diff --git a/BGL/include/CGAL/boost/graph/copy_face_graph.h b/BGL/include/CGAL/boost/graph/copy_face_graph.h
index 2a4850647ce..80337715cd9 100644
--- a/BGL/include/CGAL/boost/graph/copy_face_graph.h
+++ b/BGL/include/CGAL/boost/graph/copy_face_graph.h
@@ -24,7 +24,6 @@
 #include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/property_map.h>
 #include <boost/utility/enable_if.hpp>
-#include <boost/iterator/function_output_iterator.hpp>
 
 #include <unordered_map>
 
@@ -213,36 +212,6 @@ void copy_face_graph_impl(const SourceMesh& sm, TargetMesh& tm,
 }
 
 } // end of namespace internal
-namespace impl
-{
-template<typename PMAP>
-struct Output_iterator_functor
-{
-  typedef typename boost::property_traits<PMAP>::key_type input_t;
-  typedef typename boost::property_traits<PMAP>::value_type output_t;
-  PMAP map;
-  Output_iterator_functor(PMAP map)
-    :map(map)
-  {
-  }
-  void operator()(const typename std::pair<input_t, output_t>& pair)
-  {
-    put(map, pair.first, pair.second);
-  }
-
-};
-
-template<typename PMAP>
-boost::function_output_iterator<Output_iterator_functor<PMAP> > make_functor(PMAP map)
-{
-  return boost::make_function_output_iterator(Output_iterator_functor<PMAP>(map));
-}
-
-inline Emptyset_iterator make_functor(const internal_np::Param_not_found&)
-{
-  return Emptyset_iterator();
-}
-}//end of impl
 
 /*!
   \ingroup PkgBGLHelperFct
diff --git a/BGL/include/CGAL/boost/graph/internal/helpers.h b/BGL/include/CGAL/boost/graph/internal/helpers.h
index 98d3c7ec28b..ec6b47baf83 100644
--- a/BGL/include/CGAL/boost/graph/internal/helpers.h
+++ b/BGL/include/CGAL/boost/graph/internal/helpers.h
@@ -13,7 +13,11 @@
 
 #include <boost/graph/graph_traits.hpp>
 #include <boost/optional.hpp>
+#include <CGAL/iterator.h>
+#include <CGAL/property_map.h>
 #include <CGAL/boost/graph/iterator.h>
+#include <CGAL/Named_function_parameters.h>
+#include <boost/iterator/function_output_iterator.hpp>
 
 namespace CGAL {
 
@@ -200,6 +204,38 @@ adjust_incoming_halfedge(typename boost::graph_traits<Graph>::vertex_descriptor
 
 
 } // internal
+
+namespace impl
+{
+  template<typename PMAP>
+  struct Output_iterator_functor
+  {
+    typedef typename boost::property_traits<PMAP>::key_type input_t;
+    typedef typename boost::property_traits<PMAP>::value_type output_t;
+    PMAP map;
+    Output_iterator_functor(PMAP map)
+      :map(map)
+    {
+    }
+    void operator()(const typename std::pair<input_t, output_t>& pair)
+    {
+      put(map, pair.first, pair.second);
+    }
+
+  };
+
+  template<typename PMAP>
+  boost::function_output_iterator<Output_iterator_functor<PMAP> > make_functor(PMAP map)
+  {
+    return boost::make_function_output_iterator(Output_iterator_functor<PMAP>(map));
+  }
+
+  inline Emptyset_iterator make_functor(const internal_np::Param_not_found&)
+  {
+    return Emptyset_iterator();
+  }
+}//end of impl
+
 } // CGAL
 
 
diff --git a/Data/data/meshes/elephant.mesh b/Data/data/meshes/elephant.mesh
new file mode 100644
index 00000000000..4b22a5f896f
--- /dev/null
+++ b/Data/data/meshes/elephant.mesh
@@ -0,0 +1,9457 @@
+MeshVersionFormatted 1
+Dimension 3
+# CGAL::Mesh_complex_3_in_triangulation_3
+Vertices
+1028
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+End
diff --git a/Documentation/doc/Documentation/packages.txt b/Documentation/doc/Documentation/packages.txt
index ae1d9c9ab0b..aa061c842d8 100644
--- a/Documentation/doc/Documentation/packages.txt
+++ b/Documentation/doc/Documentation/packages.txt
@@ -90,6 +90,7 @@
 \package_listing{Mesh_2}
 \package_listing{Surface_mesher}
 \package_listing{Skin_surface_3}
+\package_listing{SMDS_3}
 \package_listing{Mesh_3}
 \package_listing{Tetrahedral_remeshing}
 \package_listing{Periodic_3_mesh_3}
diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index 74c86d2e2bc..10b9387df06 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -2,6 +2,19 @@ Release History
 ===============
 
 
+[Release 5.6](https://github.com/CGAL/cgal/releases/tag/v5.6)
+-----------
+
+Release date: Dec 2022
+
+### [3D Simplicial Mesh Data Structure](https://doc.cgal.org/5.6/Manual/packages.html#PkgSMDS3) (new package)
+
+-   This new package wraps all the existing code that deals with a `MeshComplex_3InTriangulation_3`
+    to describe 3D simplicial meshess, and makes the data structure independent
+    from the tetrahedral mesh generation package.
+
+
+
 [Release 5.5](https://github.com/CGAL/cgal/releases/tag/v5.5)
 -----------
 
@@ -247,6 +260,7 @@ Release date: January 2022
 -   Added support for the [OSQP solver](https://osqp.org/). This solver enables to efficiently compute
     the convex Quadratic Programming (QP) problems arising in the context of several packages.
 
+
 [Release 5.3](https://github.com/CGAL/cgal/releases/tag/v5.3)
 -----------
 
diff --git a/Installation/include/CGAL/SMDS_3/Mesh_complex_3_in_triangulation_3_fwd.h b/Installation/include/CGAL/SMDS_3/Mesh_complex_3_in_triangulation_3_fwd.h
new file mode 100644
index 00000000000..9b0c2d1e38e
--- /dev/null
+++ b/Installation/include/CGAL/SMDS_3/Mesh_complex_3_in_triangulation_3_fwd.h
@@ -0,0 +1,53 @@
+// Copyright (C) 2020  GeometryFactory Sarl
+//
+// This file is part of CGAL (www.cgal.org)
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
+//
+
+#ifndef CGAL_SMDS_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_FWD_H
+#define CGAL_SMDS_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_FWD_H
+
+/// \file Mesh_complex_3_in_triangulation_3_fwd.h
+/// Forward declarations of the SMDS_3 package.
+
+#ifndef DOXYGEN_RUNNING
+namespace CGAL {
+
+// fwdS for the public interface
+template <typename Tr,
+          typename CornerIndex = int,
+          typename CurveIndex = int>
+class Mesh_complex_3_in_triangulation_3;
+
+namespace IO {
+  template <class C3T3>
+  void output_to_medit(std::ostream& os,
+                       const C3T3& c3t3,
+                       bool rebind = false,
+                       bool show_patches = false
+#ifndef DOXYGEN_RUNNING
+                     , bool all_vertices = true
+                     , bool all_cells = false
+#endif
+  );
+} //namespace IO
+
+namespace SMDS_3 {
+
+  template<class Tr>
+  bool build_triangulation_from_file(std::istream& is,
+                                     Tr& tr,
+                                     bool verbose = false,
+                                     bool replace_domain_0 = false,
+                                     bool allow_non_manifold = false);
+
+} // namespace SMDS_3
+} // namespace CGAL
+#endif
+
+#endif /* CGAL_SMDS_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_FWD_H */
+
+
diff --git a/Installation/include/CGAL/license/SMDS_3.h b/Installation/include/CGAL/license/SMDS_3.h
new file mode 100644
index 00000000000..6191918e010
--- /dev/null
+++ b/Installation/include/CGAL/license/SMDS_3.h
@@ -0,0 +1,54 @@
+// Copyright (c) 2016  GeometryFactory SARL (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) : Andreas Fabri
+//
+// Warning: this file is generated, see include/CGAL/licence/README.md
+
+#ifndef CGAL_LICENSE_SMDS_3_H
+#define CGAL_LICENSE_SMDS_3_H
+
+#include <CGAL/config.h>
+#include <CGAL/license.h>
+
+#ifdef CGAL_SMDS_3_COMMERCIAL_LICENSE
+
+#  if CGAL_SMDS_3_COMMERCIAL_LICENSE < CGAL_RELEASE_DATE
+
+#    if defined(CGAL_LICENSE_WARNING)
+
+       CGAL_pragma_warning("Your commercial license for CGAL does not cover "
+                           "this release of the 3D Mesh Data Structure package.")
+#    endif
+
+#    ifdef CGAL_LICENSE_ERROR
+#      error "Your commercial license for CGAL does not cover this release \
+              of the 3D Mesh Data Structure package. \
+              You get this error, as you defined CGAL_LICENSE_ERROR."
+#    endif // CGAL_LICENSE_ERROR
+
+#  endif // CGAL_SMDS_3_COMMERCIAL_LICENSE < CGAL_RELEASE_DATE
+
+#else // no CGAL_SMDS_3_COMMERCIAL_LICENSE
+
+#  if defined(CGAL_LICENSE_WARNING)
+     CGAL_pragma_warning("\nThe macro CGAL_SMDS_3_COMMERCIAL_LICENSE is not defined."
+                          "\nYou use the CGAL 3D Simplicial Mesh Data Structure package under "
+                          "the terms of the GPLv3+.")
+#  endif // CGAL_LICENSE_WARNING
+
+#  ifdef CGAL_LICENSE_ERROR
+#    error "The macro CGAL_SMDS_3_COMMERCIAL_LICENSE is not defined.\
+            You use the CGAL 3D Simplicial Mesh Data Structure package under the terms of \
+            the GPLv3+. You get this error, as you defined CGAL_LICENSE_ERROR."
+#  endif // CGAL_LICENSE_ERROR
+
+#endif // no CGAL_SMDS_3_COMMERCIAL_LICENSE
+
+#endif // CGAL_LICENSE_SMDS_3_H
diff --git a/Installation/include/CGAL/license/gpl_package_list.txt b/Installation/include/CGAL/license/gpl_package_list.txt
index 28c3cd25f87..f023d48f375 100644
--- a/Installation/include/CGAL/license/gpl_package_list.txt
+++ b/Installation/include/CGAL/license/gpl_package_list.txt
@@ -91,6 +91,7 @@ Surface_sweep_2 2D Intersection of Curves
 TDS_2 2D Triangulation Data Structure
 TDS_3 3D Triangulation Data Structure
 Three Three
+SMDS_3 3D Simplicial Mesh Data Structure
 Triangulation_2 2D Triangulation
 Triangulation_on_sphere_2 2D Triangulation on Sphere
 Triangulation_3 3D Triangulations
diff --git a/Mesh_3/doc/Mesh_3/CGAL/Compact_mesh_cell_base_3.h b/Mesh_3/doc/Mesh_3/CGAL/Compact_mesh_cell_base_3.h
deleted file mode 100644
index 8e91b271375..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/Compact_mesh_cell_base_3.h
+++ /dev/null
@@ -1,34 +0,0 @@
-namespace CGAL {
-
-/*!
-\ingroup PkgMesh3MeshClasses
-
-The class `Compact_mesh_cell_base_3<Gt, MD>` is a model of the concept `MeshCellBase_3`.
-It is designed to serve as cell base class for the 3D triangulation
-used in the 3D mesh generation process. It is more compact in memory than
-`Mesh_cell_base_3`.
-
-\tparam Gt is the geometric traits class.
-It has to be a model of the concept `MeshTriangulationTraits_3`.
-
-\tparam MD provides the types of indices used to identify
-the faces of the input complex. It has to be a model
-of the concept `MeshDomain_3`.
-
-\tparam Tds is the triangulation data structure class to which cells
-belong. That parameter is only used by the rebind mechanism (see
-`::TriangulationDSCellBase_3::Rebind_TDS`). Users should always use the
-default parameter value `void`.
-
-\cgalModels `MeshCellBase_3`
-
-\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
-\sa `CGAL::Mesh_cell_base_3<Gt, MD, Cb>`
-
-*/
-template< typename Gt,  typename MD, typename Tds = void >
-class Compact_mesh_cell_base_3 {
-public:
-
-}; /* end Compact_mesh_cell_base_3 */
-} /* end namespace CGAL */
diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/File_avizo.h b/Mesh_3/doc/Mesh_3/CGAL/IO/File_avizo.h
deleted file mode 100644
index f4f679a9eb5..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/File_avizo.h
+++ /dev/null
@@ -1,14 +0,0 @@
-namespace CGAL{
-namespace IO {
-/**
- * \ingroup PkgMesh3IOFunctions
- * @brief outputs mesh to avizo format
- * @param os the stream
- * @param c3t3 the mesh complex
- * \see \ref IOStreamAvizo
- */
-template <class C3T3>
-void
-output_to_avizo(std::ostream& os,
-                 const C3T3& c3t3);
-}}
diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h b/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h
deleted file mode 100644
index bdbb7e0d01e..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h
+++ /dev/null
@@ -1,21 +0,0 @@
-namespace CGAL {
-namespace IO {
-/// \ingroup PkgMesh3IOFunctions
-///
-/// \brief outputs a mesh complex to the medit (`.mesh`) file format.
-///        See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
-///
-/// \param os the output stream
-/// \param c3t3 the mesh complex
-/// \param rebind if set to `true`, labels of cells are rebinded into `[1..nb_of_labels]`
-/// \param show_patches if set to `true`, patches are labeled with different labels than
-///                     cells. If set to `false`, each surface facet is written twice,
-///                     using the label of each adjacent cell.
-///
-template <class C3T3>
-void output_to_medit(std::ostream& os,
-                     const C3T3& c3t3,
-                     bool rebind = false,
-                     bool show_patches = false);
-
-}} // end namespace CGAL::IO
diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/File_tetgen.h b/Mesh_3/doc/Mesh_3/CGAL/IO/File_tetgen.h
deleted file mode 100644
index 8294618586b..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/File_tetgen.h
+++ /dev/null
@@ -1,20 +0,0 @@
-namespace CGAL{
-namespace IO {
-/**
- * \ingroup PkgMesh3IOFunctions
- * @brief outputs a mesh complex to tetgen format
- * @param filename the path to the output file
- * @param c3t3 the mesh
- * @param rebind if true, labels of cells are rebinded into [1..nb_of_labels]
- * @param show_patches if true, patches are labeled with different labels than
- * cells. If false, each surface facet is written twice, using label of
- * each adjacent cell.
- * \see \ref IOStreamTetgen
- */
-template <class C3T3>
-void
-output_to_tetgen(std::string filename,
-                 const C3T3& c3t3,
-                 bool rebind = false,
-                 bool show_patches = false);
-} }
diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h b/Mesh_3/doc/Mesh_3/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
deleted file mode 100644
index b672d4d3273..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
+++ /dev/null
@@ -1,16 +0,0 @@
-namespace CGAL {
-//! \ingroup PkgMesh3Functions
-//!
-//! \brief builds a `TriangleMesh` from the surface facets, with a consistent orientation at the interface of two subdomains.
-//!
-//! This function exports the surface as a `TriangleMesh` and appends it to `graph`, using
-//! `orient_polygon_soup()`.
-//!
-//! @tparam C3T3 a model of `MeshComplexWithFeatures_3InTriangulation_3`.
-//! @tparam TriangleMesh a model of `MutableFaceGraph` with an internal point property map. The point type should be compatible with the one used in `C3T3`.
-//!
-//! @param c3t3 an instance of `C3T3`.
-//! @param graph an instance of `TriangleMesh`.
-template<class C3T3, class TriangleMesh>
-void facets_in_complex_3_to_triangle_mesh(const C3T3& c3t3, TriangleMesh& graph);
-}
diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/output_to_vtu.h b/Mesh_3/doc/Mesh_3/CGAL/IO/output_to_vtu.h
deleted file mode 100644
index e1d9d87e4a9..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/output_to_vtu.h
+++ /dev/null
@@ -1,18 +0,0 @@
-namespace CGAL{
-namespace IO {
-//! \ingroup PkgMesh3IOFunctions
-//!
-//! \brief writes a tetrahedron mesh using the `UnstructuredGrid` XML format.
-//!
-//! \tparam C3T3 a model of `MeshComplexWithFeatures_3InTriangulation_3`.
-//!
-//! \param os the stream used for writing.
-//! \param c3t3 the instance of `C3T3` to be written.
-//! \param mode decides if the data should be written in binary (`IO::BINARY`)
-//!   or in ASCII (`IO::ASCII`).
-//!
-template <class C3T3>
-void output_to_vtu(std::ostream& os,
-                   const C3T3& c3t3,
-                   IO::Mode mode = BINARY);
-} }
diff --git a/Mesh_3/doc/Mesh_3/CGAL/Mesh_cell_base_3.h b/Mesh_3/doc/Mesh_3/CGAL/Mesh_cell_base_3.h
deleted file mode 100644
index b20e0426d83..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/Mesh_cell_base_3.h
+++ /dev/null
@@ -1,40 +0,0 @@
-
-namespace CGAL {
-
-
-/*!
-\ingroup PkgMesh3MeshClasses
-<!-- Meta-comment: this class cannot be deprecated by
-Compact_mesh_cell_base_3, because the later has a different API.
--- Laurent Rineau, 2013/10/16
-\deprecated This class is deprecated since \cgal 4.3. Use
-`CGAL::Compact_mesh_cell_base_3<Gt,MD,Tds>` instead.
--->
-
-The class `Mesh_cell_base_3<Gt, MD, Cb>` is a model of the concept `MeshCellBase_3`.
-It is designed to serve as cell base class for the 3D triangulation
-used in the 3D mesh generation process.
-
-\tparam Gt is the geometric traits class.
-It has to be a model of the concept `MeshTriangulationTraits_3`.
-
-\tparam MD provides the types of indices used to identify
-the faces of the input complex. It has to be a model
-of the concept `MeshDomain_3`.
-
-\tparam Cb is the cell base class. It has to be a model
-of the concept `RegularTriangulationCellBaseWithWeightedCircumcenter_3` and defaults to
-`Regular_triangulation_cell_base_with_weighted_circumcenter_3<Gt>`.
-
-\cgalModels `MeshCellBase_3`
-
-\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
-\sa `CGAL::Compact_mesh_cell_base_3<Gt, MD, Tds>`
-
-*/
-template< typename Gt,  typename MD, typename Cb >
-class Mesh_cell_base_3 : public Cb {
-public:
-
-}; /* end Mesh_cell_base_3 */
-} /* end namespace CGAL */
diff --git a/Mesh_3/doc/Mesh_3/CGAL/Mesh_complex_3_in_triangulation_3.h b/Mesh_3/doc/Mesh_3/CGAL/Mesh_complex_3_in_triangulation_3.h
deleted file mode 100644
index fad13d11a51..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/Mesh_complex_3_in_triangulation_3.h
+++ /dev/null
@@ -1,119 +0,0 @@
-namespace CGAL {
-
-/*!
-\ingroup PkgMesh3MeshClasses
-
-The class `Mesh_complex_3_in_triangulation_3` implements a data structure
-to store the 3D restricted Delaunay triangulation used by a mesh
-generation process.
-
-This class is a model of the concept
-`MeshComplexWithFeatures_3InTriangulation_3`.
-
-
-\tparam Tr can be instantiated with any 3D
-regular triangulation of \cgal provided that its
-vertex and cell base class are models of the concepts
-`MeshVertexBase_3` and `MeshCellBase_3`, respectively.
-
-\tparam  CornerIndex is the type of the indices for corners. It must match the `Corner_index` of the model
-of the `MeshDomainWithFeatures_3` concept used for mesh generation.
-
-\tparam CurveIndex is the type of the indices for curves.
-It must match the `Curve_index` types of the model
-of the `MeshDomainWithFeatures_3` concept used for mesh generation.
-
-Those two last template parameters defaults to `int`, so that they can be ignored
-if the domain used for mesh generation does not include 0 and 1-dimensionnal features (i.e
-is a model of the concept `MeshDomain_3`).
-
-\cgalModels `MeshComplexWithFeatures_3InTriangulation_3`
-
-\sa `CGAL::make_mesh_3()`
-\sa `CGAL::refine_mesh_3()`
-\sa `MeshComplex_3InTriangulation_3`
-\sa `MeshComplexWithFeatures_3InTriangulation_3`
-\sa `MeshCellBase_3`,
-\sa `MeshVertexBase_3`
-
-*/
-template< typename Tr, typename CornerIndex, typename CurveIndex >
-class Mesh_complex_3_in_triangulation_3 {
-public:
-
-/// \name Types
-/// @{
-
-/*!
-%Index type.
-*/
-typedef Tr::Vertex::Index Index;
-
-/*!
-Surface index type.
-*/
-typedef Tr::Cell::Surface_patch_index Surface_patch_index;
-
-/*!
-Subdomain index type.
-*/
-typedef Tr::Cell::Subdomain_index Subdomain_index;
-
-/*!
- Corner index type.
-*/
-typedef CornerIndex Corner_index;
-
-/*!
-Curve index type.
-*/
-typedef CurveIndex Curve_index;
-
-/// @}
-
-/// \name Operations
-/// @{
-
-/*!
-  The tetrahedral mesh generation algorithm implemented in `CGAL::make_mesh_3()`
-  and `CGAL::refine_mesh_3()` does not guarantee that all the points inserted
-  by the algorithm are actually present in the final mesh.
-
-  In most cases, all points are used, but if the geometry of the object
-  has small features, compared to the size of the simplices (triangles and tetrahedra),
-  it might be that the Delaunay facets that are selected in the restricted Delaunay
-  triangulation miss some vertices of the triangulation.
-  The concurrent version of the tetrahedral mesh generation algorithm
-  also inserts a small set of auxiliary vertices that belong to the triangulation
-  but are isolated from the complex at the end of the meshing process.
-
-  This function removes these so-called \em isolated vertices, that belong to the
-  triangulation but not to any cell of the `C3T3`, from the triangulation.
-*/
-void remove_isolated_vertices();
-
-/*!
-Outputs the mesh to `os`
-in medit format.
-*/
-void output_to_medit(std::ofstream& os);
-
-/**
- * Outputs the outer boundary of the entire domain with facets oriented outward.
- */
-std::ostream& output_boundary_to_off(std::ostream& out) const;
-
-/**
- * Outputs the outer boundary of the selected subdomain with facets oriented outward.
- */
-std::ostream& output_boundary_to_off(std::ostream& out, Subdomain_index subdomain) const;
-
-/**
- * Outputs the surface facets with a consistent orientation at the interface of two subdomains.
- */
-std::ostream& output_facets_in_complex_to_off(std::ostream& out) const;
-
-/// @}
-
-}; /* end Mesh_complex_3_in_triangulation_3 */
-} /* end namespace CGAL */
diff --git a/Mesh_3/doc/Mesh_3/CGAL/Mesh_vertex_base_3.h b/Mesh_3/doc/Mesh_3/CGAL/Mesh_vertex_base_3.h
deleted file mode 100644
index b0112fcc53a..00000000000
--- a/Mesh_3/doc/Mesh_3/CGAL/Mesh_vertex_base_3.h
+++ /dev/null
@@ -1,32 +0,0 @@
-namespace CGAL {
-
-/*!
-\ingroup PkgMesh3MeshClasses
-
-The class `Mesh_vertex_base_3` is a model of the concept `MeshVertexBase_3`.
-It is designed to serve as vertex base class for the 3D triangulation
-used in a 3D mesh generation process.
-
-\tparam Gt is the geometric traits class.
-It must be a model of the concept `MeshTriangulationTraits_3`.
-
-\tparam MD provides the types of indices
-used to identify
-the faces of the input complex. It must be a model
-of the concept `MeshDomain_3`.
-
-\tparam Vb is the vertex base class. It has to be a model
-of the concept `RegularTriangulationVertexBase_3` and defaults to
-`Regular_triangulation_vertex_base_3<Gt>`.
-
-\cgalModels `MeshVertexBase_3`
-
-\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
-
-*/
-template< typename Gt, typename MD, typename Vb >
-class Mesh_vertex_base_3 : public Vb {
-public:
-
-}; /* end Mesh_vertex_base_3 */
-} /* end namespace CGAL */
diff --git a/Mesh_3/doc/Mesh_3/CGAL/make_mesh_3.h b/Mesh_3/doc/Mesh_3/CGAL/make_mesh_3.h
index 08bd5ee1761..312b556343f 100644
--- a/Mesh_3/doc/Mesh_3/CGAL/make_mesh_3.h
+++ b/Mesh_3/doc/Mesh_3/CGAL/make_mesh_3.h
@@ -33,7 +33,10 @@ traverse the resulting mesh data structure or can be written to a file
 
 
 \tparam C3T3 is required to be a model of
-the concept `MeshComplex_3InTriangulation_3`. This is the return type.
+the concept `MeshComplex_3InTriangulation_3`,
+and a model of `MeshComplexWithFeatures_3InTriangulation_3`
+if the domain is a model of `MeshDomainWithFeatures_3`.
+This is the return type.
 The type `C3T3` is in particular required to provide a nested type
 `C3T3::Triangulation` for the 3D triangulation
 embedding the mesh. The vertex and cell base classes of the
diff --git a/Mesh_3/doc/Mesh_3/CGAL/refine_mesh_3.h b/Mesh_3/doc/Mesh_3/CGAL/refine_mesh_3.h
index 25ddc7311ed..afeebe8c634 100644
--- a/Mesh_3/doc/Mesh_3/CGAL/refine_mesh_3.h
+++ b/Mesh_3/doc/Mesh_3/CGAL/refine_mesh_3.h
@@ -39,7 +39,9 @@ not change from one refinement to the next one.
 
 \tparam  C3T3 is required to be a model of
 the concept
-`MeshComplex_3InTriangulation_3`.
+`MeshComplex_3InTriangulation_3`,
+and a model of `MeshComplexWithFeatures_3InTriangulation_3`
+if the domain is a model of `MeshDomainWithFeatures_3`.
 The argument `c3t3` is passed by
 reference as this object is modified by the refinement process. As the
 refinement process only adds points to the triangulation, all
diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshCellBase_3.h b/Mesh_3/doc/Mesh_3/Concepts/MeshCellBase_3.h
index d9037a2151b..a6ba2ba7d6f 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshCellBase_3.h
+++ b/Mesh_3/doc/Mesh_3/Concepts/MeshCellBase_3.h
@@ -5,7 +5,8 @@
 The concept `MeshCellBase_3` describes the requirements
 for the `Cell` type of the triangulation
 used in the 3D mesh generation process. The type `MeshCellBase_3`
-refines the concept `RegularTriangulationCellBaseWithWeightedCircumcenter_3`
+refines the concepts `SimplicialMeshCellBase_3` and
+`RegularTriangulationCellBaseWithWeightedCircumcenter_3`
 and must be copy constructible.
 The concept `MeshCellBase_3`
 includes a way to store and retrieve
@@ -40,6 +41,7 @@ and `is_facet_visited(1)` in parallel must be safe)
 Moreover, the parallel algorithms require an erase counter in
 each cell (see below).
 
+\cgalRefines `SimplicialMeshCellBase_3`
 \cgalRefines `RegularTriangulationCellBaseWithWeightedCircumcenter_3`
 \cgalRefines `CopyConstructible`
 
@@ -172,9 +174,25 @@ void increment_erase_counter();
 /*! \name Internal
 These functions are used internally by mesh optimizers.
 The class should provide storage, accessors and modificators for two `Vertex_handle`
-and two `Cell_handle`.*/
+and two `Cell_handle`, and a cache value for sliverity.*/
 /// @{
 
+/*!
+*/
+void set_sliver_value(double value);
+
+/*!
+*/
+double sliver_value() const;
+
+/*!
+*/
+bool is_cache_valid() const;
+
+/*!
+*/
+void reset_cache_validity() const;
+
 /*!
 
