f1) || !tr.is_infinite(f2));
 
     if(tr.is_infinite(f1))
-      return 3 * f2->id() + f2->index(f1);
-    else if(tr.is_infinite(f2))
-      return 3 * f1->id() + e.second;
-    else if(f1->id() < f2->id())
-      return 3 * f1->id() + e.second;
+      return f2->edge_id(f2->index(f1));
     else
-      return 3 * f2->id() + f2->index(f1);
+      return f1->edge_id(e.second);
   }
 
 private:
@@ -368,6 +364,39 @@ put(PropertyTag p, CGAL_2D_TRIANGULATION& g, const Key& key, const Value& value)
   put(pmap, key, value);
 }
 
+template < CGAL_2D_TRIANGULATION_TEMPLATE_PARAMETERS >
+void set_triangulation_ids(CGAL_2D_TRIANGULATION& g)
+{
+  typedef typename boost::graph_traits< CGAL_2D_TRIANGULATION >::vertex_descriptor   vertex_descriptor;
+  typedef typename boost::graph_traits< CGAL_2D_TRIANGULATION >::halfedge_descriptor halfedge_descriptor;
+  typedef typename boost::graph_traits< CGAL_2D_TRIANGULATION >::edge_descriptor     edge_descriptor;
+  typedef typename boost::graph_traits< CGAL_2D_TRIANGULATION >::face_descriptor     face_descriptor;
+
+  int vid = 0;
+  for(vertex_descriptor vd : vertices(g))
+    vd->id() = vid++;
+
+  int eid = 0;
+  for(edge_descriptor ed : edges(g))
+  {
+    halfedge_descriptor hd = halfedge(ed, g);
+    face_descriptor fd = face(hd, g);
+    if(fd != boost::graph_traits< CGAL_2D_TRIANGULATION >::null_face())
+      fd->edge_id(hd.second) = eid;
+
+    halfedge_descriptor opp_hd = opposite(hd, g);
+    face_descriptor opp_fd = face(opp_hd, g);
+    if(opp_fd != boost::graph_traits< CGAL_2D_TRIANGULATION >::null_face())
+      opp_fd->edge_id(opp_hd.second) = eid;
+
+    ++eid;
+  }
+
+  int fid = 0;
+  for(face_descriptor fd : faces(g))
+    fd->id() = fid++;
+}
+
 } // namespace CGAL
 
 #undef CGAL_2D_TRIANGULATION_TEMPLATE_PARAMETERS
diff --git a/Triangulation_3/include/CGAL/Triangulation_3_to_lcc.h b/Triangulation_3/include/CGAL/Triangulation_3_to_lcc.h
index be15a9e3c72..1bb09346ee9 100644
--- a/Triangulation_3/include/CGAL/Triangulation_3_to_lcc.h
+++ b/Triangulation_3/include/CGAL/Triangulation_3_to_lcc.h
@@ -15,9 +15,27 @@
 
 #include <CGAL/assertions.h>
 #include <map>
+#include <CGAL/Weighted_point_3.h>
 
 namespace CGAL {
 
+  namespace internal 
+  {
+    template<typename Point>
+    struct Get_point
+    {
+      static const Point& run(const Point& p)
+      { return p; }
+    };
+
+    template<typename Kernel>
+    struct Get_point<CGAL::Weighted_point_3<Kernel> >
+    {
+      static const typename Kernel::Point_3& run(const CGAL::Weighted_point_3<Kernel>& p)
+      { return p.point(); }
+    };
+  }
+  
   /** Convert a given Triangulation_3 into a 3D linear cell complex.
    * @param alcc the used linear cell complex.
    * @param atr the Triangulation_3.
@@ -52,7 +70,7 @@ namespace CGAL {
     for (TVertex_iterator itv = atr.vertices_begin();
          itv != atr.vertices_end(); ++itv)
     {
-      TV[itv] = alcc.create_vertex_attribute(itv->point());
+      TV[itv] = alcc.create_vertex_attribute(internal::Get_point<typename Triangulation::Point>::run(itv->point()));
     }
 
     // Create the tetrahedron and create a map to link Cell_iterator