 */
diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h b/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
index fe2749b913c..240f9b0f1fb 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
+++ b/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
@@ -124,7 +124,7 @@ following operators:
 
 `template<typename OutputIterator>`
 <br>
-`OutputIterator operator()(int n, OutputIterator pts)`
+`OutputIterator operator()(OutputIterator pts, int n)`
 
 Those two operators output a set of (`n`) surface points to the
 output iterator `pts`, as objects of type `std::pair<Point_3,
diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshVertexBase_3.h b/Mesh_3/doc/Mesh_3/Concepts/MeshVertexBase_3.h
index adbad096584..1b1cb0d712b 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshVertexBase_3.h
+++ b/Mesh_3/doc/Mesh_3/Concepts/MeshVertexBase_3.h
@@ -4,8 +4,9 @@
 
 The concept `MeshVertexBase_3` describes the requirements
 for the `Vertex` type of the triangulation
-used by a 3D mesh generation process. The type `MeshVertexBase_3` refines both
-the concept `RegularTriangulationVertexBase_3` and the concept `SurfaceMeshVertexBase_3`.
+used by a 3D mesh generation process. The type `MeshVertexBase_3` refines
+the concepts `RegularTriangulationVertexBase_3`,
+`SimplicialMeshVertexBase_3`, and `SurfaceMeshVertexBase_3`.
 It provides additional members to store and retrieve
 information about the location of the vertex with respect
 to the input domain describing the domain to be discretized.
@@ -19,6 +20,7 @@ and two `Vertex_handle` called 'intrusive'.
 The parallel algorithms require an erase counter in
 each cell (see below).
 
+\cgalRefines `SimplicialMeshVertexBase_3`
 \cgalRefines `RegularTriangulationVertexBase_3`
 \cgalRefines `SurfaceMeshVertexBase_3`
 
diff --git a/Mesh_3/doc/Mesh_3/Doxyfile.in b/Mesh_3/doc/Mesh_3/Doxyfile.in
index c5f22c38811..592155364b5 100644
--- a/Mesh_3/doc/Mesh_3/Doxyfile.in
+++ b/Mesh_3/doc/Mesh_3/Doxyfile.in
@@ -6,8 +6,10 @@ ALIASES += "cgalDescribePolylineType=A polyline is defined as a sequence of poin
 INPUT += \
       ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Polyhedral_complex_mesh_domain_3.h \
       ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Mesh_domain_with_polyline_features_3.h \
-      ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Mesh_3/generate_label_weights.h
-
+      ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Mesh_3/generate_label_weights.h \
+      ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Mesh_vertex_base_3.h \
+      ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Mesh_cell_base_3.h \
+      ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Compact_mesh_cell_base_3.h
 PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 3D Mesh Generation"
 HTML_EXTRA_FILES           =  ${CGAL_PACKAGE_DOC_DIR}/fig/implicit_domain_3.jpg \
                               ${CGAL_PACKAGE_DOC_DIR}/fig/implicit_domain_4.jpg \
diff --git a/Mesh_3/doc/Mesh_3/Mesh_3.txt b/Mesh_3/doc/Mesh_3/Mesh_3.txt
index 183e23b46e4..fabeb649e60 100644
--- a/Mesh_3/doc/Mesh_3/Mesh_3.txt
+++ b/Mesh_3/doc/Mesh_3/Mesh_3.txt
@@ -566,10 +566,10 @@ for more details.
 
 \section Mesh_3_section_io Input/Output
 Several file formats are supported for writing a mesh:
- - \ref IOStreamVTK, using `CGAL::IO::output_to_vtu()`
- - \ref IOStreamAvizo, using `CGAL::IO::output_to_avizo()`
- - \ref IOStreamMedit, using `CGAL::IO::output_to_medit()`
- - \ref IOStreamTetgen, using `CGAL::IO::output_to_tetgen()`
+ - \ref IOStreamMedit, using \link CGAL::IO::write_MEDIT() `CGAL::IO::write_MEDIT()`\endlink
+ - \ref IOStreamVTK, using \link CGAL::IO::output_to_vtu() `CGAL::IO::output_to_vtu()`\endlink
+ - \ref IOStreamAvizo, using \link CGAL::IO::output_to_avizo `CGAL::IO::output_to_avizo()`\endlink
+ - \ref IOStreamTetgen, using \link CGAL::IO::output_to_tetgen `CGAL::IO::output_to_tetgen()`\endlink
 
 \section Mesh_3_section_examples Examples
 
diff --git a/Mesh_3/doc/Mesh_3/PackageDescription.txt b/Mesh_3/doc/Mesh_3/PackageDescription.txt
index 240ca4bf294..08462c8341c 100644
--- a/Mesh_3/doc/Mesh_3/PackageDescription.txt
+++ b/Mesh_3/doc/Mesh_3/PackageDescription.txt
@@ -29,7 +29,7 @@
 
 /// \defgroup PkgMesh3IOFunctions Input/Output Functions
 /// \ingroup PkgMesh3Ref
-/// The free functions that can be used to read and write meshes.
+/// See \ref PkgSMDS3IOFunctions from \ref PkgSMDS3
 
 /*!
 \addtogroup PkgMesh3Ref
@@ -57,8 +57,6 @@
 Here are the main concepts of this package:
 
 - `MeshTriangulationTraits_3`
-- `MeshComplex_3InTriangulation_3`
-- `MeshComplexWithFeatures_3InTriangulation_3`
 - `MeshDomain_3`
 - `MeshDomainWithFeatures_3`
 - `MeshCriteria_3`
@@ -80,7 +78,6 @@ related to the template parameters of some models of the main concepts:
 
 \cgalCRPSection{Classes}
 
-- `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
 - `CGAL::Mesh_triangulation_3<MD,Gt,Concurrency_tag,Vertex_base,Cell_base>`
 - `CGAL::Mesh_vertex_base_3<Gt,MD,Vb>`
 - `CGAL::Compact_mesh_cell_base_3<Gt,MD,Tds>`
@@ -114,7 +111,6 @@ and their associated classes:
 - `CGAL::perturb_mesh_3()`
 - `CGAL::lloyd_optimize_mesh_3()`
 - `CGAL::odt_optimize_mesh_3()`
-- `CGAL::facets_in_complex_3_to_triangle_mesh()`
 - `CGAL::Mesh_3::generate_label_weights()`
 
 \cgalCRPSection{CGAL::parameters Functions}
@@ -137,9 +133,4 @@ and their associated classes:
 
 - `CGAL::Mesh_optimization_return_code`
 - `CGAL::Mesh_facet_topology`
-
-\cgalCRPSection{Input/Output Functions}
-- `CGAL::IO::output_to_medit()`
-- `CGAL::IO::output_to_vtu()`
 */
-
diff --git a/Mesh_3/doc/Mesh_3/dependencies b/Mesh_3/doc/Mesh_3/dependencies
index 8dc427e241e..be614f85b31 100644
--- a/Mesh_3/doc/Mesh_3/dependencies
+++ b/Mesh_3/doc/Mesh_3/dependencies
@@ -13,3 +13,5 @@ Polyhedron
 Miscellany
 Mesh_2
 Polygon_mesh_processing
+SMDS_3
+
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_gray_image.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_gray_image.cpp
index 40dddc6a1a9..fa7e38b7dca 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_gray_image.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_gray_image.cpp
@@ -49,7 +49,8 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_gray_image_multiple_values.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_gray_image_multiple_values.cpp
index 3ead928edf7..1c99e0379f1 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_gray_image_multiple_values.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_gray_image_multiple_values.cpp
@@ -81,7 +81,8 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_gray_vtk_image.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_gray_vtk_image.cpp
index 8bf9f62710a..a42b1144a0a 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_gray_vtk_image.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_gray_vtk_image.cpp
@@ -97,7 +97,8 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_image.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_image.cpp
index d573dde7c96..dbae9919419 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_image.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_image.cpp
@@ -54,7 +54,8 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_image_variable_size.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_image_variable_size.cpp
index 051f07dba4c..c7f205091ba 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_image_variable_size.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_image_variable_size.cpp
@@ -63,7 +63,8 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_image_with_custom_initialization.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_image_with_custom_initialization.cpp
index 5b0a8a23196..fcf5d94744d 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_image_with_custom_initialization.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_image_with_custom_initialization.cpp
@@ -11,7 +11,7 @@
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/Image_3.h>
 
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 // Domain
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_image_with_features.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_image_with_features.cpp
index 3f8a0fe362a..877fa104635 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_image_with_features.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_image_with_features.cpp
@@ -102,7 +102,8 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_3D_weighted_image.cpp b/Mesh_3/examples/Mesh_3/mesh_3D_weighted_image.cpp
index f6b072b3dcd..0374a315707 100644
--- a/Mesh_3/examples/Mesh_3/mesh_3D_weighted_image.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_3D_weighted_image.cpp
@@ -59,7 +59,9 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
+
   std::ofstream bin_file("out.binary.cgal", std::ios_base::binary);
   CGAL::IO::save_binary_file(bin_file, c3t3);
 
diff --git a/Mesh_3/examples/Mesh_3/mesh_cubes_intersection.cpp b/Mesh_3/examples/Mesh_3/mesh_cubes_intersection.cpp
index 12216cc2cbd..90577147ecb 100644
--- a/Mesh_3/examples/Mesh_3/mesh_cubes_intersection.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_cubes_intersection.cpp
@@ -91,7 +91,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out_cubes_intersection.mesh");
-  CGAL::IO::output_to_medit(medit_file, c3t3);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_cubes_intersection_with_features.cpp b/Mesh_3/examples/Mesh_3/mesh_cubes_intersection_with_features.cpp
index 61d2d78d993..fd9f1780c62 100644
--- a/Mesh_3/examples/Mesh_3/mesh_cubes_intersection_with_features.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_cubes_intersection_with_features.cpp
@@ -178,7 +178,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out_cubes_intersection_with_features.mesh");
-  CGAL::IO::output_to_medit(medit_file, c3t3);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_hybrid_mesh_domain.cpp b/Mesh_3/examples/Mesh_3/mesh_hybrid_mesh_domain.cpp
index c638395342c..c0ba926d412 100644
--- a/Mesh_3/examples/Mesh_3/mesh_hybrid_mesh_domain.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_hybrid_mesh_domain.cpp
@@ -13,7 +13,7 @@
 #include <CGAL/make_mesh_3.h>
 
 // Ouput
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 // Read 1D features from input file
 #include "read_polylines.h"
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_domains.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_domains.cpp
index d8790c25fd3..4d9187f5692 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_domains.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_domains.cpp
@@ -67,7 +67,7 @@ int main()
 
   // Output
   std::ofstream medit_file("out.mesh");
-  CGAL::IO::output_to_medit(medit_file, c3t3);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_domains_2.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_domains_2.cpp
index 6d50993bbdd..e3ec7922475 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_domains_2.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_domains_2.cpp
@@ -69,7 +69,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out.mesh");
-  CGAL::IO::output_to_medit(medit_file, c3t3);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
index 9e28374783e..da98a23a98c 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
@@ -55,7 +55,7 @@ int main()
 
   // Output
   std::ofstream medit_file("out_wo.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
   medit_file.close();
 
   // Perturbation (5s, 12degree)
@@ -66,7 +66,8 @@ int main()
 
   // Output
   medit_file.open("out_optimized.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_sphere.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_sphere.cpp
index 4521c606724..2e318913c84 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_sphere.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_sphere.cpp
@@ -52,7 +52,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_sphere_variable_size.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_sphere_variable_size.cpp
index 3eaa7ce389f..61c3952bb68 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_sphere_variable_size.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_sphere_variable_size.cpp
@@ -69,7 +69,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_optimization_example.cpp b/Mesh_3/examples/Mesh_3/mesh_optimization_example.cpp
index 9f72d6c276a..4d0e36ff5d3 100644
--- a/Mesh_3/examples/Mesh_3/mesh_optimization_example.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_optimization_example.cpp
@@ -59,10 +59,12 @@ int main(int argc, char* argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   std::ofstream medit_file_bis("out_bis.mesh");
-  c3t3_bis.output_to_medit(medit_file_bis);
+  CGAL::IO::write_MEDIT(medit_file_bis, c3t3_bis);
+  medit_file_bis.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp b/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
index e4a6e6a5dcb..b4db268fc59 100644
--- a/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
@@ -59,10 +59,12 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   std::ofstream medit_file_bis("out_bis.mesh");
-  c3t3_bis.output_to_medit(medit_file_bis);
+  CGAL::IO::write_MEDIT(medit_file_bis, c3t3_bis);
+  medit_file_bis.close();
 
   return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
index 134092b3fba..eaee6876dc8 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
@@ -80,7 +80,8 @@ int main()
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
index 789b5737892..bc4b4821dca 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
@@ -109,7 +109,8 @@ int main()
 
   //// Output
   //std::ofstream medit_file("out.mesh");
-  //c3t3.output_to_medit(medit_file);
+  //CGAL::IO::write_MEDIT(medit_file, c3t3);
+  //medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain.cpp
index f5cf67e0204..eb24c7ef70a 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain.cpp
@@ -8,6 +8,7 @@
 #include <CGAL/Polyhedral_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/refine_mesh_3.h>
+#include <CGAL/IO/File_medit.h>
 
 // Domain
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
@@ -61,7 +62,7 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out_1.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
   medit_file.close();
 
   // Set tetrahedron size (keep cell_radius_edge_ratio), ignore facets
@@ -72,7 +73,8 @@ int main(int argc, char*argv[])
 
   // Output
   medit_file.open("out_2.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_sm.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_sm.cpp
index 7cb6dda697d..c7ab9c43a4d 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_sm.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_sm.cpp
@@ -61,7 +61,7 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out_1.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
   medit_file.close();
 
   // Set tetrahedron size (keep cell_radius_edge_ratio), ignore facets
@@ -72,7 +72,8 @@ int main(int argc, char*argv[])
 
   // Output
   medit_file.open("out_2.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features.cpp
index 75b7e82e6d1..c6b092e5db1 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features.cpp
@@ -66,7 +66,7 @@ int main(int argc, char*argv[])
   std::ofstream file("out.vtu");
   CGAL::IO::output_to_vtu(file, c3t3);
   // Could be replaced by:
-  // c3t3.output_to_medit(file);
+  // CGAL::IO::write_MEDIT(file, c3t3);
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features_sm.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features_sm.cpp
index 435a205fe34..a05a3aa1669 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features_sm.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_features_sm.cpp
@@ -67,7 +67,7 @@ int main(int argc, char*argv[])
   std::ofstream file("out-sm.vtu");
   CGAL::IO::output_to_vtu(file, c3t3, CGAL::IO::ASCII);
   // Could be replaced by:
-  // c3t3.output_to_medit(file);
+  // CGAL::IO::write_MEDIT(file, c3t3);
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_lipschitz_sizing.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_lipschitz_sizing.cpp
index 1054a00baeb..d6ab36133bc 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_lipschitz_sizing.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_domain_with_lipschitz_sizing.cpp
@@ -80,7 +80,8 @@ int main(int argc, char*argv[])
 
   // Output
   std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
+  medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_two_implicit_spheres_with_balls.cpp b/Mesh_3/examples/Mesh_3/mesh_two_implicit_spheres_with_balls.cpp
index bdc5ac62e7a..7458ae88390 100644
--- a/Mesh_3/examples/Mesh_3/mesh_two_implicit_spheres_with_balls.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_two_implicit_spheres_with_balls.cpp
@@ -88,7 +88,7 @@ int main()
                                       CGAL::parameters::no_features());
 
   std::ofstream medit_file("out-no-protection.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
   medit_file.close();
   c3t3.clear();
 
@@ -97,7 +97,7 @@ int main()
 
   // Output
   medit_file.open("out-with-protection.mesh");
-  c3t3.output_to_medit(medit_file);
+  CGAL::IO::write_MEDIT(medit_file, c3t3);
   medit_file.close();
 
   return 0;
diff --git a/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h b/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
index bbd0d96de83..0283d6268d8 100644
--- a/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
+++ b/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
@@ -16,7 +16,6 @@
 
 #include <CGAL/license/Mesh_3.h>
 
-
 #include <CGAL/Mesh_3/config.h>
 
 #include <CGAL/array.h>
@@ -28,7 +27,7 @@
 #include <CGAL/Has_timestamp.h>
 
 #include <CGAL/Regular_triangulation_cell_base_3.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 
 #include <boost/type_traits/is_same.hpp>
 
@@ -709,6 +708,32 @@ public:
 
 };  // end class Compact_mesh_cell_3
 
+/*!
+\ingroup PkgMesh3MeshClasses
+
+The class `Compact_mesh_cell_base_3<GT, MD>` is a model of the concept `MeshCellBase_3`.
+It is designed to serve as cell base class for the 3D triangulation
+used in the 3D mesh generation process. It is more compact in memory than
+`Mesh_cell_base_3`.
+
+\tparam GT is the geometric traits class.
+It has to be a model of the concept `MeshTriangulationTraits_3`.
+
+\tparam MD provides the types of indices used to identify
+the faces of the input complex. It has to be a model
+of the concept `MeshDomain_3`.
+
+\tparam TDS is the triangulation data structure class to which cells
+belong. That parameter is only used by the rebind mechanism (see
+`::TriangulationDSCellBase_3::Rebind_TDS`). Users should always use the
+default parameter value `void`.
+
+\cgalModels `MeshCellBase_3`
+
+\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
+\sa `CGAL::Mesh_cell_base_3<GT, MD, Cb>`
+
+*/
 template< class GT,
           class MD,
           class TDS = void >
diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index c093cc52119..5acc5b01507 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -33,8 +33,8 @@
 
 #include <functional>
 
-#include <CGAL/Mesh_3/internal/Handle_IO_for_pair_of_int.h>
-#include <CGAL/Mesh_3/internal/indices_management.h>
+#include <CGAL/SMDS_3/internal/Handle_IO_for_pair_of_int.h>
+#include <CGAL/SMDS_3/internal/indices_management.h>
 
 // support for `CGAL::Image_3`
 #include <CGAL/Image_3.h>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h b/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
index 5a798e665e0..47f6d237051 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
@@ -13,126 +13,8 @@
 #ifndef CGAL_MESH_3_DUMP_C3T3_H
 #define CGAL_MESH_3_DUMP_C3T3_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/SMDS_3.h>
 
-#include <CGAL/disable_warnings.h>
-
-#include <CGAL/Mesh_3/io_signature.h>
-#include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h>
-#include <CGAL/IO/File_medit.h>
-
-#include <CGAL/is_streamable.h>
-
-#include <fstream>
-#include <string>
-
-namespace CGAL {
-
-template <typename C3t3,
-          bool is_streamable =
-            is_streamable<typename C3t3::Triangulation::Vertex>::value &&
-            is_streamable<typename C3t3::Triangulation::Cell>::value
-            &&
-            (is_streamable<typename C3t3::Surface_patch_index>::value ||
-             Output_rep<typename C3t3::Surface_patch_index>::is_specialized)
-            &&
-            (is_streamable<typename C3t3::Subdomain_index>::value ||
-             Output_rep<typename C3t3::Subdomain_index>::is_specialized)
-          >
-struct Dump_c3t3 {
-  void dump_c3t3(const C3t3& c3t3, std::string prefix) const
-  {
-    std::clog<<"======dump c3t3===== to: " << prefix << std::endl;
-    std::ofstream medit_file((prefix+".mesh").c_str());
-    medit_file.precision(17);
-    CGAL::IO::output_to_medit(medit_file, c3t3, false /*rebind*/, true /*show_patches*/);
-    medit_file.close();
-
-    std::string bin_filename = prefix;
-    bin_filename += ".binary.cgal";
-    std::ofstream bin_file(bin_filename.c_str(),
-                           std::ios_base::binary | std::ios_base::out);
-    std::string signature = CGAL::Get_io_signature<C3t3>()();
-    CGAL_assertion(signature != std::string());
-    bin_file << "binary CGAL c3t3 " << signature << "\n";
-    CGAL::IO::set_binary_mode(bin_file);
-    bin_file << c3t3;
-  }
-}; // end struct template Dump_c3t3<C3t3, bool>
-
-template <typename C3t3>
-struct Dump_c3t3<C3t3, false>
-{
-  void dump_c3t3(const C3t3&, std::string) {
-    std::cerr << "Warning " << __FILE__ << ":" << __LINE__ << "\n"
-              << "  the c3t3 object of following type:\n"
-              << typeid(C3t3).name() << std::endl
-              << "  cannot be dumped because some types are not streamable:\n";
-    if(!is_streamable<typename C3t3::Triangulation::Vertex>::value) {
-      std::cerr << "     - C3t3::Triangulation::Vertex is not streamble\n";
-      std::cerr << "       "
-                << typeid(typename C3t3::Triangulation::Vertex).name()
-                << "\n";
-    }
-
-    if(!is_streamable<typename C3t3::Triangulation::Cell>::value) {
-      std::cerr << "     - C3t3::Triangulation::Cell is not streamble\n";
-      std::cerr << "       "
-                << typeid(typename C3t3::Triangulation::Cell).name()
-                << "\n";
-    }
-
-    if(!is_streamable<typename C3t3::Surface_patch_index>::value &&
-       !CGAL::Output_rep<typename C3t3::Surface_patch_index>::is_specialized)
-    {
-      std::cerr << "     - C3t3::Surface_patch_index is not streamable\n";
-      std::cerr << "       "
-                << typeid(typename C3t3::Surface_patch_index).name()
-                << "\n";
-    }
-    if(!is_streamable<typename C3t3::Subdomain_index>::value &&
-       !CGAL::Output_rep<typename C3t3::Subdomain_index>::is_specialized)
-    {
-      std::cerr << "     - C3t3::Subdomain_index is not streamable\n";
-      std::cerr << "       "
-                << typeid(typename C3t3::Subdomain_index).name()
-                << "\n";
-    }
-  }
-}; // end struct template specialization Dump_c3t3<C3t3, false>
-
-template <typename C3t3>
-void dump_c3t3_edges(const C3t3& c3t3, std::string prefix)
-{
-  typename C3t3::Triangulation::Geom_traits::Construct_point_3 cp =
-    c3t3.triangulation().geom_traits().construct_point_3_object();
-
-  std::ofstream file((prefix+".polylines.txt").c_str());
-  file.precision(17);
-  for(typename C3t3::Edges_in_complex_iterator
-        edge_it = c3t3.edges_in_complex_begin(),
-        end     = c3t3.edges_in_complex_end();
-      edge_it != end; ++edge_it)
-  {
-    const typename C3t3::Triangulation::Cell_handle c = edge_it->first;
-    const int i = edge_it->second;
-    const int j = edge_it->third;
-    const typename C3t3::Triangulation::Weighted_point& ei = c3t3.triangulation().point(c, i);
-    const typename C3t3::Triangulation::Weighted_point& ej = c3t3.triangulation().point(c, j);
-    file << "2 " << cp(ei) << " "  << cp(ej) << "\n";
-  }
-}
-template <typename C3t3>
-void dump_c3t3(const C3t3& c3t3, std::string prefix)
-{
-  if(!prefix.empty()) {
-    Dump_c3t3<C3t3> dump;
-    dump.dump_c3t3(c3t3, prefix);
-  }
-}
-
-} // end namespace CGAL
-
-#include <CGAL/enable_warnings.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #endif // CGAL_MESH_3_DUMP_C3T3_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h b/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h
deleted file mode 100644
index 7511346f1f3..00000000000
--- a/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h
+++ /dev/null
@@ -1,1161 +0,0 @@
-// Copyright (c) 2003-2009  INRIA Sophia-Antipolis (France).
-// Copyright (c) 2013       GeometryFactory Sarl (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)     : Laurent Rineau, Stéphane Tayeb
-//
-//******************************************************************************
-// File Description : Implements class Mesh_complex_3_in_triangulation_3.
-//******************************************************************************
-
-#ifndef CGAL_MESH_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_BASE_H
-#define CGAL_MESH_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_BASE_H
-
-#include <CGAL/license/Triangulation_3.h>
-
-#include <CGAL/disable_warnings.h>
-
-#include <CGAL/Mesh_3/config.h>
-
-#include <CGAL/Mesh_3/utilities.h>
-#include <CGAL/iterator.h>
-#include <CGAL/IO/File_medit.h>
-#include <CGAL/IO/File_maya.h>
-#include <CGAL/Bbox_3.h>
-#include <CGAL/Mesh_3/io_signature.h>
-#include <CGAL/Union_find.h>
-#include <CGAL/Time_stamper.h>
-
-#include <boost/functional/hash.hpp>
-#include <boost/unordered_map.hpp>
-
-#include <iostream>
-#include <fstream>
-
-
-#ifdef CGAL_LINKED_WITH_TBB
-  #include <atomic>
-  #include <tbb/concurrent_hash_map.h>
-
-namespace CGAL {
-  template < class DSC, bool Const >
-  std::size_t tbb_hasher(const CGAL::internal::CC_iterator<DSC, Const>& it)
-  {
-    return CGAL::internal::hash_value(it);
-  }
-
-
-  // As Marc Glisse pointed out the TBB hash of a std::pair is
-  // simplistic and leads to the
-  // TBB Warning: Performance is not optimal because the hash function
-  //              produces bad randomness in lower bits in class
-  //              tbb::interface5::concurrent_hash_map
-  template < class DSC, bool Const >
-  std::size_t tbb_hasher(const std::pair<CGAL::internal::CC_iterator<DSC, Const>,
-                                         CGAL::internal::CC_iterator<DSC, Const> >& p)
-  {
-    return boost::hash<std::pair<CGAL::internal::CC_iterator<DSC, Const>,
-                                 CGAL::internal::CC_iterator<DSC, Const> > >()(p);
-  }
-
-  struct Hash_compare_for_TBB {
-    template < class DSC, bool Const >
-    std::size_t hash(const std::pair<CGAL::internal::CC_iterator<DSC, Const>,
-                           CGAL::internal::CC_iterator<DSC, Const> >& p) const
-    {
-      return tbb_hasher(p);
-    }
-    template < class DSC, bool Const >
-    std::size_t operator()(const CGAL::internal::CC_iterator<DSC, Const>& it)
-    {
-      return CGAL::internal::hash_value(it);
-    }
-    template <typename T>
-    bool equal(const T& v1, const T& v2) const {
-      return v1 == v2;
-    }
-  };
-}
-#endif
-
-namespace CGAL {
-namespace Mesh_3 {
-
-  namespace details {
-
-    template <typename Tr>
-    class C3t3_helper_class
-    {
-    protected:
-      typedef typename Tr::Vertex_handle Vertex_handle;
-      typedef typename Tr::Cell_handle   Cell_handle;
-      typedef typename Tr::Facet         Facet;
-      typedef typename Tr::Edge          Edge;
-
-      typedef std::pair<Vertex_handle, Vertex_handle> Pair_of_vertices;
-
-      // computes and return an ordered pair of Vertex
-      Pair_of_vertices
-      make_ordered_pair(const Vertex_handle vh1, const Vertex_handle vh2) const {
-        if (vh1 < vh2) {
-          return std::make_pair(vh1, vh2);
-        }
-        else {
-          return std::make_pair(vh2, vh1);
-        }
-      }
-
-      // same from an Edge
-      Pair_of_vertices
-      make_ordered_pair(const Edge e) const {
-        return make_ordered_pair(e.first->vertex(e.second),
-                                 e.first->vertex(e.third));
-      }
-
-      Facet canonical_facet(Cell_handle c, int i) const {
-        Cell_handle c2 = c->neighbor(i);
-        return (c2 < c) ? std::make_pair(c2,c2->index(c)) : std::make_pair(c,i);
-      }
-
-    }; // end class template C3t3_helper_class
-
-  } // end namespace Mesh_3::details
-
-/**
- * @class Mesh_complex_3_in_triangulation_3_base
- * @brief A data-structure to represent and maintain a 3D complex embedded
- * in a 3D triangulation.
- */
-template<typename Tr, typename Concurrency_tag>
-class Mesh_complex_3_in_triangulation_3_base
-  : public details::C3t3_helper_class<Tr>
-{
-  typedef Mesh_complex_3_in_triangulation_3_base<Tr, Concurrency_tag> Self;
-  typedef details::C3t3_helper_class<Tr> Base;
-
-public:
-  // Triangulation types
-  typedef Tr                            Triangulation;
-  typedef typename Tr::Vertex_handle    Vertex_handle;
-  typedef typename Tr::Cell_handle      Cell_handle;
-  typedef typename Tr::Facet            Facet;
-  typedef typename Tr::Edge             Edge;
-  typedef typename Tr::size_type        size_type;
-
-  typedef CGAL::Hash_handles_with_or_without_timestamps Hash_fct;
-
-  // Indices types
-  typedef typename Tr::Cell::Subdomain_index      Subdomain_index;
-  typedef typename Tr::Cell::Surface_patch_index  Surface_patch_index;
-  typedef typename Tr::Vertex::Index              Index;
-
-  enum Face_status{ NOT_IN_COMPLEX = 0,
-                    ISOLATED = 1, // - An ISOLATED edge is a marked edge,
-                                  //   without any incident facets.
-                    BOUNDARY,     // - An edge is on BOUNDARY if it has only
-                                  //   one incident facet.
-                                  // - A vertex is on BOUNDARY if all its
-                                  //   incident edges are REGULAR or on
-                                  //   BOUNDARY, at least one is on
-                                  //   BOUNDARY, and the incident facets
-                                  //   form only one connected component.
-                    REGULAR,      // - A facet that is in the complex is
-                                  //   REGULAR.
-                                  // - An edge is REGULAR if it has
-                                  //   exactly two incident facets.
-                                  // - A vertex is REGULAR if all it
-                                  //   incident edges are REGULAR, and the
-                                  //   incident facets form only one
-                                  //   connected component.
-                    SINGULAR};    // - SINGULAR is for all other cases.
-
-  //-------------------------------------------------------
-  // Constructors / Destructors
-  //-------------------------------------------------------
-  /**
-   * @brief Constructor
-   * Builds an empty 3D complex.
-   */
-  Mesh_complex_3_in_triangulation_3_base()
-    : Base()
-    , tr_()
-    , edge_facet_counter_() //TODO: parallel!
-    , manifold_info_initialized_(false) //TODO: parallel!
-  {
-    // We don't put it in the initialization list because
-    // std::atomic has no contructors
-    number_of_facets_ = 0;
-    number_of_cells_ = 0;
-  }
-
-  /// Copy constructor
-  Mesh_complex_3_in_triangulation_3_base(const Self& rhs)
-    : Base()
-    , tr_(rhs.tr_)
-    , edge_facet_counter_(rhs.edge_facet_counter_)
-    , manifold_info_initialized_(rhs.manifold_info_initialized_)
-  {
-    Init_number_of_elements<Concurrency_tag> init;
-    init(number_of_facets_, rhs.number_of_facets_);
-    init(number_of_cells_, rhs.number_of_cells_);
-  }
-
-  /// Move constructor
-  Mesh_complex_3_in_triangulation_3_base(Self&& rhs)
-    : Base()
-    , tr_(std::move(rhs.tr_))
-    , edge_facet_counter_(std::move(rhs.edge_facet_counter_))
-    , manifold_info_initialized_(std::exchange(rhs.manifold_info_initialized_, false))
-  {
-    Init_number_of_elements<Concurrency_tag> init;
-    init(number_of_facets_, rhs.number_of_facets_);
-    init(number_of_cells_, rhs.number_of_cells_);
-    init(rhs.number_of_facets_); // set to 0
-    init(rhs.number_of_cells_); // set to 0
-  }
-
-  /// Destructor
-  ~Mesh_complex_3_in_triangulation_3_base() {}
-
-  void clear() {
-    number_of_cells_ = 0;
-    number_of_facets_ = 0;
-    clear_manifold_info();
-    tr_.clear();
-  }
-
-  /// Assignment operator
-  Self& operator=(Self rhs)
-  {
-    swap(rhs);
-    return *this;
-  }
-
-  /// Assignment operator, also serves as move-assignment
-  Self& operator=(Self&& rhs)
-  {
-    swap(rhs);
-    return *this;
-  }
-
-  /// Returns the reference to the triangulation
-  Triangulation& triangulation() { return tr_; }
-  /// Returns a const reference to the triangulation
-  const Triangulation& triangulation() const { return tr_; }
-
-
-  /// Adds facet \c facet to the 2D complex, with surface index \c index
-  void add_to_complex(const Facet& facet, const Surface_patch_index& index)
-  {
-    add_to_complex(facet.first, facet.second, index);
-  }
-
-  /// Adds facet(\c cell, \c i) to the 2D complex, with surface index \c index
-  void add_to_complex(const Cell_handle& cell,
-                      const int i,
-                      const Surface_patch_index& index);
-
-  /// Removes facet \c facet from 2D complex
-  void remove_from_complex(const Facet& facet);
-
-  /// Removes facet(\c cell, \c i) from 2D complex
-  void remove_from_complex(const Cell_handle& c, const int i) {
-    remove_from_complex(Facet(c, i));
-  }
-
-  /// Sets surface index of facet \c facet to \c index
-  void set_surface_patch_index(const Facet& f, const Surface_patch_index& index)
-  {
-    set_surface_patch_index(f.first, f.second, index);
-  }
-
-  /// Sets surface index of facet(\c cell, \c i) to \c index
-  void set_surface_patch_index(const Cell_handle& cell,
-                         const int i,
-                         const Surface_patch_index& index) const
-  {
-    cell->set_surface_patch_index(i, index);
-  }
-
-  /// Returns `NOT_IN_COMPLEX`, `BOUNDARY`, `REGULAR`, or `SINGULAR`,
-  /// depending on the number of incident facets in the complex, and the
-  /// number of connected components of its link
-  Face_status face_status(const Vertex_handle v) const
-  {
-    if(!manifold_info_initialized_) init_manifold_info();
-    const std::size_t n = v->cached_number_of_incident_facets();
-
-    if(n == 0) return NOT_IN_COMPLEX;
-
-    //test incident edges for REGULARITY and count BOUNDARY edges
-    typename std::vector<Edge> edges;
-    edges.reserve(64);
-    if(tr_.is_parallel()) {
-      tr_.incident_edges_threadsafe(v, std::back_inserter(edges));
-    } else {
-      tr_.incident_edges(v, std::back_inserter(edges));
-    }
-    int number_of_boundary_incident_edges = 0; // could be a bool
-    for (typename std::vector<Edge>::iterator
-           eit=edges.begin(), end = edges.end();
-         eit != end; eit++)
-    {
-      switch( face_status(*eit) )
-      {
-      case NOT_IN_COMPLEX: case REGULAR: break;
-      case BOUNDARY: ++number_of_boundary_incident_edges; break;
-      default :
-#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-        std::cerr << "singular edge...\n";
-        std::cerr << tr_.point(v) << std::endl;
-#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-        return SINGULAR;
-      }
-    }
-
-    // From here all incident edges (in complex) are REGULAR or BOUNDARY.
-    const std::size_t nb_components = union_find_of_incident_facets(v);
-    if(nb_components > 1) {
-#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-      std::cerr << "singular vertex: nb_components=" << nb_components << std::endl;
-      std::cerr << tr_.point(v) << std::endl;
-#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-      return SINGULAR;
-    }
-    else { // REGULAR OR BOUNDARY
-#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-      std::cerr << "regular or boundary: " << tr_.point(v) << std::endl;
-#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-      if (number_of_boundary_incident_edges != 0)
-        return BOUNDARY;
-      else
-        return REGULAR;
-    }
-  }
-
-  /// This function should be called only when incident edges
-  /// are known to be REGULAR OR BOUNDARY
-  bool is_regular_or_boundary_for_vertices(Vertex_handle v) const {
-    return union_find_of_incident_facets(v) == 1;
-  }
-
-  /// Returns `NOT_IN_COMPLEX`, `BOUNDARY`, `REGULAR`, or `SINGULAR`,
-  /// depending on the number of incident facets in the complex
-  Face_status face_status(const Edge& edge) const
-  {
-    if(!manifold_info_initialized_) init_manifold_info();
-
-#ifdef CGAL_LINKED_WITH_TBB
-    typename Edge_facet_counter::const_accessor accessor;
-    if(!edge_facet_counter_.find(accessor,
-                                 this->make_ordered_pair(edge)))
-      return NOT_IN_COMPLEX;
-    switch(accessor->second)
-#else // not CGAL_LINKED_WITH_TBB
-    switch(edge_facet_counter_[this->make_ordered_pair(edge)])
-#endif // not CGAL_LINKED_WITH_TBB
-    {
-    case 0: return NOT_IN_COMPLEX;
-    case 1: return BOUNDARY;
-    case 2: return REGULAR;
-    default: return SINGULAR;
-    }
-  }
-
-  /// Returns true if the vertex \c v has is incident to at least a facet
-  /// of the complex
-  bool has_incident_facets_in_complex(const Vertex_handle& v) const
-  {
-    if(!manifold_info_initialized_) init_manifold_info();
-    return v->cached_number_of_incident_facets() > 0;
-  }
-
-  /// Returns true if facet \c facet is in complex
-  bool is_in_complex(const Facet& facet) const
-  {
-    return is_in_complex(facet.first, facet.second);
-  }
-
-  /// Returns true if facet (\c cell, \c i) is in 2D complex
-  bool is_in_complex(const Cell_handle& cell, const int i) const
-  {
-    return ( cell->is_facet_on_surface(i) );
-  }
-
-  /// Returns surface index of facet \c f
-  Surface_patch_index surface_patch_index(const Facet& f) const
-  {
-    return surface_patch_index(f.first,f.second);
-  }
-
-  /// Returns surface index of facet(\c cell, \c i)
-  Surface_patch_index surface_patch_index(const Cell_handle& cell,
-                                          const int i) const
-  {
-    return cell->surface_patch_index(i);
-  }
-
-  /// Returns the number of surface facets of the mesh
-  size_type number_of_facets_in_complex() const { return number_of_facets_; }
-
-  /// Adds cell \c cell to the 3D complex, with subdomain index \c index
-  void add_to_complex(const Cell_handle& cell, const Subdomain_index& index)
-  {
-    CGAL_precondition( !( index == Subdomain_index() ) );
-
-    if ( ! is_in_complex(cell) )
-    {
-      set_subdomain_index(cell, index);
-      ++number_of_cells_;
-    }
-  }
-
-  /// Removes cell \c cell from the 3D complex
-  void remove_from_complex(const Cell_handle& cell)
-  {
-    if ( is_in_complex(cell) )
-    {
-      set_subdomain_index(cell, Subdomain_index());
-      --number_of_cells_;
-    }
-  }
-
-
-  /// Sets subdomain index of cell \c cell to \c index
-  void set_subdomain_index(const Cell_handle& cell,
-                           const Subdomain_index& index) const
-  {
-    cell->set_subdomain_index(index);
-  }
-
-  /// Sets index of vertex \c vertex to \c index
-  void set_index(const Vertex_handle& vertex, const Index& index) const
-  {
-    vertex->set_index(index);
-  }
-
-  /// Sets dimension of vertex \c vertex to \c dimension
-  void set_dimension(const Vertex_handle& vertex, int dimension) const
-  {
-    vertex->set_dimension(dimension);
-  }
-
-  /// Returns the number of cells which belongs to the 3D complex
-  size_type number_of_cells_in_complex() const
-  {
-    return number_of_cells_;
-  }
-
-  /// Returns \c true if cell \c cell belongs to the 3D complex
-  bool is_in_complex(const Cell_handle& cell) const
-  {
-    return !( subdomain_index(cell) == Subdomain_index() );
-  }
-
-  /// Returns the subdomain index of cell \c cell
-  Subdomain_index subdomain_index(const Cell_handle& cell) const
-  {
-    return cell->subdomain_index();
-  }
-
-  /// Returns the dimension of the lowest dimensional face of the input 3D
-  /// complex that contains the vertex
-  int in_dimension(const Vertex_handle& v) const { return v->in_dimension(); }
-
-  /// Returns the index of vertex \c v
-  Index index(const Vertex_handle& v) const { return v->index(); }
-
-  /// Outputs the mesh to medit
-  void output_to_medit(std::ostream& os,
-                       bool rebind = true,
-                       bool show_patches = false) const
-  {
-    // Call global function
-    CGAL::IO::output_to_medit(os,*this,rebind,show_patches);
-  }
-
-  /// Outputs the mesh to maya
-  void output_to_maya(std::ostream& os,
-                      bool surfaceOnly = true) const
-  {
-    // Call global function
-    CGAL::IO::output_to_maya(os,*this,surfaceOnly);
-  }
-
-  //-------------------------------------------------------
-  // Undocumented features
-  //-------------------------------------------------------
-  /**
-   * @brief insert \c [first,last[ in the triangulation (with dimension 2)
-   * @param first the iterator on the first point to insert
-   * @param last the iterator past the last point to insert
-   *
-   * InputIterator value type must be \c std::pair<Tr::Point,Index>
-   */
-  template <typename InputIterator>
-  void insert_surface_points(InputIterator first, InputIterator last)
-  {
-    typename Tr::Geom_traits::Construct_weighted_point_3 cwp =
-      tr_.geom_traits().construct_weighted_point_3_object();
-
-    while ( first != last )
-    {
-      Vertex_handle vertex = tr_.insert(cwp((*first).first));
-      vertex->set_index((*first).second);
-      vertex->set_dimension(2);
-      ++first;
-    }
-  }
-
-  /**
-   * @brief insert \c [first,last[ in the triangulation (with dimension 2 and
-   * index \c default_index)
-   * @param first the iterator on the first point to insert
-   * @param last the iterator past the last point to insert
-   * @param default_index the index to be used to insert points
-   *
-   * InputIterator value type must be \c Tr::Point
-   */
-  template <typename InputIterator>
-  void insert_surface_points(InputIterator first,
-                             InputIterator last,
-                             const Index& default_index)
-  {
-    typename Tr::Geom_traits::Construct_weighted_point_3 cwp =
-      tr_.geom_traits().construct_weighted_point_3_object();
-
-    while ( first != last )
-    {
-      Vertex_handle vertex = tr_.insert(cwp(*first));
-      vertex->set_index(default_index);
-      vertex->set_dimension(2);
-      ++first;
-    }
-  }
-
-  /// Swaps this & rhs
-  void swap(Self& rhs)
-  {
-    Swap_elements<Concurrency_tag> swapper;
-    swapper(rhs.number_of_facets_, number_of_facets_);
-    tr_.swap(rhs.tr_);
-    swapper(rhs.number_of_cells_, number_of_cells_);
-  }
-
-  /// Returns bbox
-  Bbox_3 bbox() const;
-
-  void clear_cells_and_facets_from_c3t3() {
-    for(typename Tr::Finite_cells_iterator
-          cit = this->triangulation().finite_cells_begin(),
-          end = this->triangulation().finite_cells_end();
-        cit != end; ++cit)
-    {
-      set_subdomain_index(cit, Subdomain_index());
-    }
-    this->number_of_cells_ = 0;
-    for(typename Tr::Finite_facets_iterator
-          fit = this->triangulation().finite_facets_begin(),
-          end = this->triangulation().finite_facets_end();
-        fit != end; ++fit)
-    {
-      Facet facet = *fit;
-      set_surface_patch_index(facet.first, facet.second, Surface_patch_index());
-      if(this->triangulation().dimension() > 2) {
-        Facet mirror = tr_.mirror_facet(facet);
-        set_surface_patch_index(mirror.first, mirror.second, Surface_patch_index());
-      }
-    }
-    this->number_of_facets_ = 0;
-    clear_manifold_info();
-  }
-
-  void clear_manifold_info() {
-    edge_facet_counter_.clear();
-    manifold_info_initialized_ = false;
-  }
-
-private:
-  void init_manifold_info() const {
-    for(typename Tr::All_vertices_iterator
-          vit = triangulation().finite_vertices_begin(),
-          end = triangulation().finite_vertices_end();
-        vit != end; ++vit)
-    {
-      vit->set_c2t3_cache(0, (std::numeric_limits<size_type>::max)());
-    }
-
-    edge_facet_counter_.clear();
-
-    for(typename Tr::Finite_facets_iterator
-          fit = triangulation().finite_facets_begin(),
-          end = triangulation().finite_facets_end();
-        fit != end; ++fit)
-    {
-      if ( is_in_complex(*fit) ) {
-        const Cell_handle cell = fit->first;
-        const int i = fit->second;
-        for(int j = 0; j < 3; ++j)
-        {
-          const int edge_index_va = tr_.vertex_triple_index(i, j);
-          const int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j+1));
-          const Vertex_handle edge_va = cell->vertex(edge_index_va);
-          const Vertex_handle edge_vb = cell->vertex(edge_index_vb);
-#ifndef CGAL_LINKED_WITH_TBB
-          ++edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
-#else // CGAL_LINKED_WITH_TBB
-          {
-            typename Edge_facet_counter::accessor accessor;
-            edge_facet_counter_.insert(accessor,
-                                       this->make_ordered_pair(edge_va, edge_vb));
-            ++accessor->second;
-          }
-#endif // CGAL_LINKED_WITH_TBB
-
-          const std::size_t n = edge_va->cached_number_of_incident_facets();
-          edge_va->set_c2t3_cache(n+1, (std::numeric_limits<size_type>::max)());
-        }
-      }
-    }
-    manifold_info_initialized_ = true;
-  }
-
-  /// Extract the subset `F` of facets of the complex incident to `v` and
-  /// return the number of connected component of the adjacency graph of `F`.
-  std::size_t union_find_of_incident_facets(const Vertex_handle v) const
-  {
-    if( v->is_c2t3_cache_valid() )
-    {
-      const std::size_t n = v->cached_number_of_components();
-      if(n != (std::numeric_limits<size_type>::max)()) return n;
-    }
-
-    Union_find<Facet> facets;
-    { // fill the union find
-      std::vector<Facet> non_filtered_facets;
-      if(tr_.is_parallel()) {
-        tr_.incident_facets_threadsafe(v, std::back_inserter(non_filtered_facets));
-      } else {
-        tr_.incident_facets(v, std::back_inserter(non_filtered_facets));
-      }
-
-      for(typename std::vector<Facet>::iterator
-            fit = non_filtered_facets.begin(),
-            end = non_filtered_facets.end();
-          fit != end; ++fit)
-      {
-        if(is_in_complex(*fit)) facets.push_back(*fit);
-      }
-    }
-
-    typedef boost::unordered_map<Vertex_handle,
-                                 typename Union_find<Facet>::handle,
-                                 Hash_fct>    Vertex_set_map;
-    typedef typename Vertex_set_map::iterator Vertex_set_map_iterator;
-
-    Vertex_set_map vsmap;
-
-    for(typename Union_find<Facet>::iterator
-          it = facets.begin(), end = facets.end();
-        it != end; ++it)
-    {
-      const Cell_handle& ch = (*it).first;
-      const int& i = (*it).second;
-      for(int j=0; j < 3; ++j) {
-        const Vertex_handle w = ch->vertex(tr_.vertex_triple_index(i,j));
-        if(w != v){
-          Vertex_set_map_iterator vsm_it = vsmap.find(w);
-          if(vsm_it != vsmap.end()){
-            facets.unify_sets(vsm_it->second, it);
-          } else {
-            vsmap.insert(std::make_pair(w, it));
-          }
-        }
-      }
-    }
-    const std::size_t nb_components = facets.number_of_sets();
-
-    const std::size_t n = v->cached_number_of_incident_facets();
-    v->set_c2t3_cache(n, nb_components);
-    return nb_components;
-  }
-
-  //-------------------------------------------------------
-  // Traversal
-  //-------------------------------------------------------
-private:
-  typedef Mesh_3::internal::Iterator_not_in_complex<Self> Iterator_not_in_complex;
-
-  class Facet_iterator_not_in_complex
-  {
-    const Self* c3t3_;
-    Surface_patch_index index_; //need by SWIG: should be const Surface_patch_index
-  public:
-    Facet_iterator_not_in_complex(){} //need by SWIG
-    Facet_iterator_not_in_complex(const Self& c3t3,
-                                  const Surface_patch_index& index = Surface_patch_index())
-      : c3t3_(&c3t3)
-      , index_(index) { }
-
-    template <typename Iterator>
-    bool operator()(Iterator it) const
-    {
-      if ( index_ == Surface_patch_index() ) { return ! c3t3_->is_in_complex(*it); }
-      else { return !( c3t3_->surface_patch_index(*it) == index_ );  }
-    }
-  };
-
-  /**
-   * @class Cell_not_in_complex
-   * @brief A class to filter cells which do not belong to the complex
-   */
-  class Cell_not_in_complex
-  {
-    const Self* r_self_;
-    Subdomain_index index_;//needed by SWIG, should be const Subdomain_index
-  public:
-    Cell_not_in_complex(){}//needed by SWIG
-    Cell_not_in_complex(const Self& self,
-                        const Subdomain_index& index = Subdomain_index())
-      : r_self_(&self)
-      , index_(index) { }
-
-    bool operator()(Cell_handle ch) const
-    {
-      if ( index_ == Subdomain_index() ) { return !r_self_->is_in_complex(ch); }
-      else { return !( r_self_->subdomain_index(ch) == index_ ); }
-    }
-  }; // end class Cell_not_in_complex
-
-public:
-  /// Iterator type to visit the facets of the 2D complex.
-  typedef Filter_iterator<
-    typename Triangulation::Finite_facets_iterator,
-    Facet_iterator_not_in_complex >               Facets_in_complex_iterator;
-
-  /// Returns a Facets_in_complex_iterator to the first facet of the 2D complex
-  Facets_in_complex_iterator facets_in_complex_begin() const
-  {
-    return CGAL::filter_iterator(tr_.finite_facets_end(),
-                                 Facet_iterator_not_in_complex(*this),
-                                 tr_.finite_facets_begin());
-  }
-
-  /// Returns a Facets_in_complex_iterator to the first facet of the 2D complex
-  Facets_in_complex_iterator
-  facets_in_complex_begin(const Surface_patch_index& index) const
-  {
-    return CGAL::filter_iterator(tr_.finite_facets_end(),
-                                 Facet_iterator_not_in_complex(*this,index),
-                                 tr_.finite_facets_begin());
-  }
-
-  /// Returns past-the-end iterator on facet of the 2D complex
-  Facets_in_complex_iterator facets_in_complex_end(const Surface_patch_index = Surface_patch_index()) const
-  {
-    return CGAL::filter_iterator(tr_.finite_facets_end(),
-                                 Facet_iterator_not_in_complex(*this));
-  }
-
-  /**
-   * @class Cells_in_complex_iterator
-   * @brief Iterator type to visit the cells of triangulation belonging
-   * to the 3D complex
-   *
-   * This class is usefull to ensure that Cells_in_complex_iterator is convertible
-   * to Cell_handle
-   */
-  class Cells_in_complex_iterator :
-    public Filter_iterator<typename Triangulation::Finite_cells_iterator,
-                           Cell_not_in_complex>
-  {
-  private:
-    typedef typename Triangulation::Finite_cells_iterator Tr_iterator;
-    typedef Filter_iterator<typename Triangulation::Finite_cells_iterator,
-                            Cell_not_in_complex> Base;
-    typedef Cells_in_complex_iterator Self;
-
-  public:
-    Cells_in_complex_iterator() : Base() { }
-    Cells_in_complex_iterator(Base i) : Base(i) { }
-
-    Self& operator++() { Base::operator++(); return *this; }
-    Self& operator--() { Base::operator--(); return *this; }
-    Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
-    Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
-
-    operator Cell_handle() const { return Cell_handle(this->base()); }
-  }; // end class Cells_in_complex_iterator
-
-
-  /// Returns a \c Cells_in_complex_iterator to the first cell of the 3D complex
-  Cells_in_complex_iterator cells_in_complex_begin() const
-  {
-    return CGAL::filter_iterator(tr_.finite_cells_end(),
-                                 Cell_not_in_complex(*this),
-                                 tr_.finite_cells_begin());
-  }
-
-  /// Returns a \c Cells_in_complex_iterator to the first cell of the 3D complex
-  Cells_in_complex_iterator
-  cells_in_complex_begin(const Subdomain_index& index) const
-  {
-    return CGAL::filter_iterator(tr_.finite_cells_end(),
-                                 Cell_not_in_complex(*this,index),
-                                 tr_.finite_cells_begin());
-  }
-
-  /// Returns the past-the-end iterator for the cells of the 3D complex
-  Cells_in_complex_iterator cells_in_complex_end() const
-  {
-    return CGAL::filter_iterator(tr_.finite_cells_end(),
-                                 Cell_not_in_complex(*this));
-  }
-
-  // -----------------------------------
-  // Backward Compatibility
-  // -----------------------------------
-#ifndef CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
-  typedef Surface_patch_index   Surface_index;
-
-  void set_surface_index(const Facet& f, const Surface_index& index)
-  { set_surface_patch_index(f, index); }
-
-  void set_surface_index(const Cell_handle& c, const int i, const Surface_index& index)
-  { set_surface_patch_index(c,i,index); }
-
-  Surface_index surface_index(const Facet& f) const
-  { return surface_patch_index(f); }
-
-  Surface_index surface_index(const Cell_handle& c, const int i) const
-  { return surface_patch_index(c,i); }
-#endif // CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
-
-#ifndef CGAL_MESH_3_NO_DEPRECATED_C3T3_ITERATORS
-  typedef Facets_in_complex_iterator  Facet_iterator;
-  typedef Cells_in_complex_iterator   Cell_iterator;
-
-  Facet_iterator facets_begin() const
-  { return facets_in_complex_begin(); }
-
-  Facet_iterator facets_end() const
-  { return facets_in_complex_end(); }
-
-  Cell_iterator cells_begin() const
-  { return cells_in_complex_begin(); }
-
-  Cell_iterator cells_end() const
-  { return cells_in_complex_end(); }
-#endif // CGAL_MESH_3_NO_DEPRECATED_C3T3_ITERATORS
-  // -----------------------------------
-  // End backward Compatibility
-  // -----------------------------------
-
-  size_type number_of_facets() const
-  { return number_of_facets_in_complex(); }
-
-  size_type number_of_cells() const
-  { return number_of_cells_in_complex(); }
-
-public:
-  template <typename Tr2, typename Ct2>
-  friend
-  std::istream &
-  operator>> (std::istream& is,
-              Mesh_complex_3_in_triangulation_3_base<Tr2,Ct2> &c3t3);
-
-  void rescan_after_load_of_triangulation();
-
-  static
-  std::string io_signature()
-  {
-    return
-      Get_io_signature<Tr>()();
-  }
-private:
-
-  // Sequential: non-atomic
-  // "dummy" is here to allow the specialization (see below)
-  // See http://groups.google.com/group/comp.lang.c++.moderated/browse_thread/thread/285ab1eec49e1cb6
-  template<typename Concurrency_tag2, typename dummy = void>
-  struct Number_of_elements
-  {
-    typedef size_type type;
-  };
-
-  template<typename Concurrency_tag2, typename dummy = void>
-  struct Init_number_of_elements
-  {
-    template<typename T>
-    void operator()(T& a, const T& b)
-    {
-      a = b;
-    }
-    template<typename T>
-    void operator()(T& a)
-    {
-      a = 0;
-    }
-  };
-
-  template<typename Concurrency_tag2, typename dummy = void>
-  struct Swap_elements
-  {
-    template<typename T>
-    void operator()(T& a, T& b)
-    {
-      std::swap(a, b);
-    }
-  };
-#ifdef CGAL_LINKED_WITH_TBB
-  // Parallel: atomic
-  template<typename dummy>
-  struct Number_of_elements<Parallel_tag, dummy>
-  {
-    typedef std::atomic<size_type> type;
-  };
-
-  template<typename dummy>
-  struct Init_number_of_elements<Parallel_tag, dummy>
-  {
-    template<typename T>
-    void operator()(T& a, const T& b)
-    {
-      a = b.load();
-    }
-    template<typename T>
-    void operator()(T& a)
-    {
-      a = 0;
-    }
-  };
-
-  template<typename dummy>
-  struct Swap_elements<Parallel_tag, dummy>
-  {
-    template<typename T>
-    void operator()(T& a, T& b)
-    {
-      T tmp;
-      tmp.exchange(a);
-      a.exchange(b);
-      b.exchange(tmp);
-    }
-  };
-#endif // CGAL_LINKED_WITH_TBB
-
-  // Private date members
-  Triangulation tr_;
-
-  typedef typename Base::Pair_of_vertices Pair_of_vertices;
-#ifdef CGAL_LINKED_WITH_TBB
-  typedef tbb::concurrent_hash_map<Pair_of_vertices, int,
-                                   Hash_compare_for_TBB> Edge_facet_counter;
-#else // not CGAL_LINKED_WITH_TBB
-  typedef std::map<Pair_of_vertices, int> Edge_facet_counter;
-#endif // not CGAL_LINKED_WITH_TBB
-
-  mutable Edge_facet_counter edge_facet_counter_;
-
-  typename Number_of_elements<Concurrency_tag>::type number_of_facets_;
-  typename Number_of_elements<Concurrency_tag>::type number_of_cells_;
-
-  mutable bool manifold_info_initialized_;
-};  // end class Mesh_complex_3_in_triangulation_3_base
-
-
-template <typename Tr, typename Ct>
-void
-Mesh_complex_3_in_triangulation_3_base<Tr,Ct>::add_to_complex(
-    const Cell_handle& cell,
-    const int i,
-    const Surface_patch_index& index)
-{
-  CGAL_precondition( !( index == Surface_patch_index() ) );
-
-  if ( ! is_in_complex(cell,i) )
-  {
-    Facet mirror = tr_.mirror_facet(std::make_pair(cell,i));
-    set_surface_patch_index(cell, i, index);
-    set_surface_patch_index(mirror.first, mirror.second, index);
-    ++number_of_facets_;
-    if(manifold_info_initialized_) {
-      for(int j = 0; j < 3; ++j)
-      {
-        int edge_index_va = tr_.vertex_triple_index(i, j);
-        int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j+1));
-        Vertex_handle edge_va = cell->vertex(edge_index_va);
-        Vertex_handle edge_vb = cell->vertex(edge_index_vb);
-#ifdef CGAL_LINKED_WITH_TBB
-        {
-          typename Edge_facet_counter::accessor accessor;
-          edge_facet_counter_.insert(accessor,
-                                     this->make_ordered_pair(edge_va, edge_vb));
-          ++accessor->second;
-        }
-#else // not CGAL_LINKED_WITH_TBB
-        ++edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
-#endif // not CGAL_LINKED_WITH_TBB
-
-        const std::size_t n = edge_va->cached_number_of_incident_facets();
-        const std::size_t m = edge_va->cached_number_of_components();
-        edge_va->set_c2t3_cache(n+1, m);
-      }
-      const int dimension_plus_1 = tr_.dimension() + 1;
-      // update c2t3 for vertices of f
-      for (int j = 0; j < dimension_plus_1; j++) {
-        if (j != i) {
-#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-          if(cell->vertex(j)->is_c2t3_cache_valid())
-            std::cerr << "(" << tr_.point(cell, j) << ")->invalidate_c2t3_cache()\n";
-#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-          cell->vertex(j)->invalidate_c2t3_cache();
-        }
-      }
-    }
-  }
-}
-
-
-template <typename Tr, typename Ct>
-void
-Mesh_complex_3_in_triangulation_3_base<Tr,Ct>::remove_from_complex(const Facet& facet)
-{
-  if ( is_in_complex(facet) )
-  {
-    Facet mirror = tr_.mirror_facet(facet);
-    set_surface_patch_index(facet.first, facet.second, Surface_patch_index());
-    set_surface_patch_index(mirror.first, mirror.second, Surface_patch_index());
-    --number_of_facets_;
-    if(manifold_info_initialized_) {
-      const Cell_handle cell = facet.first;
-      const int i = facet.second;
-      for(int j = 0; j < 3; ++j)
-      {
-        const int edge_index_va = tr_.vertex_triple_index(i, j);
-        const int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j+1));
-        const Vertex_handle edge_va = cell->vertex(edge_index_va);
-        const Vertex_handle edge_vb = cell->vertex(edge_index_vb);
-#ifdef CGAL_LINKED_WITH_TBB
-        {
-          typename Edge_facet_counter::accessor accessor;
-          edge_facet_counter_.insert(accessor,
-                                     this->make_ordered_pair(edge_va, edge_vb));
-          --accessor->second;
-        }
-#else // not CGAL_LINKED_WITH_TBB
-        --edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
-#endif // not CGAL_LINKED_WITH_TBB
-
-        const std::size_t n = edge_va->cached_number_of_incident_facets();
-        CGAL_assertion(n>0);
-        const std::size_t m = edge_va->cached_number_of_components();
-        edge_va->set_c2t3_cache(n-1, m);
-      }
-      const int dimension_plus_1 = tr_.dimension() + 1;
-      // update c2t3 for vertices of f
-      for (int j = 0; j < dimension_plus_1; j++) {
-        if (j != facet.second) {
-#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-          if(cell->vertex(j)->is_c2t3_cache_valid())
-            std::cerr << "(" << tr_.point(cell, j) << ")->invalidate_c2t3_cache()\n";
-#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
-          cell->vertex(j)->invalidate_c2t3_cache();
-        }
-      }
-    }
-  }
-}
-
-
-// -----------------------------------
-// Undocumented
-// -----------------------------------
-template <typename Tr, typename Ct>
-Bbox_3
-Mesh_complex_3_in_triangulation_3_base<Tr,Ct>::
-bbox() const
-{
-  if ( 0 == triangulation().number_of_vertices() )
-  {
-    return Bbox_3();
-  }
-
-  typename Tr::Finite_vertices_iterator vit = tr_.finite_vertices_begin();
-  Bbox_3 result = tr_.point(vit++).bbox();
-
-  for(typename Tr::Finite_vertices_iterator end = tr_.finite_vertices_end();
-      vit != end ; ++vit)
-  {
-    result = result + tr_.point(vit).bbox();
-  }
-
-  return result;
-}
-
-template <typename Tr, typename Ct>
-std::ostream &
-operator<< (std::ostream& os,
-            const Mesh_complex_3_in_triangulation_3_base<Tr,Ct> &c3t3)
-{
-  return os << c3t3.triangulation();
-}
-
-
-template <typename Tr, typename Ct>
-std::istream &
-operator>> (std::istream& is,
-            Mesh_complex_3_in_triangulation_3_base<Tr,Ct> &c3t3)
-{
-  c3t3.clear();
-  is >> c3t3.triangulation();
-
-  if(!is) {
-    c3t3.clear();
-    return is;
-  }
-
-  c3t3.rescan_after_load_of_triangulation();
-  return is;
-}
-
-template <typename Tr, typename Ct>
-void
-Mesh_complex_3_in_triangulation_3_base<Tr,Ct>::
-rescan_after_load_of_triangulation() {
-  this->number_of_facets_ = 0;
-  for(typename Tr::Finite_facets_iterator
-        fit = this->triangulation().finite_facets_begin(),
-        end = this->triangulation().finite_facets_end();
-      fit != end; ++fit)
-  {
-    if ( this->is_in_complex(*fit) ) {
-      ++this->number_of_facets_;
-    }
-  }
-
-  this->number_of_cells_ = 0;
-  for(typename Tr::Finite_cells_iterator
-        cit = this->triangulation().finite_cells_begin(),
-        end = this->triangulation().finite_cells_end();
-      cit != end; ++cit)
-  {
-    if ( this->is_in_complex(cit) ) {
-      ++this->number_of_cells_;
-    }
-  }
-}
-
-}  // end namespace Mesh_3
-}  // end namespace CGAL
-
-#include <CGAL/enable_warnings.h>
-
-#endif // CGAL_MESH_3_MESH_COMPLEX_3_IN_TRIANGULATION_3_BASE_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesh_surface_cell_base_3.h b/Mesh_3/include/CGAL/Mesh_3/Mesh_surface_cell_base_3.h
index 3e5437c8244..f0db722f898 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesh_surface_cell_base_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesh_surface_cell_base_3.h
@@ -18,13 +18,13 @@
 #ifndef CGAL_MESH_3_MESH_SURFACE_CELL_BASE_3_H
 #define CGAL_MESH_3_MESH_SURFACE_CELL_BASE_3_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 
 #include <CGAL/Mesh_3/config.h>
 
 #include <CGAL/Regular_triangulation_cell_base_3.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 
 #ifdef CGAL_LINKED_WITH_TBB
 # include <atomic>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
index 2ba606c5de3..1a13e725a44 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
@@ -36,7 +36,7 @@
 
 #include <CGAL/Mesh_error_code.h>
 
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #include <CGAL/Mesh_3/Refine_facets_3.h>
 #include <CGAL/Mesh_3/Refine_facets_manifold_base.h>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
index e7877ab6635..767240429c2 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
@@ -28,11 +28,11 @@
 #include <CGAL/disable_warnings.h>
 #include <CGAL/Mesh_3/config.h>
 
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #ifdef CGAL_MESH_3_DUMP_FEATURES_PROTECTION_ITERATIONS
 #  include <CGAL/IO/File_binary_mesh_3.h>
 #endif
-#include <CGAL/Mesh_3/utilities.h>
+#include <CGAL/SMDS_3/utilities.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 #include <CGAL/iterator.h>
 #include <CGAL/Mesh_error_code.h>
@@ -108,7 +108,7 @@ void debug_dump_c3t3(const std::string filename, const C3t3& c3t3)
 
 template <typename C3T3, typename MeshDomain, typename SizingFunction>
 class Protect_edges_sizing_field
-  : public CGAL::Mesh_3::internal::Debug_messages_tools
+  : public CGAL::SMDS_3::internal::Debug_messages_tools
 {
   typedef Protect_edges_sizing_field          Self;
 
diff --git a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
index eef04d11b70..2f0db096e09 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
@@ -38,7 +38,7 @@
 #ifdef CGAL_MESH_3_PROFILING
   #include <CGAL/Mesh_3/Profiling_tools.h>
 #endif
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #include <CGAL/Object.h>
 
diff --git a/Mesh_3/include/CGAL/Mesh_3/config.h b/Mesh_3/include/CGAL/Mesh_3/config.h
index ccb05647ef5..6fc06788902 100644
--- a/Mesh_3/include/CGAL/Mesh_3/config.h
+++ b/Mesh_3/include/CGAL/Mesh_3/config.h
@@ -12,21 +12,20 @@
 #ifndef CGAL_MESH_3_CONFIG_H
 #define CGAL_MESH_3_CONFIG_H 1
 
-#include <CGAL/license/Triangulation_3.h>
-
+#include <CGAL/license/Mesh_3.h>
 
 #include <CGAL/config.h>
 
 //#define CGAL_MESH_3_VERBOSE 1
 
 // Use optimisations of Mesh_3
-#  define CGAL_INTRUSIVE_LIST 1
 #  define CGAL_CONSTRUCT_INTRUSIVE_LIST_RANGE_CONSTRUCTOR 1
 #  define CGAL_MESH_3_NEW_GET_FACETS 1
 #  define CGAL_MESH_3_GET_FACETS_USING_INTRUSIVE_LIST 1
 #  define CGAL_MESH_3_SIZING_FIELD_INEXACT_LOCATE 1
 #  define FORCE_STRUCTURAL_FILTERING 1
 #  define CGAL_NEW_INCIDENT_SLIVERS 1
+#  define CGAL_INTRUSIVE_LIST 1
 
 //experimental
 #  define CGAL_FASTER_BUILD_QUEUE 1
diff --git a/Mesh_3/include/CGAL/Mesh_3/internal/check_weights.h b/Mesh_3/include/CGAL/Mesh_3/internal/check_weights.h
index 2b8a505d725..4d228953ad5 100644
--- a/Mesh_3/include/CGAL/Mesh_3/internal/check_weights.h
+++ b/Mesh_3/include/CGAL/Mesh_3/internal/check_weights.h
@@ -22,7 +22,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/tags.h>
-#include <CGAL/Mesh_3/Has_features.h>
+#include <CGAL/SMDS_3/Has_features.h>
 #include <boost/type_traits/is_same.hpp>
 
 namespace CGAL {
diff --git a/Mesh_3/include/CGAL/Mesh_3/io_signature.h b/Mesh_3/include/CGAL/Mesh_3/io_signature.h
index 2c0f02ab3b0..5b43ac9c69b 100644
--- a/Mesh_3/include/CGAL/Mesh_3/io_signature.h
+++ b/Mesh_3/include/CGAL/Mesh_3/io_signature.h
@@ -13,351 +13,8 @@
 #ifndef CGAL_MESH_3_IO_SIGNATURE_H
 #define CGAL_MESH_3_IO_SIGNATURE_H
 
-#include <CGAL/license/Triangulation_3.h>
-
-#define CGAL_MESH_3_IO_H // the old include macro, tested by other files
-
-#include <CGAL/Point_3.h>
-#include <CGAL/Weighted_point_3.h>
-#include <CGAL/Delaunay_triangulation_3.h>
-#include <CGAL/Triangulation_vertex_base_3.h>
-#include <CGAL/Triangulation_vertex_base_with_info_3.h>
-#include <CGAL/Triangulation_cell_base_3.h>
-#include <CGAL/Triangulation_cell_base_with_info_3.h>
-#include <CGAL/Regular_triangulation_3.h>
-#include <CGAL/Regular_triangulation_cell_base_3.h>
-#include <CGAL/Regular_triangulation_cell_base_with_weighted_circumcenter_3.h>
-
-#ifdef CGAL_PERIODIC_3_MESH_3_CONFIG_H
-#include <CGAL/Periodic_3_triangulation_3.h>
-#include <CGAL/Periodic_3_regular_triangulation_3.h>
-#endif
-
-#include <boost/variant.hpp>
-#include <boost/tuple/tuple.hpp>
-#include <utility>
-
-namespace CGAL {
-
-// SFINAE test
-template <typename T, typename U>
-class has_io_signature
-{
-private:
-  template <U> struct helper;
-  template <typename V> static char check(helper<&V::io_signature> *);
-  template <typename V> static char (&check(...))[2];
-
-public:
-  enum { value = (sizeof(check<T>(0)) == sizeof(char)) };
-};
-
-template <class T, bool has_io_signature>
-struct Get_io_signature_aux
-{
-  std::string operator() () const
-  {
-    return T::io_signature();
-  }
-}; // end struct template Get_io_signature_aux
-
-template <class T>
-struct Get_io_signature_aux<T, false>
-{
-  std::string operator()() const
-  {
-    std::cerr << "Type without signature: " << typeid(T).name() << std::endl;
-    return std::string();
-  }
-}; // end template partial specialization Get_io_signature_aux<T, false>
-
-
-template <class T>
-struct Get_io_signature
-  : public Get_io_signature_aux<
-  T,
-  (has_io_signature<T, std::string (T::*)() >::value ||
-   has_io_signature<T, std::string (T::*)() const >::value ||
-   has_io_signature<T, std::string (*)() >::value )  // signature for
-                                                     // static mem func
-  >
-{
-};
-
-template <>
-struct Get_io_signature<int>
-{
-  std::string operator()() {
-    return "i";
-  }
-};
-
-template <>
-struct Get_io_signature<unsigned int>
-{
-  std::string operator()() {
-    return "ui";
-  }
-};
-
-template <>
-struct Get_io_signature<char>
-{
-  std::string operator()() {
-    return "c";
-  }
-};
-
-template <>
-struct Get_io_signature<unsigned char>
-{
-  std::string operator()() {
-    return "uc";
-  }
-};
-
-template <>
-struct Get_io_signature<signed char>
-{
-  std::string operator()() {
-    return "sc";
-  }
-};
-
-template <>
-struct Get_io_signature<short int>
-{
-  std::string operator()() {
-    return "s";
-  }
-};
-
-template <>
-struct Get_io_signature<unsigned short int>
-{
-  std::string operator()() {
-    return "us";
-  }
-};
-
-template <>
-struct Get_io_signature<double>
-{
-  std::string operator()() {
-    return "d";
-  }
-};
-
-template <typename T, typename U>
-struct Get_io_signature<boost::variant<T,U> >
-{
-    std::string operator()() {
-      return std::string("boost::variant<") +
-        Get_io_signature<T>()() + "," +
-        Get_io_signature<U>()() + ">";
-  }
-};
-
-template <typename T, typename U>
-struct Get_io_signature<std::pair<T,U> >
-{
-    std::string operator()() {
-      return std::string("std::pair<") +
-        Get_io_signature<T>()() + "," +
-        Get_io_signature<U>()() + ">";
-  }
-};
-
-template <typename T, typename U>
-struct Get_io_signature<boost::tuple<T,U> >
-{
-    std::string operator()() {
-      return std::string("std::pair<") +
-        Get_io_signature<T>()() + "," +
-        Get_io_signature<U>()() + ">";
-  }
-};
-
-template <typename T, typename U, typename V>
-struct Get_io_signature<boost::variant<T,U,V> >
-{
-    std::string operator()() {
-      return std::string("boost::variant<") +
-        Get_io_signature<T>()() + "," +
-        Get_io_signature<U>()() + "," +
-        Get_io_signature<V>()() + ">";
-  }
-};
-
-template <typename T, typename U,
-          typename V, typename W>
-struct Get_io_signature<boost::variant<T,U,V,W> >
-{
-    std::string operator()() {
-      return std::string("boost::variant<") +
-        Get_io_signature<T>()() + "," +
-        Get_io_signature<U>()() + "," +
-        Get_io_signature<V>()() + "," +
-        Get_io_signature<W>()() + ">";
-  }
-};
-
-template <class Kernel>
-struct Get_io_signature<Point_3<Kernel> >
-{
-  std::string operator()() {
-    return "Point_3";
-  }
-};
-
-template <class K>
-struct Get_io_signature<Weighted_point_3<K> >
-{
-  std::string operator()() {
-    return std::string("Weighted_point<") + Get_io_signature<Point_3<K> >()() + ">";
-  }
-};
-
-#ifdef CGAL_TRIANGULATION_3_H
-template <class Gt, class Tds>
-struct
-Get_io_signature<Triangulation_3<Gt, Tds > >
-{
-  std::string operator()() {
-    return std::string("Triangulation_3(") +
-      Get_io_signature<typename Tds::Vertex::Point>()() +
-      ",Vb(" + Get_io_signature<typename Tds::Vertex>()() +
-      "),Cb(" + Get_io_signature<typename Tds::Cell>()() +
-      "))";
-  }
-};
-#endif
-
-#ifdef CGAL_DELAUNAY_TRIANGULATION_3_H
-template <class Gt, class Tds>
-struct
-Get_io_signature<Delaunay_triangulation_3<Gt, Tds> >
-{
-  std::string operator()() {
-    return Get_io_signature<Triangulation_3<Gt, Tds> >()();
-  }
-};
-#endif
-
-#ifdef CGAL_REGULAR_TRIANGULATION_3_H
-template <class Gt, class Tds>
-struct
-Get_io_signature<Regular_triangulation_3<Gt, Tds> >
-{
-  std::string operator()() {
-    return Get_io_signature<Triangulation_3<Gt, Tds> >()();
-  }
-};
-#endif
-
-#ifdef CGAL_PERIODIC_3_TRIANGULATION_3_H
-template <class Gt, class Tds>
-struct
-Get_io_signature<Periodic_3_triangulation_3<Gt, Tds> >
-{
-  std::string operator()() {
-    return std::string("Periodic_3_triangulation_3(") +
-      Get_io_signature<typename Tds::Vertex::Point>()() +
-      ",Vb(" + Get_io_signature<typename Tds::Vertex>()() +
-      "),Cb(" + Get_io_signature<typename Tds::Cell>()() +
-      "))";
-  }
-};
-#endif
-
-#ifdef CGAL_PERIODIC_3_REGULAR_TRIANGULATION_3_H
-template <class Gt, class Tds>
-struct
-Get_io_signature<Periodic_3_regular_triangulation_3<Gt, Tds> >
-{
-  std::string operator()() {
-    return Get_io_signature<Periodic_3_triangulation_3<Gt, Tds> >()();
-  }
-};
-#endif
-
-#ifdef CGAL_TRIANGULATION_VERTEX_BASE_3_H
-template <class Gt, class Vb>
-struct Get_io_signature<Triangulation_vertex_base_3<Gt, Vb> >
-{
-  std::string operator()() {
-    return "Tvb_3";
-  }
-};
-#endif
-
-#ifdef CGAL_REGULAR_TRIANGULATION_VERTEX_BASE_3_H
-template <class Gt, class Vb>
-struct Get_io_signature<Regular_triangulation_vertex_base_3<Gt, Vb> >
-{
-  // identical to Triangulation_vertex_base_3
-  std::string operator()() {
-    return "Tvb_3";
-  }
-};
-#endif
-
-#ifdef CGAL_TRIANGULATION_VERTEX_BASE_WITH_INFO_3_H
-template <class Info, class Gt, class Vb>
-struct
-Get_io_signature<Triangulation_vertex_base_with_info_3<Info, Gt, Vb> >
-{
-  std::string operator()() {
-    return Get_io_signature<Vb>()();
-  }
-};
-#endif
-
-#ifdef CGAL_TRIANGULATION_CELL_BASE_3_H
-template <class Gt, class Cb>
-struct
-Get_io_signature<Triangulation_cell_base_3<Gt, Cb> >
-{
-  std::string operator()() {
-    return "Tcb_3";
-  }
-};
-#endif
-
-#ifdef CGAL_TRIANGULATION_CELL_BASE_WITH_INFO_3_H
-template <class Info, class Gt, class Cb>
-struct
-Get_io_signature<Triangulation_cell_base_with_info_3<Info, Gt, Cb> >
-{
-  std::string operator()() {
-    return Get_io_signature<Cb>()();
-  }
-};
-#endif
-
-#ifdef CGAL_REGULAR_TRIANGULATION_CELL_BASE_3_H
-template <class Gt, class Cb, class Container>
-struct
-Get_io_signature<Regular_triangulation_cell_base_3<Gt, Cb, Container> >
-{
-  std::string operator()() {
-    return "RTcb_3";
-  }
-};
-#endif
-
-#ifdef CGAL_REGULAR_TRIANGULATION_CELL_BASE_WITH_CIRCUMCENTER_3_H
-template <class Gt, class Cb>
-struct
-Get_io_signature<Regular_triangulation_cell_base_with_weighted_circumcenter_3<Gt, Cb> >
-{
-  std::string operator()() {
-    return "RTWWCcb_3";
-  }
-};
-#endif
-
-} // end namespace CGAL
+#include <CGAL/license/SMDS_3.h>
 
+#include <CGAL/SMDS_3/io_signature.h>
 
 #endif // CGAL_MESH_3_IO_SIGNATURE_H
diff --git a/Mesh_3/include/CGAL/Mesh_cell_base_3.h b/Mesh_3/include/CGAL/Mesh_cell_base_3.h
index b620a78f86d..787124c3ec7 100644
--- a/Mesh_3/include/CGAL/Mesh_cell_base_3.h
+++ b/Mesh_3/include/CGAL/Mesh_cell_base_3.h
@@ -15,7 +15,7 @@
 #ifndef CGAL_MESH_CELL_BASE_3_H
 #define CGAL_MESH_CELL_BASE_3_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/Mesh_3.h>
 
 
 // #define CGAL_DEPRECATED_HEADER "<CGAL/Mesh_cell_base_3.h>"
@@ -27,7 +27,7 @@
 #include <CGAL/Regular_triangulation_cell_base_3.h>
 #include <CGAL/Regular_triangulation_cell_base_with_weighted_circumcenter_3.h>
 #include <CGAL/Mesh_3/Mesh_surface_cell_base_3.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <CGAL/tags.h>
 
 #include <boost/type_traits/is_convertible.hpp>
@@ -95,14 +95,46 @@ protected:
 // Class Mesh_cell_base_3
 // Cell base class used in 3D meshing process.
 // Adds information to Cb about the cell of the input complex containing it
+/*!
+\ingroup PkgMesh3MeshClasses
+<!-- Meta-comment: this class cannot be deprecated by
+Compact_mesh_cell_base_3, because the latter has a different API.
+-- Laurent Rineau, 2013/10/16
+\deprecated This class is deprecated since \cgal 4.3. Use
+`CGAL::Compact_mesh_cell_base_3<GT,MD,Tds>` instead.
+-->
+
+The class `Mesh_cell_base_3<GT, MD, Cb>` is a model of the concept `MeshCellBase_3`.
+It is designed to serve as cell base class for the 3D triangulation
+used in the 3D mesh generation process.
+
+\tparam GT is the geometric traits class.
+It has to be a model of the concept `MeshTriangulationTraits_3`.
+
+\tparam MD provides the types of indices used to identify
+the faces of the input complex. It has to be a model
+of the concept `MeshDomain_3`.
+
+\tparam Cb is the cell base class. It has to be a model
+of the concept `RegularTriangulationCellBaseWithWeightedCircumcenter_3` and defaults to
+`Regular_triangulation_cell_base_with_weighted_circumcenter_3<GT>`.
+
+\cgalModels `MeshCellBase_3`
+
+\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
+\sa `CGAL::Compact_mesh_cell_base_3<GT, MD, Tds>`
+
+*/
 template< class GT,
   class MD,
   class Cb= CGAL::Regular_triangulation_cell_base_with_weighted_circumcenter_3<
               GT, CGAL::Regular_triangulation_cell_base_3<GT> > >
 class Mesh_cell_base_3
-: public Mesh_3::Mesh_surface_cell_base_3<GT, MD, Cb>,
-  public Mesh_cell_base_3_base<
+: public Mesh_3::Mesh_surface_cell_base_3<GT, MD, Cb>
+#ifndef DOXYGEN_RUNNING
+, public Mesh_cell_base_3_base<
     typename Mesh_3::Mesh_surface_cell_base_3<GT, MD, Cb>::Tds::Concurrency_tag>
+#endif
 {
   typedef typename GT::FT FT;
 
diff --git a/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h b/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
deleted file mode 100644
index b887a6b6223..00000000000
--- a/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
+++ /dev/null
@@ -1,857 +0,0 @@
-// Copyright (c) 2009-2014 INRIA Sophia-Antipolis (France).
-// Copyright (c) 2010-2013 GeometryFactory Sarl (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)     : Stephane Tayeb, Clement Jamin
-//
-//******************************************************************************
-// File Description :
-//******************************************************************************
-
-#ifndef CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
-#define CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
-
-#include <CGAL/license/Triangulation_3.h>
-
-#include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_fwd.h>
-#include <CGAL/disable_warnings.h>
-#include <CGAL/iterator.h>
-#include <CGAL/Mesh_3/utilities.h>
-#include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h>
-#include <CGAL/Mesh_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h>
-#include <CGAL/Time_stamper.h>
-
-#include <boost/bimap/bimap.hpp>
-#include <boost/bimap/multiset_of.hpp>
-#include <CGAL/boost/iterator/transform_iterator.hpp>
-#include <boost/iterator/iterator_adaptor.hpp>
-#include <boost/mpl/if.hpp>
-#include <boost/unordered_map.hpp>
-
-namespace CGAL {
-
-
-template <typename Tr,
-          typename CornerIndex,
-          typename CurveIndex>
-class Mesh_complex_3_in_triangulation_3 :
-  public Mesh_3::Mesh_complex_3_in_triangulation_3_base<
-    Tr, typename Tr::Concurrency_tag>
-  , public CGAL::Mesh_3::internal::Debug_messages_tools
-{
-public:
-  typedef typename Tr::Concurrency_tag                   Concurrency_tag;
-
-private:
-  typedef Mesh_complex_3_in_triangulation_3<
-    Tr,CornerIndex,CurveIndex>                                    Self;
-  typedef Mesh_3::Mesh_complex_3_in_triangulation_3_base<
-                                          Tr,Concurrency_tag>     Base;
-
-public:
-  typedef typename Base::size_type                        size_type;
-
-  typedef typename Tr::Point                              Point;
-  typedef typename Base::Edge                             Edge;
-  typedef typename Base::Facet                            Facet;
-  typedef typename Base::Vertex_handle                    Vertex_handle;
-  typedef typename Base::Cell_handle                      Cell_handle;
-  typedef CornerIndex                                     Corner_index;
-  typedef CurveIndex                                      Curve_index;
-
-  typedef CGAL::Hash_handles_with_or_without_timestamps   Hash_fct;
-
-#ifndef CGAL_NO_DEPRECATED_CODE
-  typedef CurveIndex Curve_segment_index;
-#endif
-
-  typedef typename Base::Triangulation                    Triangulation;
-  typedef typename Base::Subdomain_index                  Subdomain_index;
-
-  using Base::surface_patch_index;
-
-private:
-  // Type to store the edges:
-  //  - a set of std::pair<Vertex_handle,Vertex_handle> (ordered at insertion)
-  //  - which allows fast lookup from one Vertex_handle
-  //  - each element of the set has an associated info (Curve_index) value
-  typedef boost::bimaps::bimap<
-    boost::bimaps::multiset_of<Vertex_handle>,
-    boost::bimaps::multiset_of<Vertex_handle>,
-    boost::bimaps::set_of_relation<>,
-    boost::bimaps::with_info<Curve_index> >           Edge_map;
-
-  typedef typename Edge_map::value_type               Internal_edge;
-
-  // Type to store the corners
-  typedef boost::unordered_map<Vertex_handle,
-                               Corner_index,
-                               Hash_fct>              Corner_map;
-
-  // Type to store far vertices
-  typedef std::vector<Vertex_handle>                  Far_vertices_vec;
-
-public:
-  /**
-   * Constructor
-   */
-  Mesh_complex_3_in_triangulation_3() = default;
-
-  /**
-   * Copy constructor
-   */
-  Mesh_complex_3_in_triangulation_3(const Self& rhs);
-
-  /**
-   * Move constructor
-   */
-  Mesh_complex_3_in_triangulation_3(Self&& rhs)
-    : Base(std::move(rhs))
-    , edges_(std::move(rhs.edges_))
-    , corners_(std::move(rhs.corners_))
-    , far_vertices_(std::move(rhs.far_vertices_))
-  {}
-
-  /**
-   * Assignement operator, also serves as move-assignement
-   */
-  Self& operator=(Self rhs)
-  {
-    swap(rhs);
-    return *this;
-  }
-
-  /**
-   * Swaps this & rhs
-   */
-  void swap(Self& rhs)
-  {
-    Base::swap(rhs);
-    edges_.swap(rhs.edges_);
-    corners_.swap(rhs.corners_);
-    far_vertices_.swap(rhs.far_vertices_);
-  }
-
-  /**
-   * Clears data of c3t3
-   */
-  void clear()
-  {
-    Base::clear();
-    edges_.clear();
-    corners_.clear();
-    far_vertices_.clear();
-  }
-
-  /// Import Base functions
-  using Base::is_in_complex;
-  using Base::add_to_complex;
-  using Base::remove_from_complex;
-  using Base::triangulation;
-  using Base::set_surface_patch_index;
-
-
-
-  /**
-   * Add edge e to complex, with Curve_index index
-   */
-  void add_to_complex(const Edge& e,
-                      const Curve_index& index)
-  {
-    add_to_complex(e.first->vertex(e.second),
-                   e.first->vertex(e.third),
-                   index);
-  }
-
-  /**
-   * Add edge (v1,v2) to complex, with Curve_index index
-   */
-  void add_to_complex(const Vertex_handle& v1,
-                      const Vertex_handle& v2,
-                      const Curve_index& index)
-  {
-    add_to_complex(make_internal_edge(v1,v2), index);
-  }
-
-  /**
-   * Mark vertex \c v as a corner of the complex
-   */
-  void add_to_complex(const Vertex_handle& v, const Corner_index& index)
-  {
-    v->set_dimension(0);
-    corners_.insert(std::make_pair(v,index));
-  }
-
-  /**
-   * Remove edge \c e from complex
-   */
-  void remove_from_complex(const Edge& e)
-  {
-    remove_from_complex(e.first->vertex(e.second), e.first->vertex(e.third));
-  }
-
-  /**
-   * Remove edge (v1,v2) from complex
-   */
-  void remove_from_complex(const Vertex_handle& v1, const Vertex_handle& v2)
-  {
-    remove_from_complex(make_internal_edge(v1,v2));
-  }
-
-  /**
-   * Remove vertex \c v from complex
-   */
-  void remove_from_complex(const Vertex_handle& v)
-  {
-    corners_.erase(v);
-    v->set_dimension(-1);
-  }
-
-  std::size_t number_of_far_points() const
-  {
-    return far_vertices_.size();
-  }
-
-  void add_far_point(const Point &p)
-  {
-    far_vertices_.push_back(triangulation().insert(p));
-  }
-
-  void add_far_point(Vertex_handle vh)
-  {
-    far_vertices_.push_back(vh);
-  }
-
-  void remove_isolated_vertex(Vertex_handle v)
-  {
-    Triangulation& tr = triangulation();
-
-    std::vector<Cell_handle> new_cells;
-    new_cells.reserve(32);
-    tr.remove_and_give_new_cells(v, std::back_inserter(new_cells));
-
-    typename std::vector<Cell_handle>::iterator nc_it = new_cells.begin();
-    typename std::vector<Cell_handle>::iterator nc_it_end = new_cells.end();
-    for (; nc_it != nc_it_end; ++nc_it)
-    {
-      Cell_handle c = *nc_it;
-      for (int i = 0; i < 4; ++i)
-      {
-        Facet mirror_facet = tr.mirror_facet(std::make_pair(c, i));
-        if (is_in_complex(mirror_facet))
-        {
-          set_surface_patch_index(c, i,
-            surface_patch_index(mirror_facet));
-          c->set_facet_surface_center(i,
-            mirror_facet.first->get_facet_surface_center(mirror_facet.second));
-        }
-      }
-      /*int i_inf;
-      if (c->has_vertex(tr.infinite_vertex(), i_inf))
-      {
-        Facet mirror_facet = tr.mirror_facet(std::make_pair(c, i_inf));
-        if (is_in_complex(mirror_facet))
-        {
-          set_surface_patch_index(c, i_inf,
-                                  surface_patch_index(mirror_facet));
-        }
-      }*/
-    }
-  }
-
-  void remove_far_points()
-  {
-    //triangulation().remove(far_vertices_.begin(), far_vertices_.end());
-    typename Far_vertices_vec::const_iterator it = far_vertices_.begin();
-    typename Far_vertices_vec::const_iterator it_end = far_vertices_.end();
-    for ( ; it != it_end ; ++it)
-    {
-      remove_isolated_vertex(*it);
-    }
-    far_vertices_.clear();
-  }
-
-  void remove_isolated_vertices()
-  {
-    Triangulation& tr = triangulation();
-    for (Vertex_handle v : tr.finite_vertex_handles())
-      v->set_meshing_info(0);
-
-    for (typename Base::Cells_in_complex_iterator c = this->cells_in_complex_begin();
-         c != this->cells_in_complex_end();
-         ++c)
-    {
-      for (int i = 0; i < 4; ++i)
-      {
-        Vertex_handle vi = c->vertex(i);
-        vi->set_meshing_info(vi->meshing_info() + 1);
-      }
-    }
-
-    for (typename Base::Facets_in_complex_iterator fit = this->facets_in_complex_begin();
-         fit != this->facets_in_complex_end();
-         ++fit)
-    {
-      Facet f = *fit;
-      for (int i = 1; i < 4; ++i)
-      {
-        Vertex_handle vi = f.first->vertex((f.second + i) % 4);
-        vi->set_meshing_info(vi->meshing_info() + 1);
-      }
-    }
-
-    std::vector<Vertex_handle> isolated;
-    for (Vertex_handle v : tr.finite_vertex_handles())
-    {
-      if (v->meshing_info() == 0.)
-        isolated.push_back(v);
-    }
-
-#ifdef CGAL_MESH_3_VERBOSE
-    std::cout << "Remove " << isolated.size() << " isolated vertices...";
-    std::cout.flush();
-#endif
-
-    CGAL_assertion(far_vertices_.size() <= isolated.size());
-    far_vertices_.clear();
-
-    for (Vertex_handle v : isolated)
-      remove_isolated_vertex(v);
-
-#ifdef CGAL_MESH_3_VERBOSE
-    std::cout << "\nRemove " << isolated.size() << " isolated vertices done." << std::endl;
-#endif
-  }
-
-  /**
-   * Returns the number of edges of c3t3
-   */
-  size_type number_of_edges_in_complex() const
-  {
-    return edges_.size();
-  }
-  size_type number_of_edges() const
-  {
-    return edges_.size();
-  }
-
-  /**
-   * Returns the number of corners of c3t3
-   */
-  size_type number_of_vertices_in_complex() const
-  {
-    return corners_.size();
-  }
-  size_type number_of_corners() const
-  {
-    return corners_.size();
-  }
-
-  void rescan_after_load_of_triangulation();
-
-  /**
-   * Returns true if edge \c e is in complex
-   */
-  bool is_in_complex(const Edge& e) const
-  {
-    return is_in_complex(e.first->vertex(e.second), e.first->vertex(e.third));
-  }
-
-  /**
-   * Returns true if edge (v1,v2) is in C3T3
-   */
-  bool is_in_complex(const Vertex_handle& v1, const Vertex_handle& v2) const
-  {
-    return is_in_complex(make_internal_edge(v1,v2));
-  }
-
-  /**
-   * Returns true if \c v is a 0-dimensionnal feature in the c3t3
-   */
-  bool is_in_complex(const Vertex_handle& v) const
-  {
-    return (corners_.find(v) != corners_.end());
-  }
-
-  /**
-   * Returns Curve_index of edge \c e
-   */
-  Curve_index curve_index(const Edge& e) const
-  {
-    return curve_index(e.first->vertex(e.second),
-                       e.first->vertex(e.third));
-  }
-
-  Curve_index curve_index(const Vertex_handle& v1,
-                          const Vertex_handle& v2) const
-  {
-    return curve_index(make_internal_edge(v1,v2));
-  }
-
-#ifndef CGAL_NO_DEPRECATED_CODE
-  CGAL_DEPRECATED
-  Curve_index curve_segment_index(const Edge& e) const
-  {
-    return curve_index(e);
-  }
-
-  CGAL_DEPRECATED
-  Curve_index curve_segment_index(const Vertex_handle& v1,
-                                  const Vertex_handle& v2) const
-  {
-    return curve_index(v1, v2);
-  }
-#endif // CGAL_NO_DEPRECATED_CODE
-
-  /**
-   * Returns Corner_index of vertex \c v
-   */
-  Corner_index corner_index(const Vertex_handle& v) const
-  {
-    typename Corner_map::const_iterator it = corners_.find(v);
-    if ( corners_.end() != it ) { return it->second; }
-    return Corner_index();
-  }
-
-  /**
-   * Outputs the outer boundary of the entire domain with facets oriented outward.
-   */
-  std::ostream& output_boundary_to_off(std::ostream& out) const
-  {
-    internal::output_boundary_of_c3t3_to_off(*this, 0, out, false);
-    return out;
-  }
-
-  /**
-   * Outputs the outer boundary of the selected subdomain with facets oriented outward.
-   */
-  std::ostream& output_boundary_to_off(std::ostream& out, Subdomain_index subdomain) const
-  {
-    output_boundary_of_c3t3_to_off(*this, subdomain, out);
-    return out;
-  }
-
-  /**
-   * Outputs the surface facets with a consistent orientation at the interface of two subdomains.
-   */
-  std::ostream& output_facets_in_complex_to_off(std::ostream& out) const
-  {
-    internal::output_facets_in_complex_to_off(*this, out);
-    return out;
-  }
-
-  /**
-   * Fills \c out with incident edges (1-dimensional features of \c v.
-   * OutputIterator value type is std::pair<Vertex_handle,Curve_index>
-   * \pre v->in_dimension() < 2
-   */
-  template <typename OutputIterator>
-  OutputIterator
-  adjacent_vertices_in_complex(const Vertex_handle& v, OutputIterator out) const;
-
-  // -----------------------------------
-  // Undocumented
-  // -----------------------------------
-
-  /**
-   * Returns true if c3t3 is valid
-   */
-  bool is_valid(bool verbose = false) const;
-
-  // -----------------------------------
-  // Complex traversal
-  // -----------------------------------
-private:
-  class Edge_iterator_not_in_complex
-  {
-    const Self& c3t3_;
-    const Curve_index index_;
-  public:
-    Edge_iterator_not_in_complex(const Self& c3t3,
-                                 const Curve_index& index = Curve_index())
-    : c3t3_(c3t3)
-    , index_(index) { }
-
-    template <typename Iterator>
-    bool operator()(Iterator it) const
-    {
-      if ( index_ == Curve_index() ) { return ! c3t3_.is_in_complex(*it); }
-      else { return c3t3_.curve_index(*it) != index_;  }
-    }
-  };
-
-  class Vertex_iterator_not_in_complex
-  {
-    const Self& c3t3_;
-    const Corner_index index_;
-  public:
-    Vertex_iterator_not_in_complex(const Self& c3t3,
-                                   const Corner_index& index = Corner_index())
-    : c3t3_(c3t3)
-    , index_(index) { }
-
-    template <typename ItMap>
-    bool operator()(const ItMap it) const
-    {
-      if ( index_ == Corner_index() ) { return false; }
-      else { return it->second != index_;  }
-    }
-  };
-
-  // Filtered iterator
-  typedef Filter_iterator<
-    typename Corner_map::const_iterator,
-    Vertex_iterator_not_in_complex >            Vertex_map_filter_iterator;
-
-  // Iterator type to get the first element of pair
-  typedef boost::transform_iterator <
-    Mesh_3::internal::First_of<typename Vertex_map_filter_iterator::value_type>,
-    Vertex_map_filter_iterator >                Vertex_map_iterator_first;
-
-  // Iterator type to remove a level of referencing
-  class Vertex_map_iterator_first_dereference
-    : public boost::iterator_adaptor <
-        Vertex_map_iterator_first_dereference,
-        Vertex_map_iterator_first,
-        typename Vertex_map_iterator_first::value_type::value_type,
-        boost::use_default,
-        typename Vertex_map_iterator_first::value_type::reference >
-  {
-    typedef Vertex_map_iterator_first_dereference Self;
-    typedef boost::iterator_adaptor <
-        Vertex_map_iterator_first_dereference,
-        Vertex_map_iterator_first,
-        typename Vertex_map_iterator_first::value_type::value_type,
-        boost::use_default,
-        typename Vertex_map_iterator_first::value_type::reference > iterator_adaptor_;
-  public:
-    typedef typename  Vertex_map_iterator_first::reference  pointer;
-    typedef typename iterator_adaptor_::reference           reference;
-
-    Vertex_map_iterator_first_dereference() : Self::iterator_adaptor_() { }
-
-    template < typename Iterator >
-    Vertex_map_iterator_first_dereference(Iterator i)
-      : Self::iterator_adaptor_(typename Self::iterator_adaptor_::base_type(i))
-    { }
-
-    pointer operator->() const { return *(this->base()); }
-    reference operator*() const { return **(this->base()); }
-
-    operator Vertex_handle() { return Vertex_handle(*(this->base())); }
-  };
-
-public:
-  /// Iterator type to visit the edges of the 1D complex.
-  typedef Filter_iterator<
-    typename Triangulation::Finite_edges_iterator,
-    Edge_iterator_not_in_complex >          Edges_in_complex_iterator;
-
-  /// Returns a Facets_in_complex_iterator to the first facet of the 1D complex
-  Edges_in_complex_iterator edges_in_complex_begin() const
-  {
-    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
-                                 Edge_iterator_not_in_complex(*this),
-                                 this->triangulation().finite_edges_begin());
-  }
-
-  /// Returns a Facets_in_complex_iterator to the first facet of the 1D complex
-  Edges_in_complex_iterator
-  edges_in_complex_begin(const Curve_index& index) const
-  {
-    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
-                                 Edge_iterator_not_in_complex(*this,index),
-                                 this->triangulation().finite_edges_begin());
-  }
-
-  /// Returns past-the-end iterator on facet of the 1D complex
-  Edges_in_complex_iterator edges_in_complex_end(const Curve_index& = Curve_index()) const
-  {
-    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
-                                 Edge_iterator_not_in_complex(*this));
-  }
-
-  /// Iterator type to visit the edges of the 0D complex.
-  typedef Vertex_map_iterator_first_dereference Vertices_in_complex_iterator;
-
-  /// Returns a Vertices_in_complex_iterator to the first vertex of the 0D complex
-  Vertices_in_complex_iterator vertices_in_complex_begin() const
-  {
-    return CGAL::filter_iterator(corners_.end(),
-                                 Vertex_iterator_not_in_complex(*this),
-                                 corners_.begin());
-  }
-
-  /// Returns a Vertices_in_complex_iterator to the first vertex of the 0D complex
-  Vertices_in_complex_iterator
-  vertices_in_complex_begin(const Corner_index& index) const
-  {
-    return CGAL::filter_iterator(corners_.end(),
-                                 Vertex_iterator_not_in_complex(*this,index),
-                                 corners_.begin());
-  }
-
-  /// Returns past-the-end iterator on facet of the 0D complex
-  Vertices_in_complex_iterator vertices_in_complex_end() const
-  {
-    return CGAL::filter_iterator(corners_.end(),
-                                 Vertex_iterator_not_in_complex(*this));
-  }
-
-
-private:
-  /**
-   * Creates an Internal_edge object (i.e a pair of ordered Vertex_handle)
-   */
-  Internal_edge make_internal_edge(const Vertex_handle& v1,
-                                   const Vertex_handle& v2) const
-  {
-    if ( v1 < v2 ) { return Internal_edge(v1,v2); }
-    else { return Internal_edge(v2,v1); }
-  }
-
-  /**
-   * Returns true if \c edge is in C3T3
-   */
-  bool is_in_complex(const Internal_edge& edge) const
-  {
-    return (curve_index(edge) != Curve_index() );
-  }
-
-  /**
-   * Add edge \c edge to complex, with Curve_index index
-   */
-  void add_to_complex(const Internal_edge& edge, const Curve_index& index)
-  {
-    CGAL_precondition(!is_in_complex(edge));
-#if CGAL_MESH_3_PROTECTION_DEBUG & 1
-    std::cerr << "Add edge ( " << disp_vert(edge.left)
-              << " , " << disp_vert(edge.right) << " ), curve_index=" << index
-              << " to c3t3.\n";
-#endif // CGAL_MESH_3_PROTECTION_DEBUG
-    std::pair<typename Edge_map::iterator, bool> it = edges_.insert(edge);
-    it.first->info = index;
-  }
-
-  /**
-   * Remove edge \c edge from complex
-   */
-  void remove_from_complex(const Internal_edge& edge)
-  {
-    edges_.erase(edge);
-  }
-
-  /**
-   * Returns Curve_index of edge \c edge
-   */
-  Curve_index curve_index(const Internal_edge& edge) const
-  {
-    typename Edge_map::const_iterator it = edges_.find(edge);
-    if ( edges_.end() != it ) { return it->info; }
-    return Curve_index();
-  }
-
-private:
-  Edge_map edges_;
-  Corner_map corners_;
-  Far_vertices_vec far_vertices_;
-};
-
-
-template <typename Tr, typename CI_, typename CSI_>
-Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
-Mesh_complex_3_in_triangulation_3(const Self& rhs)
-  : Base(rhs)
-  , edges_()
-  , corners_()
-{
-  // Copy edges
-  for ( typename Edge_map::const_iterator it = rhs.edges_.begin(),
-       end = rhs.edges_.end() ; it != end ; ++it )
-  {
-    const Vertex_handle& va = it->right;
-    const Vertex_handle& vb = it->left;
-
-    Vertex_handle new_va;
-    this->triangulation().is_vertex(rhs.triangulation().point(va), new_va);
-
-    Vertex_handle new_vb;
-    this->triangulation().is_vertex(rhs.triangulation().point(vb), new_vb);
-
-    this->add_to_complex(make_internal_edge(new_va,new_vb), it->info);
-  }
-
-  // Copy corners
-  for ( typename Corner_map::const_iterator it = rhs.corners_.begin(),
-       end = rhs.corners_.end() ; it != end ; ++it )
-  {
-    Vertex_handle new_v;
-    this->triangulation().is_vertex(rhs.triangulation().point(it->first), new_v);
-    this->add_to_complex(new_v, it->second);
-  }
-
-  // Parse vertices to identify far vertices
-  if (rhs.far_vertices_.size() > 0)
-  {
-    Triangulation &tr = triangulation();
-    typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin();
-    for(typename Tr::Finite_vertices_iterator end = tr.finite_vertices_end();
-        vit != end ; ++vit)
-    {
-      if (vit->in_dimension() == -1)
-        far_vertices_.push_back(vit);
-    }
-    CGAL_assertion(far_vertices_.size() == rhs.far_vertices_.size());
-  }
-}
-
-
-template <typename Tr, typename CI_, typename CSI_>
-template <typename OutputIterator>
-OutputIterator
-Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
-adjacent_vertices_in_complex(const Vertex_handle& v, OutputIterator out) const
-{
-  CGAL_precondition(v->in_dimension() < 2);
-
-  typedef typename Edge_map::right_const_iterator Rcit;
-  typedef typename Edge_map::left_const_iterator Lcit;
-
-  // Add edges containing v is on the left
-  std::pair<Rcit,Rcit> range_right = edges_.right.equal_range(v);
-  for ( Rcit rit = range_right.first ; rit != range_right.second ; ++rit )
-  {
-    *out++ = std::make_pair(rit->second, rit->info);
-  }
-
-  // Add edges containing v on the right
-  std::pair<Lcit,Lcit> range_left = edges_.left.equal_range(v);
-  for ( Lcit lit = range_left.first ; lit != range_left.second ; ++lit )
-  {
-    *out++ = std::make_pair(lit->second, lit->info);
-  }
-
-  return out;
-}
-
-
-template <typename Tr, typename CI_, typename CSI_>
-bool
-Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
-is_valid(bool verbose) const
-{
-  typedef typename Tr::Weighted_point                         Weighted_point;
-  typedef boost::unordered_map<Vertex_handle, int, Hash_fct>  Vertex_map;
-
-  Vertex_map vertex_map;
-
-  // Fill map counting neighbor number for each vertex of an edge
-  for ( typename Edge_map::const_iterator it = edges_.begin(),
-       end = edges_.end() ; it != end ; ++it )
-  {
-    const Vertex_handle& v1 = it->right;
-    if ( vertex_map.find(v1) == vertex_map.end() ) { vertex_map[v1] = 1; }
-    else { vertex_map[v1] += 1; }
-
-    const Vertex_handle& v2 = it->left;
-    if ( vertex_map.find(v2) == vertex_map.end() ) { vertex_map[v2] = 1; }
-    else { vertex_map[v2] += 1; }
-  }
-
-  // Verify that each vertex has 2 neighbors if it's not a corner
-  for ( typename Vertex_map::iterator vit = vertex_map.begin(),
-       vend = vertex_map.end() ; vit != vend ; ++vit )
-  {
-    if ( vit->first->in_dimension() != 0 && vit->second != 2 )
-    {
-      if(verbose)
-        std::cerr << "Validity error: vertex " << (void*)(&*vit->first)
-                  << " (" << this->triangulation().point(vit->first) << ") "
-                  << "is not a corner (dimension " << vit->first->in_dimension()
-                  << ") but has " << vit->second << " neighbor(s)!\n";
-      return false;
-    }
-  }
-
-  // Verify that balls of each edge intersect
-  for ( typename Edge_map::const_iterator it = edges_.begin(),
-       end = edges_.end() ; it != end ; ++it )
-  {
-    typename Tr::Geom_traits::Compute_weight_3 cw =
-      this->triangulation().geom_traits().compute_weight_3_object();
-    typename Tr::Geom_traits::Construct_point_3 cp =
-      this->triangulation().geom_traits().construct_point_3_object();
-    typename Tr::Geom_traits::Construct_sphere_3 sphere =
-      this->triangulation().geom_traits().construct_sphere_3_object();
-    typename Tr::Geom_traits::Do_intersect_3 do_intersect =
-      this->triangulation().geom_traits().do_intersect_3_object();
-
-    const Weighted_point& itrwp = this->triangulation().point(it->right);
-    const Weighted_point& itlwp = this->triangulation().point(it->left);
-
-    if ( ! do_intersect(sphere(cp(itrwp), cw(itrwp)), sphere(cp(itlwp), cw(itlwp))) )
-    {
-      std::cerr << "Points p[" << disp_vert(it->right) << "], dim=" << it->right->in_dimension()
-                << " and q[" << disp_vert(it->left) << "], dim=" << it->left->in_dimension()
-                << " form an edge but do not intersect !\n";
-      return false;
-    }
-  }
-
-  return true;
-}
-
-template <typename Tr, typename CI_, typename CSI_>
-void
-Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
-rescan_after_load_of_triangulation() {
-  corners_.clear();
-  for(typename Tr::Finite_vertices_iterator
-        vit = this->triangulation().finite_vertices_begin(),
-        end = this->triangulation().finite_vertices_end();
-      vit != end; ++vit)
-  {
-    if ( vit->in_dimension() == 0 ) {
-      add_to_complex(vit, Corner_index(1));
-    }
-  }
-  Base::rescan_after_load_of_triangulation();
-}
-
-template <typename Tr, typename CI_, typename CSI_>
-std::ostream &
-operator<< (std::ostream& os,
-            const Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_> &c3t3)
-{
-  // TODO: implement edge saving
-  typedef typename Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::Concurrency_tag Concurrency_tag;
-  return os << static_cast<
-    const Mesh_3::Mesh_complex_3_in_triangulation_3_base<Tr, Concurrency_tag>&>(c3t3);
-}
-
-
-template <typename Tr, typename CI_, typename CSI_>
-std::istream &
-operator>> (std::istream& is,
-            Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_> &c3t3)
-{
-  // TODO: implement edge loading
-  typedef typename Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::Concurrency_tag Concurrency_tag;
-  is >> static_cast<
-    Mesh_3::Mesh_complex_3_in_triangulation_3_base<Tr, Concurrency_tag>&>(c3t3);
-  c3t3.rescan_after_load_of_triangulation();
-  return is;
-}
-
-} //namespace CGAL
-
-#include <CGAL/enable_warnings.h>
-
-#endif // CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
diff --git a/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h b/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
index 67006e8bbea..e9a58de83d5 100644
--- a/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
+++ b/Mesh_3/include/CGAL/Mesh_domain_with_polyline_features_3.h
@@ -29,7 +29,7 @@
 #include <CGAL/is_streamable.h>
 #include <CGAL/Real_timer.h>
 #include <CGAL/property_map.h>
-#include <CGAL/Mesh_3/internal/indices_management.h>
+#include <CGAL/SMDS_3/internal/indices_management.h>
 
 #include <vector>
 #include <set>
diff --git a/Mesh_3/include/CGAL/Mesh_triangulation_3.h b/Mesh_3/include/CGAL/Mesh_triangulation_3.h
index 68e168b6e00..8d8012806c7 100644
--- a/Mesh_3/include/CGAL/Mesh_triangulation_3.h
+++ b/Mesh_3/include/CGAL/Mesh_triangulation_3.h
@@ -28,7 +28,7 @@
 
 #include <CGAL/Mesh_vertex_base_3.h>
 #include <CGAL/Compact_mesh_cell_base_3.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 
 namespace CGAL {
 
diff --git a/Mesh_3/include/CGAL/Mesh_vertex_base_3.h b/Mesh_3/include/CGAL/Mesh_vertex_base_3.h
index c7e79141f73..3ab58a03384 100644
--- a/Mesh_3/include/CGAL/Mesh_vertex_base_3.h
+++ b/Mesh_3/include/CGAL/Mesh_vertex_base_3.h
@@ -20,12 +20,12 @@
 #ifndef CGAL_COMPACT_MESH_VERTEX_BASE_3_H
 #define CGAL_COMPACT_MESH_VERTEX_BASE_3_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/Mesh_3.h>
 
 
 #include <CGAL/Regular_triangulation_vertex_base_3.h>
-#include <CGAL/Mesh_3/internal/indices_management.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/internal/indices_management.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <CGAL/Has_timestamp.h>
 #include <CGAL/tags.h>
 #include <atomic>
@@ -289,6 +289,30 @@ public:
   }
 };  // end class Mesh_vertex_3
 
+
+/*!
+\ingroup PkgMesh3MeshClasses
+
+The class `Mesh_vertex_base_3` is a model of the concept `MeshVertexBase_3`.
+It is designed to serve as vertex base class for the 3D triangulation
+used in a 3D mesh generation process.
+
+\tparam GT is the geometric traits class.
+It must be a model of the concept `MeshTriangulationTraits_3`.
+
+\tparam MD provides the types of indices
+used to identify
+the faces of the input complex. It must be a model
+of the concept `MeshDomain_3`.
+
+\tparam Vb is the vertex base class. It has to be a model
+of the concept `RegularTriangulationVertexBase_3` and defaults to
+`Regular_triangulation_vertex_base_3<GT>`.
+
+\cgalModels `MeshVertexBase_3`
+
+\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
+*/
 template<class GT,
          class MD,
          class Vb = Regular_triangulation_vertex_base_3<GT> >
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
index 91c5e57e7e3..96743cc70e3 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
@@ -59,9 +59,9 @@
 
 // To handle I/O for Surface_patch_index if that is a pair of `int` (the
 // default)
-#include <CGAL/Mesh_3/internal/Handle_IO_for_pair_of_int.h>
+#include <CGAL/SMDS_3/internal/Handle_IO_for_pair_of_int.h>
 
-#include <CGAL/Mesh_3/internal/indices_management.h>
+#include <CGAL/SMDS_3/internal/indices_management.h>
 
 namespace CGAL {
 
diff --git a/Mesh_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h b/Mesh_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h
deleted file mode 100644
index 1262ef6f74a..00000000000
--- a/Mesh_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h
+++ /dev/null
@@ -1,187 +0,0 @@
-// Copyright (c) 2009-2017 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)     : Maxime Gimeno,
-//                 Mael Rouxel-Labbé
-
-#ifndef CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
-#define CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
-
-#include <CGAL/license/Triangulation_3.h>
-
-#include <CGAL/array.h>
-#include <CGAL/boost/graph/Euler_operations.h>
-#include <CGAL/Cartesian_converter.h>
-#include <CGAL/Kernel_traits.h>
-#include <CGAL/Polygon_mesh_processing/orient_polygon_soup.h>
-#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>
-#include <CGAL/Time_stamper.h>
-
-#include <boost/tuple/tuple.hpp>
-
-#include <algorithm>
-#include <cstddef>
-#include <iterator>
-#include <unordered_map>
-#include <vector>
-
-namespace CGAL {
-
-namespace Mesh_3 {
-
-namespace internal {
-
-template <class Polygon>
-void resize(Polygon& p, std::size_t size)
-{
-  p.resize(size);
-}
-
-template <std::size_t N, class INT>
-void resize(std::array<INT, N>&, std::size_t CGAL_assertion_code(size))
-{
-  CGAL_assertion(size == N);
-}
-
-template<class C3T3, class PointContainer, class FaceContainer>
-void facets_in_complex_3_to_triangle_soup(const C3T3& c3t3,
-                                          const typename C3T3::Subdomain_index sd_index,
-                                          PointContainer& points,
-                                          FaceContainer& faces,
-                                          const bool normals_point_outside_of_the_subdomain = true,
-                                          const bool export_all_facets = false)
-{
-  typedef typename PointContainer::value_type                            Point_3;
-  typedef typename FaceContainer::value_type                             Face;
-
-  typedef typename C3T3::Triangulation                                   Tr;
-
-  typedef typename Tr::Cell_handle                                       Cell_handle;
-  typedef typename Tr::Weighted_point                                    Weighted_point;
-
-  typedef typename C3T3::Facets_in_complex_iterator                      Ficit;
-
-  typedef std::unordered_map<Point_3, std::size_t>                       PIM;
-
-  typedef typename C3T3::size_type                                       size_type;
-
-  // triangulation point to range point
-  CGAL::Cartesian_converter<typename CGAL::Kernel_traits<typename Tr::Geom_traits::Point_3>::type,
-                            typename CGAL::Kernel_traits<Point_3>::type> t2r;
-
-  size_type nf = c3t3.number_of_facets_in_complex();
-  faces.reserve(faces.size() + nf);
-  points.reserve(points.size() + nf/2); // approximating Euler
-
-  PIM p_to_ids;
-  std::size_t inum = 0;
-
-  for(Ficit fit = c3t3.facets_in_complex_begin(),
-            end = c3t3.facets_in_complex_end(); fit != end; ++fit)
-  {
-    Cell_handle c = fit->first;
-    int s = fit->second;
-    Face f;
-    resize(f, 3);
-
-    typename C3T3::Subdomain_index cell_sdi = c3t3.subdomain_index(c);
-    typename C3T3::Subdomain_index opp_sdi = c3t3.subdomain_index(c->neighbor(s));
-
-    if(!export_all_facets && cell_sdi != sd_index && opp_sdi != sd_index)
-      continue;
-
-    for(std::size_t i=1; i<4; ++i)
-    {
-      CGAL_assertion_code(typedef typename Tr::Vertex_handle Vertex_handle;)
-      CGAL_assertion_code(Vertex_handle v = c->vertex((s+i)&3);)
-      CGAL_assertion(v != Vertex_handle() && !c3t3.triangulation().is_infinite(v));
-
-      const Weighted_point& wp = c3t3.triangulation().point(c, (s+i)&3);
-      const Point_3& bp = t2r(c3t3.triangulation().geom_traits().construct_point_3_object()(wp));
-
-      auto insertion_res = p_to_ids.emplace(bp, inum);
-      if(insertion_res.second) // new point
-      {
-        points.push_back(bp);
-        ++inum;
-      }
-
-      f[i-1] = insertion_res.first->second;
-    }
-
-    if(export_all_facets)
-    {
-      if((cell_sdi > opp_sdi) == (s%2 == 1))
-        std::swap(f[0], f[1]);
-    }
-    else
-    {
-      if(((cell_sdi == sd_index) == (s%2 == 1)) == normals_point_outside_of_the_subdomain)
-        std::swap(f[0], f[1]);
-    }
-
-    faces.push_back(f);
-  }
-}
-
-template<class C3T3, class PointContainer, class FaceContainer>
-void facets_in_complex_3_to_triangle_soup(const C3T3& c3t3,
-                                          PointContainer& points,
-                                          FaceContainer& faces)
-{
-  typedef typename C3T3::Subdomain_index              Subdomain_index;
-  Subdomain_index useless = Subdomain_index();
-  facets_in_complex_3_to_triangle_soup(c3t3, useless, points, faces,
-                                       true/*point outward*/, true /*extract all facets*/);
-}
-
-} // end namespace internal
-
-} // end namespace Mesh_3
-
-//! \ingroup PkgMesh3Functions
-//!
-//! \brief builds a `TriangleMesh` from the surface facets, with a consistent orientation
-//!        at the interface of two subdomains.
-//!
-//! This function exports the surface as a `TriangleMesh` and appends it to `graph`, using
-//! `orient_polygon_soup()`.
-//!
-//! @tparam C3T3 a model of `MeshComplexWithFeatures_3InTriangulation_3`.
-//! @tparam TriangleMesh a model of `MutableFaceGraph` with an internal point property map.
-//!         The point type should be compatible with the one used in `C3T3`.
-//!
-//! @param c3t3 an instance of `C3T3`.
-//! @param graph an instance of `TriangleMesh`.
-template<class C3T3, class TriangleMesh>
-void facets_in_complex_3_to_triangle_mesh(const C3T3& c3t3, TriangleMesh& graph)
-{
-  namespace PMP = CGAL::Polygon_mesh_processing;
-
-  typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type  VertexPointMap;
-  typedef typename boost::property_traits<VertexPointMap>::value_type              Point_3;
-
-  typedef std::array<std::size_t, 3>                                               Face;
-
-  std::vector<Face> faces;
-  std::vector<Point_3> points;
-
-  Mesh_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, points, faces);
-
-  if(!PMP::is_polygon_soup_a_polygon_mesh(faces))
-    PMP::orient_polygon_soup(points, faces);
-  CGAL_postcondition(PMP::is_polygon_soup_a_polygon_mesh(faces));
-
-  PMP::polygon_soup_to_polygon_mesh(points, faces, graph);
-}
-
-} // namespace CGAL
-
-#endif // CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
diff --git a/Mesh_3/include/CGAL/make_mesh_3.h b/Mesh_3/include/CGAL/make_mesh_3.h
index a75e120da69..39acb952459 100644
--- a/Mesh_3/include/CGAL/make_mesh_3.h
+++ b/Mesh_3/include/CGAL/make_mesh_3.h
@@ -26,7 +26,7 @@
 #include <CGAL/refine_mesh_3.h>
 #include <CGAL/tags.h>
 #include <CGAL/Mesh_3/Protect_edges_sizing_field.h>
-#include <CGAL/Mesh_3/Has_features.h>
+#include <CGAL/SMDS_3/Has_features.h>
 #include <CGAL/Mesh_3/C3T3_helpers.h>
 
 #include <boost/mpl/has_xxx.hpp>
diff --git a/Mesh_3/include/CGAL/refine_mesh_3.h b/Mesh_3/include/CGAL/refine_mesh_3.h
index 0c1e550f41e..bfa15f78f06 100644
--- a/Mesh_3/include/CGAL/refine_mesh_3.h
+++ b/Mesh_3/include/CGAL/refine_mesh_3.h
@@ -24,10 +24,10 @@
 #include <CGAL/config.h>
 #include <CGAL/boost/parameter.h>
 #include <CGAL/Mesh_3/config.h>
-#include <CGAL/Mesh_3/Dump_c3t3.h>
 #include <CGAL/Mesh_3/Mesher_3.h>
 #include <CGAL/Mesh_error_code.h>
 #include <CGAL/optimize_mesh_3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #include <boost/parameter/preprocessor.hpp>
 
diff --git a/Mesh_3/package_info/Mesh_3/dependencies b/Mesh_3/package_info/Mesh_3/dependencies
index e616acd30b8..65eec56b360 100644
--- a/Mesh_3/package_info/Mesh_3/dependencies
+++ b/Mesh_3/package_info/Mesh_3/dependencies
@@ -31,6 +31,7 @@ Principal_component_analysis_LGPL
 Profiling_tools
 Property_map
 Random_numbers
+SMDS_3
 STL_Extension
 Solver_interface
 Spatial_searching
diff --git a/Mesh_3/test/Mesh_3/CMakeLists.txt b/Mesh_3/test/Mesh_3/CMakeLists.txt
index 40643d7538c..3f91ea357bd 100644
--- a/Mesh_3/test/Mesh_3/CMakeLists.txt
+++ b/Mesh_3/test/Mesh_3/CMakeLists.txt
@@ -23,16 +23,12 @@ if ( CGAL_FOUND )
   endif()
 
   create_single_source_cgal_program( "test_boost_has_xxx.cpp" )
-  create_single_source_cgal_program( "test_c3t3.cpp" )
   create_single_source_cgal_program( "test_mesh_capsule_var_distance_bound.cpp" )
   create_single_source_cgal_program( "test_implicit_multi_domain_to_labeling_function_wrapper.cpp" )
-  create_single_source_cgal_program( "test_c3t3_io.cpp" )
-  create_single_source_cgal_program( "test_c3t3_with_features.cpp" )
   create_single_source_cgal_program( "test_criteria.cpp" )
   create_single_source_cgal_program( "test_domain_with_polyline_features.cpp" )
   create_single_source_cgal_program( "test_labeled_mesh_domain_3.cpp" )
   create_single_source_cgal_program( "test_mesh_criteria_creation.cpp" )
-  create_single_source_cgal_program( "test_c3t3_into_facegraph.cpp" )
   create_single_source_cgal_program( "test_without_detect_features.cpp" )
   if(CGAL_ImageIO_USE_ZLIB)
     create_single_source_cgal_program( "test_meshing_3D_image.cpp" )
@@ -52,7 +48,6 @@ if ( CGAL_FOUND )
   create_single_source_cgal_program( "test_meshing_unit_tetrahedron.cpp" )
   create_single_source_cgal_program( "test_meshing_with_default_edge_size.cpp" )
   create_single_source_cgal_program( "test_meshing_determinism.cpp" )
-  create_single_source_cgal_program( "test_c3t3_extract_subdomains_boundaries.cpp" )
   create_single_source_cgal_program( "test_mesh_3_issue_1554.cpp" )
   create_single_source_cgal_program( "test_mesh_polyhedral_domain_with_features_deprecated.cpp" )
   create_single_source_cgal_program( "test_meshing_with_one_step.cpp" )
@@ -60,16 +55,12 @@ if ( CGAL_FOUND )
 
   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
@@ -85,7 +76,6 @@ if ( CGAL_FOUND )
       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_mesh_cell_base_3
diff --git a/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp b/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
index 68de83c5e41..03b91d15d8c 100644
--- a/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
+++ b/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
@@ -60,9 +60,10 @@ int main()
   // Mesh generation
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);
 
-  // Output
-  std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+//  // Output
+//  std::ofstream medit_file("out.mesh");
+//  CGAL::IO::write_MEDIT(medit_file, c3t3);
+//  medit_file.close();
 
   return 0;
 }
diff --git a/Mesh_3/test/Mesh_3/test_mesh_cell_base_3.cpp b/Mesh_3/test/Mesh_3/test_mesh_cell_base_3.cpp
index d4b01ec740a..8e3e650625c 100644
--- a/Mesh_3/test/Mesh_3/test_mesh_cell_base_3.cpp
+++ b/Mesh_3/test/Mesh_3/test_mesh_cell_base_3.cpp
@@ -4,7 +4,7 @@
 
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 #include <CGAL/Mesh_3/Robust_intersection_traits_3.h>
 #include <CGAL/Polyhedral_mesh_domain_with_features_3.h>
 #include <CGAL/Mesh_cell_base_3.h>
@@ -49,7 +49,7 @@ int main (int argc, char** argv){
     return 1;
   }
   C3t3 c3t3;
-  if(CGAL::build_triangulation_from_file<C3t3::Triangulation, true>(in, c3t3.triangulation()))
+  if(CGAL::SMDS_3::build_triangulation_from_file(in, c3t3.triangulation()))
   {
     for( C3t3::Triangulation::Finite_cells_iterator
          cit = c3t3.triangulation().finite_cells_begin();
diff --git a/Mesh_3/test/Mesh_3/test_mesh_polyhedral_domain_with_features_deprecated.cpp b/Mesh_3/test/Mesh_3/test_mesh_polyhedral_domain_with_features_deprecated.cpp
index 6642e03693c..9827a5f2b68 100644
--- a/Mesh_3/test/Mesh_3/test_mesh_polyhedral_domain_with_features_deprecated.cpp
+++ b/Mesh_3/test/Mesh_3/test_mesh_polyhedral_domain_with_features_deprecated.cpp
@@ -44,7 +44,10 @@ int main()
   // Mesh generation
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);
 
-  // Output
-  std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
+//  // Output
+//  std::ofstream medit_file("out.mesh");
+//  CGAL::IO::write_MEDIT(medit_file, c3t3);
+//  medit_file.close();
+
+  return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/test/Mesh_3/test_meshing_determinism.cpp b/Mesh_3/test/Mesh_3/test_meshing_determinism.cpp
index d359509388f..ef92a338025 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_determinism.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_determinism.cpp
@@ -76,7 +76,7 @@ void test()
                                         no_perturb(),
                                         no_exude());
     std::ostringstream oss;
-    c3t3.output_to_medit(oss);
+    CGAL::IO::write_MEDIT(oss, c3t3);
     output_c3t3.push_back(oss.str()); //[5*i]
     oss.clear();
     Polyhedron out_poly;
@@ -88,7 +88,7 @@ void test()
 
     //LLOYD (1)
     CGAL::lloyd_optimize_mesh_3(c3t3, domain, max_iteration_number = nb_lloyd);
-    c3t3.output_to_medit(oss);
+    CGAL::IO::write_MEDIT(oss, c3t3);
     output_c3t3.push_back(oss.str());//[i*5+1]
     oss.clear();
     CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, out_poly);
@@ -99,7 +99,7 @@ void test()
 
     //ODT (2)
     CGAL::odt_optimize_mesh_3(c3t3, domain, max_iteration_number = nb_odt);
-    c3t3.output_to_medit(oss);
+    CGAL::IO::write_MEDIT(oss, c3t3);
     output_c3t3.push_back(oss.str());//[i*5+2]
     oss.clear();
     CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, out_poly);
@@ -110,7 +110,7 @@ void test()
 
     //PERTURB (3)
     CGAL::perturb_mesh_3(c3t3, domain, sliver_bound=perturb_bound);
-    c3t3.output_to_medit(oss);
+    CGAL::IO::write_MEDIT(oss, c3t3);
     output_c3t3.push_back(oss.str());//[i*5+3]
     oss.clear();
     CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, out_poly);
@@ -121,7 +121,7 @@ void test()
 
     //EXUDE (4)
     CGAL::exude_mesh_3(c3t3, sliver_bound=exude_bound);
-    c3t3.output_to_medit(oss);
+    CGAL::IO::write_MEDIT(oss, c3t3);
     output_c3t3.push_back(oss.str());//[i*5+4]
     oss.clear();
     CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, out_poly);
diff --git a/Mesh_3/test/Mesh_3/test_meshing_polyhedron.cpp b/Mesh_3/test/Mesh_3/test_meshing_polyhedron.cpp
index b758086448e..3f8b51cf7c4 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_polyhedron.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_polyhedron.cpp
@@ -15,14 +15,14 @@
 // File Description :
 //******************************************************************************
 
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include "test_meshing_utilities.h"
 #include <CGAL/Polyhedral_mesh_domain_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 
 #include <boost/type_traits/is_same.hpp>
 
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #include <CGAL/disable_warnings.h>
 
diff --git a/Mesh_3/test/Mesh_3/test_meshing_polyhedron_with_features.cpp b/Mesh_3/test/Mesh_3/test_meshing_polyhedron_with_features.cpp
index 9babdd1a160..5cfdd17ca79 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_polyhedron_with_features.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_polyhedron_with_features.cpp
@@ -136,7 +136,7 @@ struct Polyhedron_with_features_tester : public Tester<K>
                  Polyhedral_tag()); //, 1099, 1099, 1158, 1158, 4902, 4902);
 
     std::ofstream out_medit("test-medit.mesh");
-    CGAL::IO::output_to_medit(out_medit, c3t3);
+    CGAL::IO::write_MEDIT(out_medit, c3t3);
     CGAL::IO::output_to_tetgen("test-tetgen", c3t3);
     std::ofstream out_binary("test-binary.mesh.cgal",
                              std::ios_base::out|std::ios_base::binary);
diff --git a/Mesh_3/test/Mesh_3/test_meshing_polylines_only.cpp b/Mesh_3/test/Mesh_3/test_meshing_polylines_only.cpp
index a8ad7dfc6a9..8dd7e0cbcb3 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_polylines_only.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_polylines_only.cpp
@@ -89,11 +89,12 @@ int main(int argc, char** argv)
 
   // CGAL::Mesh_3::internal::init_c3t3_with_features(c3t3, domain, criteria);
 
-  // Output
-  std::ofstream medit_file("out-mesh-polylines.mesh");
-  c3t3.output_to_medit(medit_file);
-  std::ofstream binary_file("out-mesh-polylines.binary.cgal", std::ios::binary|std::ios::out);
-  CGAL::IO::save_binary_file(binary_file, c3t3);
+//  // Output
+//  std::ofstream medit_file("out-mesh-polylines.mesh");
+//  CGAL::IO::write_MEDIT(medit_file, c3t3);
+//  std::ofstream binary_file("out-mesh-polylines.binary.cgal", std::ios::binary|std::ios::out);
+//  CGAL::IO::save_binary_file(binary_file, c3t3);
+
   std::cout << "Number of vertices in c3t3: "
             << c3t3.triangulation().number_of_vertices() << std::endl;
   assert(c3t3.triangulation().number_of_vertices() > 900);
diff --git a/Mesh_3/test/Mesh_3/test_meshing_unit_tetrahedron.cpp b/Mesh_3/test/Mesh_3/test_meshing_unit_tetrahedron.cpp
index 85989f0e485..5781f445050 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_unit_tetrahedron.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_unit_tetrahedron.cpp
@@ -6,7 +6,7 @@
 #include <CGAL/Mesh_criteria_3.h>
 #include <CGAL/Polyhedral_mesh_domain_with_features_3.h>
 #include <CGAL/make_mesh_3.h>
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 
 #include <sstream>
 
diff --git a/Mesh_3/test/Mesh_3/test_meshing_with_one_step.cpp b/Mesh_3/test/Mesh_3/test_meshing_with_one_step.cpp
index aa0ace6255a..19199d8e08f 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_with_one_step.cpp
+++ b/Mesh_3/test/Mesh_3/test_meshing_with_one_step.cpp
@@ -72,9 +72,10 @@ int main(int argc, char*argv[])
   assert(c3t3.triangulation().number_of_vertices() > 200);
   // Output
   mesher.display_number_of_bad_elements();
-  std::ofstream medit_file("out.mesh");
-  c3t3.output_to_medit(medit_file);
-  medit_file.close();
+
+//  std::ofstream medit_file("out.mesh");
+//  CGAL::IO::write_MEDIT(medit_file, c3t3);
+//  medit_file.close();
 
   return EXIT_SUCCESS;
 }
diff --git a/Mesh_3/test/Mesh_3/test_without_detect_features.cpp b/Mesh_3/test/Mesh_3/test_without_detect_features.cpp
index 92fb2129ff3..2e5c76606d1 100644
--- a/Mesh_3/test/Mesh_3/test_without_detect_features.cpp
+++ b/Mesh_3/test/Mesh_3/test_without_detect_features.cpp
@@ -22,7 +22,7 @@ struct Tester {
   // Criteria
   typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
 
-  int operator()(const std::string fname, const std::string out_fname)
+  int operator()(const std::string fname, const std::string /*out_fname*/)
   {
     std::ifstream input(fname);
     using namespace CGAL::parameters;
@@ -52,9 +52,10 @@ struct Tester {
     // Mesh generation
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);
 
-    // Output
-    std::ofstream medit_file(out_fname);
-    c3t3.output_to_medit(medit_file);
+//    // Output
+//    std::ofstream medit_file(out_fname);
+//    CGAL::IO::write_MEDIT(medit_file, c3t3);
+
     return EXIT_SUCCESS;
   }
 };
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
index dda69561ff2..260f521d03b 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
@@ -308,7 +308,7 @@ void output_to_medit(std::ostream& os,
 #endif
   CGAL_precondition(c3t3.triangulation().is_1_cover());
 
-  typedef CGAL::Mesh_3::Medit_pmap_generator<C3T3, rebind, no_patch>  Generator;
+  typedef CGAL::SMDS_3::Medit_pmap_generator<C3T3, rebind, no_patch>  Generator;
   typedef typename Generator::Cell_pmap                               Cell_pmap;
   typedef typename Generator::Facet_pmap                              Facet_pmap;
   typedef typename Generator::Facet_pmap_twice                        Facet_pmap_twice;
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
index 5be36b550e6..9c4d91afea9 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
@@ -31,12 +31,12 @@
 
 #include <CGAL/license/Periodic_3_mesh_3.h>
 
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #ifdef CGAL_MESH_3_DUMP_FEATURES_PROTECTION_ITERATIONS
 #include <CGAL/IO/File_binary_mesh_3.h>
 #endif
 #include <CGAL/Mesh_3/Protect_edges_sizing_field.h>
-#include <CGAL/Mesh_3/utilities.h>
+#include <CGAL/SMDS_3/utilities.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 
 #include <CGAL/enum.h>
@@ -75,7 +75,7 @@ namespace Periodic_3_mesh_3 {
 
 template <typename C3T3, typename MeshDomain, typename SizingFunction>
 class Protect_edges_sizing_field
-  : public CGAL::Mesh_3::internal::Debug_messages_tools
+  : public CGAL::SMDS_3::internal::Debug_messages_tools
 {
   typedef Protect_edges_sizing_field          Self;
 
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
index e977701c77b..64f113fa331 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
@@ -38,7 +38,7 @@
 #include <CGAL/Cartesian_converter.h>
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Kernel_traits.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <CGAL/tags.h>
 
 #include <iostream>
diff --git a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
index acb3b35decd..de1b05fbf0a 100644
--- a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
@@ -21,7 +21,7 @@
 #include <CGAL/Periodic_3_mesh_3/config.h>
 
 #include <CGAL/Mesh_3/C3T3_helpers.h>
-#include <CGAL/Mesh_3/Dump_c3t3.h>
+#include <CGAL/SMDS_3/Dump_c3t3.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 #include <CGAL/refine_mesh_3.h>
 #include <CGAL/Time_stamper.h>
diff --git a/Periodic_3_mesh_3/package_info/Periodic_3_mesh_3/dependencies b/Periodic_3_mesh_3/package_info/Periodic_3_mesh_3/dependencies
index 7fb9ae91209..daab68c8c70 100644
--- a/Periodic_3_mesh_3/package_info/Periodic_3_mesh_3/dependencies
+++ b/Periodic_3_mesh_3/package_info/Periodic_3_mesh_3/dependencies
@@ -22,6 +22,7 @@ Modular_arithmetic
 Number_types
 Periodic_3_mesh_3
 Periodic_3_triangulation_3
+Polygon_mesh_processing
 Principal_component_analysis
 Principal_component_analysis_LGPL
 Profiling_tools
@@ -31,6 +32,8 @@ STL_Extension
 Solver_interface
 Spatial_sorting
 Stream_support
+SMDS_3
 TDS_3
 Triangulation_3
 Union_find
+
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
index 45f76b3aa71..2360904b966 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
@@ -21,6 +21,7 @@
 #include <CGAL/boost/graph/Euler_operations.h>
 #include <CGAL/boost/graph/iterator.h>
 #include <CGAL/boost/graph/named_params_helper.h>
+#include <CGAL/boost/graph/internal/helpers.h>
 #include <CGAL/Dynamic_property_map.h>
 #include <CGAL/property_map.h>
 
@@ -74,9 +75,13 @@ public:
       m_pm(pm)
   { }
 
-  template <typename PolygonMesh, typename VertexPointMap>
+  template <typename PolygonMesh, typename VertexPointMap,
+            typename V2V, //pointindex-2-vertex
+            typename F2F> //polygonindex-2-face
   void operator()(PolygonMesh& pmesh,
                   VertexPointMap vpm,
+                  V2V i2v,
+                  F2F i2f,
                   const bool insert_isolated_vertices = true)
   {
     typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor    vertex_descriptor;
@@ -109,6 +114,7 @@ public:
       vertices[i] = add_vertex(pmesh);
       PM_Point pi = convert_to_pm_point<PM_Point>(get(m_pm, m_points[i]));
       put(vpm, vertices[i], pi);
+      *i2v++ = std::make_pair(i, vertices[i]);
     }
 
     for(std::size_t i = 0, end = m_polygons.size(); i < end; ++i)
@@ -121,9 +127,10 @@ public:
       for(std::size_t j = 0; j < size; ++j)
         vr[j] = vertices[polygon[j] ];
 
-      CGAL_assertion_code(typename boost::graph_traits<PolygonMesh>::face_descriptor fd =)
+      typename boost::graph_traits<PolygonMesh>::face_descriptor fd =
           CGAL::Euler::add_face(vr, pmesh);
       CGAL_assertion(fd != boost::graph_traits<PolygonMesh>::null_face());
+      *i2f++ = std::make_pair(i, fd);
     }
   }
 
@@ -131,7 +138,11 @@ public:
   void operator()(PolygonMesh& pmesh,
                   const bool insert_isolated_vertices = true)
   {
-    return operator()(pmesh, get(CGAL::vertex_point, pmesh), insert_isolated_vertices);
+    return operator()(pmesh,
+             get(CGAL::vertex_point, pmesh),
+             CGAL::Emptyset_iterator(),
+             CGAL::Emptyset_iterator(),
+             insert_isolated_vertices);
   }
 
 private:
@@ -250,6 +261,23 @@ bool is_polygon_soup_a_polygon_mesh(const PolygonRange& polygons)
 *                    of the vertex point map associated to the polygon mesh}
 *     \cgalParamDefault{`CGAL::Identity_property_map`}
 *   \cgalParamNEnd
+*
+*  \cgalParamNBegin{point_to_vertex_output_iterator}
+*   \cgalParamDescription{an `OutputIterator` containing the pairs source-vertex-index
+*                         from `points`, target-vertex.}
+*   \cgalParamType{a class model of `OutputIterator` accepting
+*                  `std::pair<int, boost::graph_traits<PolygonMesh>::%vertex_descriptor>`}
+*   \cgalParamDefault{`Emptyset_iterator`}
+* \cgalParamNEnd
+*
+*  \cgalParamNBegin{polygon_to_face_output_iterator}
+*   \cgalParamDescription{an `OutputIterator` containing the pairs polygon-index
+*                         from `polygons`, target-face.}
+*   \cgalParamType{a class model of `OutputIterator` accepting
+*                  `std::pair<int, boost::graph_traits<PolygonMesh>::%face_descriptor>`}
+*   \cgalParamDefault{`Emptyset_iterator`}
+* \cgalParamNEnd
+*
 * \cgalNamedParamsEnd
 *
 * @param np_pm an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
@@ -292,7 +320,11 @@ void polygon_soup_to_polygon_mesh(const PointRange& points,
                                           get_property_map(CGAL::vertex_point, out));
 
   internal::PS_to_PM_converter<PointRange, PolygonRange, Point_map> converter(points, polygons, pm);
-  converter(out, vpm);
+  converter(out, vpm,
+    choose_parameter(get_parameter(np_ps, internal_np::point_to_vertex_output_iterator),
+                     impl::make_functor(get_parameter(np_ps, internal_np::vertex_to_vertex_map))),
+    choose_parameter(get_parameter(np_ps, internal_np::polygon_to_face_output_iterator),
+                     impl::make_functor(get_parameter(np_ps, internal_np::face_to_face_map))));
 }
 
 } // namespace Polygon_mesh_processing
diff --git a/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
index 04af9bf3621..28a0be5359e 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/IO/VTK_io_plugin.cpp
@@ -10,7 +10,7 @@
 //                 Jane Tournois
 //
 
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <QtCore/qglobal.h>
 
 #include "Scene_surface_mesh_item.h"
@@ -37,7 +37,7 @@
 #include <CGAL/boost/graph/Euler_operations.h>
 #include <CGAL/property_map.h>
 #include <CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h>
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 #include <CGAL/IO/output_to_vtu.h>
 #include <CGAL/boost/graph/io.h>
 
@@ -377,7 +377,7 @@ public:
     if (is_c3t3)
     {
       typedef std::array<int, 3> Facet; // 3 = id
-      typedef std::array<int, 5> Tet_with_ref; // first 4 = id, fifth = reference
+      typedef std::array<int, 4> Tet; // first 4 = id, fifth = reference
       Scene_c3t3_item* c3t3_item = new Scene_c3t3_item();
       c3t3_item->set_valid(false);
       //build a triangulation from data:
@@ -388,7 +388,8 @@ public:
         double *p = dataP->GetPoint(i);
         points.push_back(Tr::Point(p[0],p[1],p[2]));
       }
-      std::vector<Tet_with_ref> finite_cells;
+      std::vector<Tet> finite_cells;
+      std::vector<C3t3::Subdomain_index> subdomains;
       bool has_mesh_domain = data->GetCellData()->HasArray("MeshDomain");
       vtkDataArray* domains = data->GetCellData()->GetArray("MeshDomain");
       for(int i = 0; i< data->GetNumberOfCells(); ++i)
@@ -396,12 +397,15 @@ public:
         if(data->GetCellType(i) != 10 )
           continue;
         vtkIdList* pids = data->GetCell(i)->GetPointIds();
-        Tet_with_ref cell;
+        Tet cell;
         for(int j = 0; j<4; ++j)
           cell[j] = pids->GetId(j);
-        cell[4] = has_mesh_domain ? static_cast<int>(domains->GetComponent(i,0))
-                                  :1;
         finite_cells.push_back(cell);
+
+        const auto si = has_mesh_domain
+          ? static_cast<int>(domains->GetComponent(i, 0))
+          : 1;
+        subdomains.push_back(si);
       }
       std::map<Facet, int> border_facets;
       //Preprocessing for build_triangulation
@@ -420,9 +424,11 @@ public:
           std::swap(finite_cells[i][1], finite_cells[i][3]);
         }
       }
-      std::vector<typename Tr::Vertex_handle> new_vertices;
-      CGAL::build_triangulation<Tr, true>(c3t3_item->c3t3().triangulation(),
-        points, finite_cells, border_facets, new_vertices);
+
+      CGAL::SMDS_3::build_triangulation_with_subdomains_range(
+        c3t3_item->c3t3().triangulation(),
+        points, finite_cells, subdomains, border_facets,
+        false, false, true);
 
       for( C3t3::Triangulation::Finite_cells_iterator
            cit = c3t3_item->c3t3().triangulation().finite_cells_begin();
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 755e5e8730e..3f2b08782fb 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/C3t3_io_plugin.cpp
@@ -1,6 +1,6 @@
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include "Scene_c3t3_item.h"
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 #include <CGAL/Three/Polyhedron_demo_io_plugin_interface.h>
 #include <CGAL/Three/Three.h>
 #include <CGAL/IO/File_avizo.h>
@@ -129,13 +129,11 @@ Polyhedron_demo_c3t3_binary_io_plugin::load(
       item->setName(fileinfo.baseName());
       item->set_valid(false);
 
-      if(CGAL::build_triangulation_from_file<C3t3::Triangulation, true>(in, item->c3t3().triangulation(), true))
+      if(CGAL::SMDS_3::build_triangulation_from_file(in, item->c3t3().triangulation(),
+         /*verbose = */true, /*replace_subdomain_0 = */false, /*allow_non_manifold = */true))
       {
         item->c3t3().rescan_after_load_of_triangulation(); //fix counters for facets and cells
-        for( C3t3::Triangulation::Finite_cells_iterator
-             cit = item->c3t3().triangulation().finite_cells_begin();
-             cit != item->c3t3().triangulation().finite_cells_end();
-             ++cit)
+        for( C3t3::Cell_handle cit : item->c3t3().triangulation().finite_cell_handles())
         {
             CGAL_assertion(cit->subdomain_index() >= 0);
             if(cit->subdomain_index() != C3t3::Triangulation::Cell::Subdomain_index())
@@ -152,22 +150,19 @@ Polyhedron_demo_c3t3_binary_io_plugin::load(
         //if there is no facet in the complex, we add the border facets.
         if(item->c3t3().number_of_facets_in_complex() == 0)
         {
-          for( C3t3::Triangulation::Finite_facets_iterator
-               fit = item->c3t3().triangulation().finite_facets_begin();
-               fit != item->c3t3().triangulation().finite_facets_end();
-               ++fit)
+          for( C3t3::Facet fit : item->c3t3().triangulation().finite_facets())
           {
             typedef C3t3::Triangulation::Cell_handle      Cell_handle;
 
-            Cell_handle c = fit->first;
-            Cell_handle nc = c->neighbor(fit->second);
+            Cell_handle c = fit.first;
+            Cell_handle nc = c->neighbor(fit.second);
 
             // By definition, Subdomain_index() is supposed to be the id of the exterior
             if(c->subdomain_index() != C3t3::Triangulation::Cell::Subdomain_index() &&
                nc->subdomain_index() == C3t3::Triangulation::Cell::Subdomain_index())
             {
               // Color the border facet with the index of its cell
-              item->c3t3().add_to_complex(c, fit->second, c->subdomain_index());
+              item->c3t3().add_to_complex(c, fit.second, c->subdomain_index());
             }
           }
         }
@@ -236,7 +231,9 @@ save(QFileInfo fileinfo, QList<Scene_item *> &items)
   else  if (fileinfo.suffix() == "mesh")
   {
     std::ofstream medit_file (qPrintable(path));
-    c3t3_item->c3t3().output_to_medit(medit_file,true,true);
+    CGAL::IO::write_MEDIT(medit_file, c3t3_item->c3t3(),
+                          CGAL::parameters::rebind_labels(true)
+                          .show_patches(true));
     items.pop_front();
     return true;
   }
diff --git a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
index ba71e754425..7f1389b8ba4 100644
--- a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.cpp
@@ -210,9 +210,18 @@ bool Scene_c3t3_item::is_facet_oriented(const T3::Facet& f)const
   return (index % 2 == 1) == d->c3t3.is_in_complex(cell);
 }
 
+QString Scene_c3t3_item::toolTip() const {
+  return tr("<p><b>3D complex in a 3D triangulation</b></p>"
+    "<p>Number of vertices: %1<br />"
+    "Number of surface facets: %2<br />"
+    "Number of volume tetrahedra: %3</p>%4")
+    .arg(c3t3().triangulation().number_of_vertices())
+    .arg(c3t3().number_of_facets_in_complex())
+    .arg(c3t3().number_of_cells_in_complex())
+    .arg(property("toolTip").toString());
+}
 QMenu* Scene_c3t3_item::contextMenu()
 {
-
   const char* prop_name = "Menu modified by Scene_c3t3_item.";
 
   QMenu* menu = Scene_triangulation_3_item::contextMenu();
@@ -278,6 +287,26 @@ bool Scene_c3t3_item::load_binary(std::istream& is)
     return false;
 }
 
+void Scene_c3t3_item::compute_bbox() const
+{
+  if (isEmpty())
+    _bbox = Bbox();
+  else
+  {
+    CGAL::Bbox_3 result;//default is [+infinity; -infinity]
+    for (Tr::Cell_handle c : c3t3().cells_in_complex())
+    {
+      Tr::Vertex_handle v = (c->vertex(0) != c3t3().triangulation().infinite_vertex())
+                           ? c->vertex(0)
+                           : c->vertex(1);
+      result += v->point().bbox();
+    }
+    _bbox = Bbox(result.xmin(), result.ymin(), result.zmin(),
+                 result.xmax(), result.ymax(), result.zmax());
+  }
+}
+
+
 void Scene_c3t3_item::export_facets_in_complex()
 {
   SMesh outmesh;
diff --git a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.h b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.h
index ea3a5572e10..834f3527edc 100644
--- a/Polyhedron/demo/Polyhedron/Scene_c3t3_item.h
+++ b/Polyhedron/demo/Polyhedron/Scene_c3t3_item.h
@@ -59,6 +59,8 @@ using namespace CGAL::Three;
     }
     bool load_binary(std::istream& is) override;
 
+    void compute_bbox() const override;
+
     bool is_valid() const;//true if the c3t3 is correct, false if it was made from a .mesh, for example
     void set_valid(bool);
     QMenu* contextMenu() override;
@@ -95,6 +97,7 @@ using namespace CGAL::Three;
     bool do_take_vertex(const T3::Vertex_handle &)const override;
     bool is_facet_oriented(const T3::Facet&)const override;
     bool is_surface()const override;
+    QString toolTip() const override;
     void common_constructor(bool is_surface);
   };
 
diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h b/SMDS_3/doc/SMDS_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h
similarity index 99%
rename from Mesh_3/doc/Mesh_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h
rename to SMDS_3/doc/SMDS_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h
index 50b2751ac74..f97cdcb318b 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h
+++ b/SMDS_3/doc/SMDS_3/Concepts/MeshComplexWithFeatures_3InTriangulation_3.h
@@ -1,5 +1,5 @@
 /*!
-\ingroup PkgMesh3Concepts
+\ingroup PkgSMDS3Concepts
 \cgalConcept
 
 The concept `MeshComplexWithFeatures_3InTriangulation_3` describes a data structure
diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshComplex_3InTriangulation_3.h b/SMDS_3/doc/SMDS_3/Concepts/MeshComplex_3InTriangulation_3.h
similarity index 99%
rename from Mesh_3/doc/Mesh_3/Concepts/MeshComplex_3InTriangulation_3.h
rename to SMDS_3/doc/SMDS_3/Concepts/MeshComplex_3InTriangulation_3.h
index 3d3e28c7e2f..c3b1696a58d 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshComplex_3InTriangulation_3.h
+++ b/SMDS_3/doc/SMDS_3/Concepts/MeshComplex_3InTriangulation_3.h
@@ -1,5 +1,5 @@
 /*!
-\ingroup PkgMesh3Concepts
+\ingroup PkgSMDS3Concepts
 \cgalConcept
 
 The concept `MeshComplex_3InTriangulation_3` describes a data structure
@@ -46,7 +46,7 @@ The data structure encodes the final mesh at the end of the meshing process.
 
 \sa `MeshDomain_3`
 \sa `MeshComplexWithFeatures_3InTriangulation_3`
-\sa `CGAL::make_mesh_3()`
+\sa \link CGAL::make_mesh_3() `CGAL::make_mesh_3()`\endlink
 
 */
 
diff --git a/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshCellBase_3.h b/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshCellBase_3.h
new file mode 100644
index 00000000000..4ac54ef66db
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshCellBase_3.h
@@ -0,0 +1,80 @@
+/*!
+\ingroup PkgSMDS3Concepts
+\cgalConcept
+
+The concept `SimplicialMeshCellBase_3` describes the requirements
+for the `TriangulationDataStructure_3::Cell` type of the triangulation
+used in the 3D simplicial mesh data structure. The type `SimplicialMeshCellBase_3`
+refines the concept `TriangulationCellBase_3`
+and must be copy constructible.
+The concept `SimplicialMeshCellBase_3`
+includes a way to store and retrieve
+if a given cell of the triangulation is inside a subdomain or not,
+and which subdomain it belongs to
+in case of a multi-domain.
+
+Moreover, this concept adds four markers per cell to mark the facets
+of the triangulation that are surface facets.
+
+\cgalRefines `TriangulationCellBase_3 `
+\cgalRefines `CopyConstructible`
+
+\cgalHasModel `CGAL::Compact_mesh_cell_base_3`
+\cgalHasModel `CGAL::Mesh_cell_base_3`
+\cgalHasModel `CGAL::Simplicial_mesh_cell_base_3`
+\cgalHasModel `CGAL::Tetrahedral_remeshing::Remeshing_cell_base_3`
+
+*/
+
+class SimplicialMeshCellBase_3 {
+public:
+
+/// \name Types
+/// @{
+
+/*!
+Type of indices for cells of the mesh complex.
+Must match the type `MeshDomain_3::Subdomain_index` in the context of mesh generation.
+*/
+typedef unspecified_type Subdomain_index;
+
+/*!
+Type of indices for surface patches of the mesh complex.
+Must match the type `MeshDomain_3::Surface_patch_index` in the context of mesh generation.
+*/
+typedef unspecified_type Surface_patch_index;
+
+
+/// @}
+
+/// \name Operations
+/// @{
+
+/*!
+returns the index of the input subdomain that contains the cell.
+*/
+Subdomain_index subdomain_index();
+
+/*!
+Sets the subdomain index of the cell.
+*/
+void set_subdomain_index(Subdomain_index index);
+
+/*!
+returns `true` iff `facet(i)` is a surface facet.
+*/
+bool is_facet_on_surface(int i);
+
+/*!
+returns `Surface_patch_index` of facet `i`.
+*/
+Surface_patch_index surface_patch_index(int i);
+
+/*!
+sets `Surface_patch_index` of facet `i` to `index`.
+*/
+void set_surface_patch_index(int i, Surface_patch_index index);
+
+/// @}
+
+}; /* end SimplicialMeshCellBase_3 */
diff --git a/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshVertexBase_3.h b/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshVertexBase_3.h
new file mode 100644
index 00000000000..0ada434d3eb
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/Concepts/SimplicialMeshVertexBase_3.h
@@ -0,0 +1,91 @@
+/*!
+\ingroup PkgSMDS3Concepts
+\cgalConcept
+
+The concept `SimplicialMeshVertexBase_3` describes the requirements
+for the `Vertex` type of the triangulation
+used in the 3D simplicial mesh data structure. The type `SimplicialMeshVertexBase_3`
+refines the concept `TriangulationVertexBase_3`.
+It provides additional members to store and retrieve
+information about the location of the vertex with respect
+to the input domain describing the discretized domain.
+More specifically, the concept `SimplicialMeshVertexBase_3` provides read-write access
+to an integer representing the dimension of the lowest dimensional face
+of the input 3D complex on which the vertex lies,
+and to an index characteristic of this face.
+
+\cgalRefines `TriangulationVertexBase_3`
+
+\cgalHasModel `CGAL::Mesh_vertex_base_3`
+\cgalHasModel `CGAL::Simplicial_mesh_vertex_base_3`
+\cgalHasModel `CGAL::Tetrahedral_remeshing::Remeshing_vertex_base_3`
+
+*/
+
+class SimplicialMeshVertexBase_3 {
+public:
+
+/// \name Types
+/// @{
+
+/*!
+Index type.
+*/
+typedef unspecified_type Index;
+
+/*!
+Numerical type.
+*/
+typedef unspecified_type FT;
+
+/// @}
+
+/// \name Operations
+/// @{
+
+/*!
+Returns the dimension of the lowest dimensional face of the input 3D complex that contains the vertex.
+*/
+int in_dimension() const;
+
+/*!
+Sets the dimension of the lowest dimensional face of the input 3D complex that contains the vertex.
+*/
+void set_dimension(int);
+
+/*!
+Returns the index of the lowest dimensional face of the input 3D complex that contains the vertex.
+*/
+Index index();
+
+/*!
+Sets the index of the lowest dimensional face of the input 3D complex that contains the vertex.
+*/
+void set_index(Index);
+
+/*!
+Returns `true` if the cache is valid.
+*/
+bool is_c2t3_cache_valid();
+
+/*!
+Invalidates the cache.
+*/
+void invalidate_c2t3_cache();
+
+/*!
+Returns the cached number of facets of the complex incident to the vertex.
+*/
+int cached_number_of_incident_facets();
+
+/*!
+This method concerns the adjacency
+graph of the facets of the complex incident to the vertex
+and returns a cached value for the number of connected components this graph.
+*/
+int cached_number_of_components();
+
+/// @}
+
+
+}; /* end SimplicialMeshVertexBase_3 */
diff --git a/SMDS_3/doc/SMDS_3/Doxyfile.in b/SMDS_3/doc/SMDS_3/Doxyfile.in
new file mode 100644
index 00000000000..78025668400
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/Doxyfile.in
@@ -0,0 +1,12 @@
+@INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
+
+PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 3D Simplicial Mesh Data Structures"
+
+#custom options
+EXTRACT_ALL                     =  false
+HIDE_UNDOC_CLASSES      =  true
+HIDE_UNDOC_MEMBERS     =  true
+WARN_IF_UNDOCUMENTED =  false
+
+EXCLUDE = ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/internal/SMDS_3
+
diff --git a/SMDS_3/doc/SMDS_3/PackageDescription.txt b/SMDS_3/doc/SMDS_3/PackageDescription.txt
new file mode 100644
index 00000000000..8b5ad64a507
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/PackageDescription.txt
@@ -0,0 +1,78 @@
+/// \defgroup PkgSMDS3Ref 3D Simplicial Mesh Data Structures Reference
+
+/// \defgroup PkgSMDS3Concepts Concepts
+/// \ingroup PkgSMDS3Ref
+/// The main concepts of this package.
+
+/// \defgroup PkgSMDS3Classes Classes
+/// \ingroup PkgSMDS3Ref
+/// The classes describing a 3D simplicial mesh data structure.
+
+/// \defgroup PkgSMDS3Functions Functions
+/// \ingroup PkgSMDS3Ref
+/// The functions to work with the 3D mesh data structures.
+
+/// \defgroup PkgSMDS3ExportFunctions Export Functions
+/// \ingroup PkgSMDS3Ref
+/// The free functions that can be used to export meshes to given output file formats.
+
+/// \defgroup PkgSMDS3IOFunctions Input/Output Functions
+/// \ingroup PkgSMDS3Ref
+/// The free functions that can be used to read and write meshes.
+
+/*!
+\addtogroup PkgSMDS3Ref
+\cgalPkgDescriptionBegin{3D Simplicial Mesh Data Structure,PkgSMDS3}
+\cgalPkgPicture{knot_small.png}
+
+\cgalPkgSummaryBegin
+\cgalPkgAuthors{Pierre Alliez, Clément Jamin, Laurent Rineau, Stéphane Tayeb, Jane Tournois, Mariette Yvinec}
+\cgalPkgDesc{This package provides a data structure to store three-dimensional
+  simplicial meshes and their subcomplexes.
+  It provides an API for tetrahedral meshes generated with %CGAL or not,
+  to be processed with %CGAL 3D mesh generation and remeshing algorithms,
+  along with iterators, IO functions, and additional helper functions.
+  }
+\cgalPkgManuals{Chapter_3D_Simplicial_Mesh_Data_Structure,PkgSMDS3Ref}
+\cgalPkgSummaryEnd
+
+\cgalPkgShortInfoBegin
+\cgalPkgSince{5.6}
+\cgalPkgDependsOn{\ref PkgTriangulation3}
+\cgalPkgBib{cgal:ajrtty-mds3}
+\cgalPkgLicense{\ref licensesGPL  "GPL"}
+\cgalPkgDemo{Polyhedron demo,polyhedron_3.zip}
+\cgalPkgShortInfoEnd
+\cgalPkgDescriptionEnd
+
+\cgalClassifedRefPages
+
+\cgalCRPSection{Concepts}
+
+- `MeshComplex_3InTriangulation_3`
+- `MeshComplexWithFeatures_3InTriangulation_3`
+- `SimplicialMeshCellBase_3`
+- `SimplicialMeshVertexBase_3`
+
+\cgalCRPSection{Classes}
+
+- `CGAL::Mesh_complex_3_in_triangulation_3`
+- `CGAL::Simplicial_mesh_vertex_base_3`
+- `CGAL::Simplicial_mesh_cell_base_3`
+
+\cgalCRPSection{Function Templates}
+
+- `CGAL::facets_in_complex_3_to_triangle_mesh()`
+- `CGAL::tetrahedron_soup_to_triangulation_3()`
+
+\cgalCRPSection{Input/Output Functions}
+
+- `CGAL::IO::write_MEDIT()`
+- `CGAL::IO::read_MEDIT()`
+- `CGAL::IO::output_to_vtu()`
+- `CGAL::IO::output_to_tetgen()`
+- `CGAL::IO::save_binary_file()`
+- `CGAL::IO::load_binary_file()`
+- `CGAL::IO::output_to_medit()` (deprecated)
+*/
+
diff --git a/SMDS_3/doc/SMDS_3/SMDS_3.txt b/SMDS_3/doc/SMDS_3/SMDS_3.txt
new file mode 100644
index 00000000000..7fcd35d7336
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/SMDS_3.txt
@@ -0,0 +1,91 @@
+namespace CGAL {
+/*!
+
+\mainpage User Manual
+\anchor Chapter_3D_Simplicial_Mesh_Data_Structure
+\anchor userchaptersmds3
+\authors Pierre Alliez, Clément Jamin, Laurent Rineau, Stéphane Tayeb, Jane Tournois, Mariette Yvinec
+\cgalAutoToc
+
+\cgalFigureBegin{figure_tetmesh_knot,knot_full.jpg}
+A multi-domain tetrahedral mesh generated from a polyhedral surface with multiple surface patches.
+The complete triangulation is displayed, including cells that belong or do not
+belong to the mesh complex, surface patches, and feature edges.
+\cgalFigureEnd
+
+
+\section SMDS_3_section_c3t3 Mesh Complex
+
+This package is devoted to the representation of 3-Dimensional simplicial mesh data structures.
+
+A 3D simplicial complex is composed of points, line segments, triangles,
+tetrahedra, and their corresponding combinatorial description
+(namely vertices, edges, faces and cells).
+CGAL provides 3D triangulations, that describe
+both the geometry and connectivity of a 3D simplicial complex,
+implemented in the
+the \ref PkgTriangulation3 and \ref PkgTDS3 packages.
+
+We introduce the concept of \em mesh \em complex, that encodes extra information
+on top of a 3D triangulation to represent a valid simplicial
+complex. A mesh complex describes four subcomplexes
+of simplices
+of the support 3D triangulation, per dimension from 0 to 3:
+- corner vertices (0D),
+- feature edges (1D),
+- surface facets (2D),
+- domain cells (3D). See Figure \cgalFigureRef{figure_c3t3_cells}.
+
+The concept `MeshComplex_3InTriangulation_3` is a data structure devised to
+represent these three-dimensional complexes embedded in a `Triangulation_3`.
+
+\cgalFigureBegin{figure_c3t3_cells,c3t3_cells.jpg}
+(Left and Middle) A multi-domain 3D mesh is represented by its tetrahedral cells,
+with subdomain indices, and surface indices (depicted with different colors here).
+(Right) The underlying `Triangulation_3` triangulates the whole convex hull of its vertices.
+The cells that lie outside the meshing domain are drawn in wire frame.
+\cgalFigureEnd
+
+
+\section SMDS_3_section_examples Examples
+
+\subsection TetSoupExample From Tetrahedron Soup to Triangulation_3
+
+In the first example of this section, we build a random
+`Delaunay_triangulation_3` and use it to build a consistent though
+connectivity-free tetrahedron soup.
+The tetrahedron soup is then put back together in a
+`CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3` before
+being set as the reference triangulation of a `Mesh_complex_3_in_triangulation_3`.
+
+\cgalExample{SMDS_3/tetrahedron_soup_to_c3t3_example.cpp}
+
+
+\subsection IOExample Input/Output Example
+
+The example below illustrates how to use the IO functions
+for reading and writing a triangulation with the `Medit` file format
+(See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.).
+
+\cgalExample{SMDS_3/c3t3_example.cpp}
+
+
+\subsection MoreExamples More Examples In Other Packages
+
+The `Mesh_complex_3_in_triangulation_3` is widely used in the \ref PkgMesh3 package.
+Many more examples can be found in its \ref Mesh_3_section_examples section.
+
+The package \ref PkgTetrahedralRemeshing also makes use of the
+`Mesh_complex_3_in_triangulation_3` since it serves as a post-processing for
+tetrahedral mesh generation. Some examples can be found in the \ref secTetRemeshingExamples
+section.
+
+
+\section SMDS_3History Implementation History
+
+The code of the `MeshComplex_3InTriangulation_3` and its variants were initially part of the package \ref PkgMesh3.
+With the meshing and remeshing processes becoming more versatile, it was moved to its own package in the
+release 5.6 of \cgal.
+
+*/
+} /* namespace CGAL */
diff --git a/SMDS_3/doc/SMDS_3/dependencies b/SMDS_3/doc/SMDS_3/dependencies
new file mode 100644
index 00000000000..bfc4a01dbe7
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/dependencies
@@ -0,0 +1,14 @@
+Manual
+BGL
+Kernel_23
+STL_Extension
+Algebraic_foundations
+Stream_support
+Triangulation_3
+Periodic_3_triangulation_3
+TDS_3
+Polyhedron
+Miscellany
+Mesh_3
+Tetrahedral_remeshing
+Polygon_mesh_processing
diff --git a/SMDS_3/doc/SMDS_3/examples.txt b/SMDS_3/doc/SMDS_3/examples.txt
new file mode 100644
index 00000000000..fe33a6e5c64
--- /dev/null
+++ b/SMDS_3/doc/SMDS_3/examples.txt
@@ -0,0 +1,4 @@
+/*!
+\example SMDS_3/c3t3_example.cpp
+\example SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
+*/
diff --git a/SMDS_3/doc/SMDS_3/fig/c3t3_cells.jpg b/SMDS_3/doc/SMDS_3/fig/c3t3_cells.jpg
new file mode 100644
index 00000000000..62a8b2201cc
Binary files /dev/null and b/SMDS_3/doc/SMDS_3/fig/c3t3_cells.jpg differ
diff --git a/SMDS_3/doc/SMDS_3/fig/knot_full.jpg b/SMDS_3/doc/SMDS_3/fig/knot_full.jpg
new file mode 100644
index 00000000000..f46488dfbe1
Binary files /dev/null and b/SMDS_3/doc/SMDS_3/fig/knot_full.jpg differ
diff --git a/SMDS_3/doc/SMDS_3/fig/knot_small.png b/SMDS_3/doc/SMDS_3/fig/knot_small.png
new file mode 100644
index 00000000000..1a1174466a6
Binary files /dev/null and b/SMDS_3/doc/SMDS_3/fig/knot_small.png differ
diff --git a/SMDS_3/examples/SMDS_3/CMakeLists.txt b/SMDS_3/examples/SMDS_3/CMakeLists.txt
new file mode 100644
index 00000000000..54bb8f0ecf1
--- /dev/null
+++ b/SMDS_3/examples/SMDS_3/CMakeLists.txt
@@ -0,0 +1,17 @@
+# Created by the script cgal_create_CMakeLists
+# This is the CMake script for compiling a set of CGAL applications.
+
+cmake_minimum_required(VERSION 3.1...3.20)
+
+project(SMDS_3_Examples)
+
+# CGAL and its components
+find_package(CGAL REQUIRED)
+
+# Boost and its components
+find_package(Boost REQUIRED)
+
+# Creating entries for all C++ files with "main" routine
+# ##########################################################
+create_single_source_cgal_program( "c3t3_example.cpp" )
+create_single_source_cgal_program( "tetrahedron_soup_to_c3t3_example.cpp" )
diff --git a/SMDS_3/examples/SMDS_3/c3t3_example.cpp b/SMDS_3/examples/SMDS_3/c3t3_example.cpp
new file mode 100644
index 00000000000..3b9de3190dd
--- /dev/null
+++ b/SMDS_3/examples/SMDS_3/c3t3_example.cpp
@@ -0,0 +1,56 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Triangulation_3.h>
+#include <CGAL/Triangulation_data_structure_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+
+#include <CGAL/tetrahedral_remeshing.h>
+
+#include <CGAL/tags.h>
+
+#include <CGAL/IO/File_medit.h>
+#include <fstream>
+
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+
+using Subdomain_index = int;
+using Surface_patch_index = unsigned char;
+using Curve_index = char;
+using Corner_index = short;
+
+using Cb = CGAL::Simplicial_mesh_cell_base_3<Subdomain_index, Surface_patch_index>;
+using Vb = CGAL::Simplicial_mesh_vertex_base_3<K, Subdomain_index, Surface_patch_index,
+                                                  Curve_index, Corner_index>;
+
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb, CGAL::Sequential_tag>;
+using Triangulation = CGAL::Triangulation_3<K, Tds>;
+
+using C3t3 = CGAL::Mesh_complex_3_in_triangulation_3<Triangulation>;
+
+
+int main(int argc, char* argv[])
+{
+  std::string filename = (argc > 1) ? std::string(argv[1])
+                       : CGAL::data_file_path("meshes/elephant.mesh");
+
+  Triangulation tr;
+
+  std::ifstream is(filename, std::ios_base::in);
+  CGAL::IO::read_MEDIT(is, tr);
+
+  // [call a remeshing algorithm]
+
+  std::ofstream os("after_remeshing.mesh");
+  CGAL::IO::write_MEDIT(os, tr, CGAL::parameters::all_vertices(true));
+  os.close();
+
+  Triangulation tr2;
+  std::ifstream is2("after_remeshing.mesh");
+  CGAL::IO::read_MEDIT(is2, tr2);
+  is2.close();
+
+  return EXIT_SUCCESS;
+}
diff --git a/SMDS_3/examples/SMDS_3/tetrahedron_soup_to_c3t3_example.cpp b/SMDS_3/examples/SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
new file mode 100644
index 00000000000..7492736d6f6
--- /dev/null
+++ b/SMDS_3/examples/SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
@@ -0,0 +1,78 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/point_generators_3.h>
+#include <CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+
+#include <CGAL/tetrahedron_soup_to_triangulation_3.h>
+#include <CGAL/IO/File_medit.h>
+
+#include <vector>
+#include <unordered_map>
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+
+using DT3 = CGAL::Delaunay_triangulation_3<K>;
+using Remeshing_triangulation = CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3<K>;
+using C3T3 = CGAL::Mesh_complex_3_in_triangulation_3<Remeshing_triangulation>;
+
+using Point_3 = K::Point_3;
+using Tetrahedron_3 = K::Tetrahedron_3;
+using Vertex_handle = DT3::Vertex_handle;
+using Subdomain_index = C3T3::Subdomain_index;
+
+int main(int , char* [])
+{
+  const int nbv = 100;
+
+  //a triangulation
+  DT3 delaunay;
+  std::unordered_map<Vertex_handle, int> v2i;
+  std::vector<DT3::Point>                points(nbv);
+  std::vector<Tetrahedron_3>             tetrahedra;
+  std::vector<std::array<int, 4> >       tets_by_indices;
+  std::vector< Subdomain_index>          subdomains;
+
+  //insert random points
+  CGAL::Random_points_in_cube_3<Point_3> randp(2.);
+  int i = 0;
+  while (i < nbv)
+  {
+    points[i] = *randp++;
+    Vertex_handle v = delaunay.insert(points[i]);
+    v2i[v] = i++;
+  }
+
+  tetrahedra.reserve(delaunay.number_of_finite_cells());
+  tets_by_indices.reserve(delaunay.number_of_finite_cells());
+  subdomains.reserve(delaunay.number_of_finite_cells());
+  for (DT3::Cell_handle c : delaunay.finite_cell_handles())
+  {
+    tetrahedra.push_back(delaunay.tetrahedron(c));
+    tets_by_indices.push_back( { v2i.at(c->vertex(0)),
+                                 v2i.at(c->vertex(1)),
+                                 v2i.at(c->vertex(2)),
+                                 v2i.at(c->vertex(3)) } );
+    subdomains.push_back(Subdomain_index(1));
+  }
+
+  //build triangulation from tetrahedra
+  Remeshing_triangulation tr
+    = CGAL::tetrahedron_soup_to_triangulation_3<Remeshing_triangulation>(tetrahedra);
+
+  //build triangulation from indices
+  Remeshing_triangulation tr2
+    = CGAL::tetrahedron_soup_to_triangulation_3<Remeshing_triangulation>(
+        points, tets_by_indices,
+        CGAL::parameters::subdomain_indices(std::cref(subdomains)));
+
+  //build a C3T3
+  C3T3 c3t3;
+  c3t3.triangulation() = tr;
+
+  std::ofstream ofs("c3t3_output.mesh");
+  CGAL::IO::write_MEDIT(ofs, c3t3);
+
+  return EXIT_SUCCESS;
+}
diff --git a/Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h b/SMDS_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
similarity index 100%
rename from Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
rename to SMDS_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
diff --git a/Mesh_3/include/CGAL/IO/File_avizo.h b/SMDS_3/include/CGAL/IO/File_avizo.h
similarity index 93%
rename from Mesh_3/include/CGAL/IO/File_avizo.h
rename to SMDS_3/include/CGAL/IO/File_avizo.h
index f2b31d68d6c..6ad6530ceaa 100644
--- a/Mesh_3/include/CGAL/IO/File_avizo.h
+++ b/SMDS_3/include/CGAL/IO/File_avizo.h
@@ -13,7 +13,7 @@
 #ifndef CGAL_IO_FILE_AVIZO_H
 #define CGAL_IO_FILE_AVIZO_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 
 #include <CGAL/IO/File_medit.h>
@@ -27,9 +27,11 @@ namespace CGAL {
 namespace IO {
 
 /**
- * @brief outputs mesh to avizo format
- * @param os the stream
- * @param c3t3 the mesh
+ * @ingroup PkgSMDS3ExportFunctions
+ * @brief exports a mesh complex to the Avizo (`.am`) file format
+ * @tparam C3T3 a class model of `MeshComplex_3InTriangulation_3`
+ * @param os the output stream
+ * @param c3t3 the mesh complex
  * \see \ref IOStreamAvizo
  */
 template <class C3T3>
diff --git a/Mesh_3/include/CGAL/IO/File_binary_mesh_3.h b/SMDS_3/include/CGAL/IO/File_binary_mesh_3.h
similarity index 68%
rename from Mesh_3/include/CGAL/IO/File_binary_mesh_3.h
rename to SMDS_3/include/CGAL/IO/File_binary_mesh_3.h
index a2a87ee45ca..e7363047a92 100644
--- a/Mesh_3/include/CGAL/IO/File_binary_mesh_3.h
+++ b/SMDS_3/include/CGAL/IO/File_binary_mesh_3.h
@@ -13,23 +13,38 @@
 #ifndef CGAL_IO_FILE_BINARY_MESH_3_H
 #define CGAL_IO_FILE_BINARY_MESH_3_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 
 #include <iostream>
 #include <string>
 #include <limits>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 
 namespace CGAL {
 
 namespace IO {
 
+  /**
+   * @ingroup PkgSMDS3IOFunctions
+   * @brief outputs a mesh complex to the CGAL binary file format (`.binary.cgal`).
+   *
+   * @tparam C3T3 Type of mesh complex, model of `MeshComplex_3InTriangulation_3`
+   *
+   * @param os the output stream, opened in binary mode
+   * @param c3t3 the mesh complex
+   *
+   * @sa `CGAL::IO::load_binary_file()`
+   */
 template <class C3T3>
 bool
 save_binary_file(std::ostream& os,
-                 const C3T3& c3t3,
-                 bool binary = true)
+                 const C3T3& c3t3
+#ifdef DOXYGEN_RUNNING
+                 )
+#else
+               , bool binary = true)
+#endif
 {
   typedef typename C3T3::Triangulation::Geom_traits::FT FT;
   if(binary) os << "binary ";
@@ -44,6 +59,17 @@ save_binary_file(std::ostream& os,
   // call operator!() twice, because operator bool() is C++11
 }
 
+/**
+ * @ingroup PkgSMDS3IOFunctions
+ * @brief loads a mesh complex from a file written in CGAL binary file format (`.binary.cgal`).
+ *
+ * @tparam C3T3 Type of mesh complex, model of `MeshComplex_3InTriangulation_3`
+ *
+ * @param is the input stream, opened in binary mode
+ * @param c3t3 the mesh complex
+ *
+ * @sa `CGAL::IO::save_binary_file()`
+ */
 template <class C3T3>
 bool load_binary_file(std::istream& is, C3T3& c3t3)
 {
diff --git a/Mesh_3/include/CGAL/IO/File_maya.h b/SMDS_3/include/CGAL/IO/File_maya.h
similarity index 99%
rename from Mesh_3/include/CGAL/IO/File_maya.h
rename to SMDS_3/include/CGAL/IO/File_maya.h
index 4546132bb95..682f9540642 100644
--- a/Mesh_3/include/CGAL/IO/File_maya.h
+++ b/SMDS_3/include/CGAL/IO/File_maya.h
@@ -12,7 +12,7 @@
 #ifndef CGAL_IO_FILE_MAYA_H
 #define CGAL_IO_FILE_MAYA_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/Time_stamper.h>
 #include <CGAL/utility.h>
diff --git a/Mesh_3/include/CGAL/IO/File_medit.h b/SMDS_3/include/CGAL/IO/File_medit.h
similarity index 64%
rename from Mesh_3/include/CGAL/IO/File_medit.h
rename to SMDS_3/include/CGAL/IO/File_medit.h
index 95585dc1b82..831dca9e121 100644
--- a/Mesh_3/include/CGAL/IO/File_medit.h
+++ b/SMDS_3/include/CGAL/IO/File_medit.h
@@ -14,10 +14,11 @@
 #ifndef CGAL_IO_FILE_MEDIT_H
 #define CGAL_IO_FILE_MEDIT_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
-#include <CGAL/Mesh_3/config.h>
-#include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_fwd.h>
+#include <CGAL/SMDS_3/Mesh_complex_3_in_triangulation_3_fwd.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 
 #include <CGAL/utility.h>
 #include <CGAL/basic.h>
@@ -26,16 +27,20 @@
 #include <boost/unordered_map.hpp>
 #include <boost/utility/enable_if.hpp>
 
+#include <CGAL/Named_function_parameters.h>
+#include <CGAL/boost/graph/named_params_helper.h>
+
 #include <iomanip>
 #include <iostream>
 #include <map>
 #include <set>
 #include <string>
 #include <vector>
+#include <unordered_map>
 
 namespace CGAL {
 
-namespace Mesh_3 {
+namespace SMDS_3 {
 
 //-------------------------------------------------------
 // Needed in verbose mode
@@ -65,14 +70,9 @@ public:
   Rebind_cell_pmap(const C3T3& c3t3)
     : r_c3t3_(c3t3)
   {
-    typedef typename C3T3::Cells_in_complex_iterator Cell_iterator;
+    int index_counter = 1;
 
-    int first_index = 0;
-    int index_counter = first_index + 1;
-
-    for( Cell_iterator cell_it = r_c3t3_.cells_in_complex_begin();
-         cell_it != r_c3t3_.cells_in_complex_end();
-         ++cell_it)
+    for( Cell_handle cell_it : r_c3t3_.cells_in_complex())
     {
       // Add subdomain index in internal map if needed
       std::pair<typename Subdomain_map::iterator, bool> is_insert_successful =
@@ -84,7 +84,7 @@ public:
     }
 
     // Rebind indices in alphanumeric order
-    index_counter = first_index + 1;
+    index_counter = 1;
     for ( typename Subdomain_map::iterator mit = subdomain_map_.begin() ;
           mit != subdomain_map_.end() ;
           ++mit )
@@ -125,7 +125,7 @@ private:
     if ( elt_it != subdomain_map_.end() )
       return elt_it->second;
     else
-      return -1;
+      return 0;
   }
 
 private:
@@ -170,12 +170,9 @@ public:
 
   size_type subdomain_number() const
   {
-    typedef typename C3T3::Cells_in_complex_iterator Cell_iterator;
     std::set<Subdomain_index> subdomain_set;
 
-    for( Cell_iterator cell_it = r_c3t3_.cells_in_complex_begin();
-        cell_it != r_c3t3_.cells_in_complex_end();
-        ++cell_it)
+    for( Cell_handle cell_it : r_c3t3_.cells_in_complex())
     {
       // Add subdomain index in set
       subdomain_set.insert(subdomain_index(cell_it));
@@ -214,30 +211,23 @@ public:
     : r_c3t3_(c3t3)
     , cell_pmap_(cell_pmap)
   {
-    typedef typename C3T3::Facets_in_complex_iterator Facet_iterator;
-
     int first_index = 1;
     int index_counter = first_index;
 
-    for( Facet_iterator facet_it = r_c3t3_.facets_in_complex_begin();
-        facet_it != r_c3t3_.facets_in_complex_end();
-        ++facet_it)
+    for( Facet facet_it : r_c3t3_.facets_in_complex())
     {
       // Add surface index in internal map if needed
       std::pair<typename Surface_map::iterator, bool> is_insert_successful =
-          surface_map_.insert(std::make_pair(r_c3t3_.surface_patch_index(*facet_it),
+          surface_map_.insert(std::make_pair(r_c3t3_.surface_patch_index(facet_it),
                                              index_counter));
       if(is_insert_successful.second)
         ++index_counter;
     }
 
     // Find cell_pmap_ unused indices
-    typedef typename C3T3::Cells_in_complex_iterator Cell_iterator;
     std::set<int> cell_label_set;
 
-    for( Cell_iterator cell_it = r_c3t3_.cells_in_complex_begin();
-        cell_it != r_c3t3_.cells_in_complex_end();
-        ++cell_it)
+    for( typename C3T3::Cell_handle cell_it : r_c3t3_.cells_in_complex())
     {
       // Add subdomain index in set
       cell_label_set.insert(get(cell_pmap_, cell_it));
@@ -588,7 +578,7 @@ public:
       break;
 
     default:
-      // should not happen
+      // must not happen
       return -1;
       break;
     }
@@ -703,7 +693,9 @@ struct Medit_pmap_generator<C3T3, false, false>
 template <class C3T3, bool rebind, bool no_patch>
 void
 output_to_medit(std::ostream& os,
-                const C3T3& c3t3)
+                const C3T3& c3t3,
+                const bool all_vertices,
+                const bool all_cells)
 {
 #ifdef CGAL_MESH_3_IO_VERBOSE
   std::cerr << "Output to medit:\n";
@@ -726,7 +718,9 @@ output_to_medit(std::ostream& os,
                   facet_pmap,
                   cell_pmap,
                   facet_pmap_twice,
-                  Generator().print_twice());
+                  Generator().print_twice(),
+                  all_vertices,
+                  all_cells);
 
 #ifdef CGAL_MESH_3_IO_VERBOSE
   std::cerr << "done.\n";
@@ -747,14 +741,14 @@ output_to_medit(std::ostream& os,
                 const Facet_index_property_map& facet_pmap,
                 const Cell_index_property_map& cell_pmap,
                 const Facet_index_property_map_twice& facet_twice_pmap = Facet_index_property_map_twice(),
-                const bool print_each_facet_twice = false)
+                const bool print_each_facet_twice = false,
+                const bool all_vertices = true,
+                const bool all_cells = false)
 {
   typedef typename C3T3::Triangulation Tr;
-  typedef typename C3T3::Facets_in_complex_iterator Facet_iterator;
-  typedef typename C3T3::Cells_in_complex_iterator Cell_iterator;
 
-  typedef typename Tr::Finite_vertices_iterator Finite_vertices_iterator;
   typedef typename Tr::Vertex_handle Vertex_handle;
+  typedef typename Tr::Cell_handle   Cell_handle;
   typedef typename Tr::Point Point; //can be weighted or not
 
   const Tr& tr = c3t3.triangulation();
@@ -770,32 +764,61 @@ output_to_medit(std::ostream& os,
 
   os << "MeshVersionFormatted 1\n"
      << "Dimension 3\n";
-
+  os << "# CGAL::Mesh_complex_3_in_triangulation_3\n";
 
   //-------------------------------------------------------
   // Vertices
   //-------------------------------------------------------
-  os << "Vertices\n" << tr.number_of_vertices() << '\n';
 
-  boost::unordered_map<Vertex_handle, int> V;
+  std::unordered_map<Vertex_handle, int> V;
   int inum = 1;
-  for( Finite_vertices_iterator vit = tr.finite_vertices_begin();
-       vit != tr.finite_vertices_end();
-       ++vit)
+  if (all_vertices || all_cells)
   {
-    V[vit] = inum++;
-    Point p = tr.point(vit);
-    os << CGAL::to_double(p.x()) << ' '
-       << CGAL::to_double(p.y()) << ' '
-       << CGAL::to_double(p.z()) << ' '
-       << get(vertex_pmap, vit)
-       << '\n';
+    os << "Vertices\n" << tr.number_of_vertices() << '\n';
+
+    for (typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin();
+         vit != tr.finite_vertices_end();
+         ++vit)
+    {
+      V[vit] = inum++;
+      const Point& p = tr.point(vit);
+      os << CGAL::to_double(p.x()) << ' '
+        << CGAL::to_double(p.y()) << ' '
+        << CGAL::to_double(p.z()) << ' '
+        << get(vertex_pmap, vit)
+        << '\n';
+    }
+  }
+  else
+  {
+    std::ostringstream oss;
+    for (Cell_handle c : c3t3.cells_in_complex())
+    {
+      for (int i = 0; i < 4; ++i)
+      {
+        Vertex_handle vit = c->vertex(i);
+        if (V.find(vit) == V.end())
+        {
+          V[vit] = inum++;
+          const Point& p = tr.point(vit);
+          oss << CGAL::to_double(p.x()) << ' '
+            << CGAL::to_double(p.y()) << ' '
+            << CGAL::to_double(p.z()) << ' '
+            << get(vertex_pmap, vit)
+            << '\n';
+        }
+      }
+    }
+    os << "Vertices\n" << V.size() << "\n";
+    os << oss.str();
   }
 
   //-------------------------------------------------------
   // Facets
   //-------------------------------------------------------
-  typename C3T3::size_type number_of_triangles = c3t3.number_of_facets_in_complex();
+  typename C3T3::size_type number_of_triangles
+    = std::distance(c3t3.facets_in_complex_begin(),
+                    c3t3.facets_in_complex_end());
 
   if ( print_each_facet_twice )
     number_of_triangles += number_of_triangles;
@@ -803,12 +826,8 @@ output_to_medit(std::ostream& os,
   os << "Triangles\n"
      << number_of_triangles << '\n';
 
-  for( Facet_iterator fit = c3t3.facets_in_complex_begin();
-       fit != c3t3.facets_in_complex_end();
-       ++fit)
+  for(typename C3T3::Facet f : c3t3.facets_in_complex())
   {
-    typename C3T3::Facet f = (*fit);
-
     // Apply priority among subdomains, to get consistent facet orientation per subdomain-pair interface.
     if ( print_each_facet_twice )
     {
@@ -827,30 +846,47 @@ output_to_medit(std::ostream& os,
       std::swap(vh2, vh3);
 
     os << V[vh1] << ' ' << V[vh2] << ' ' << V[vh3] << ' ';
-    os << get(facet_pmap, *fit) << '\n';
+    os << get(facet_pmap, f) << '\n';
 
     // Print triangle again if needed, with opposite orientation
     if ( print_each_facet_twice )
     {
       os << V[vh3] << ' ' << V[vh2] << ' ' << V[vh1] << ' ';
-      os << get(facet_twice_pmap, *fit) << '\n';
+      os << get(facet_twice_pmap, f) << '\n';
     }
   }
 
   //-------------------------------------------------------
   // Tetrahedra
   //-------------------------------------------------------
+  typename C3T3::size_type number_of_cells
+    = all_cells
+    ? c3t3.triangulation().number_of_finite_cells()
+    : std::distance(c3t3.cells_in_complex_begin(), c3t3.cells_in_complex_end());;
   os << "Tetrahedra\n"
-     << c3t3.number_of_cells_in_complex() << '\n';
+     << number_of_cells << '\n';
 
-  for( Cell_iterator cit = c3t3.cells_in_complex_begin() ;
-       cit != c3t3.cells_in_complex_end() ;
-       ++cit )
+  if (all_cells)
   {
-    for (int i=0; i<4; i++)
-      os << V[cit->vertex(i)] << ' ';
+    for (auto cit = c3t3.triangulation().finite_cells_begin();
+         cit != c3t3.triangulation().finite_cells_end();
+         ++cit)
+    {
+      for (int i = 0; i < 4; i++)
+        os << V[cit->vertex(i)] << ' ';
 
-    os << get(cell_pmap, cit) << '\n';
+      os << get(cell_pmap, cit) << '\n';
+    }
+  }
+  else
+  {
+    for (Cell_handle cit : c3t3.cells_in_complex())
+    {
+      for (int i = 0; i < 4; i++)
+        os << V[cit->vertex(i)] << ' ';
+
+      os << get(cell_pmap, cit) << '\n';
+    }
   }
 
   //-------------------------------------------------------
@@ -865,53 +901,222 @@ output_to_medit(std::ostream& os,
 namespace IO {
 
 /**
- * @brief outputs mesh to medit format
- * @param os the stream
- * @param c3t3 the mesh
- * @param rebind if true, labels of cells are rebinded into [1..nb_of_labels]
- * @param show_patches if true, patches are labeled with different labels than
- * cells. If false, each surface facet is written twice, using label of
- * each adjacent cell.
+ * @ingroup PkgSMDS3IOFunctions
+ * @deprecated This function is deprecated. Users should instead use `CGAL::IO::write_MEDIT()`
+ * @brief outputs a mesh complex to the medit (`.mesh`) file format.
+        See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
+ * @param os the output stream
+ * @param c3t3 the mesh complex
+ * @param rebind if `true`, labels of cells are rebinded into `[1..nb_of_labels]`
+ * @param show_patches if `true`, patches are labeled with different labels than
+ *                     cells. If `false`, each surface facet is written twice,
+ *                     using the label of each adjacent cell.
  * \see \ref IOStreamMedit
  */
 template <class C3T3>
 void
 output_to_medit(std::ostream& os,
                 const C3T3& c3t3,
-                bool rebind = false,
-                bool show_patches = false)
+                bool rebind,      // = false,
+                bool show_patches // = false
+#ifndef DOXYGEN_RUNNING
+              , bool all_vertices // = true
+              , bool all_cells    // = false
+#endif
+)
 {
   if ( rebind )
   {
     if ( show_patches )
-      Mesh_3::output_to_medit<C3T3,true,false>(os,c3t3);
+      CGAL::SMDS_3::output_to_medit<C3T3,true,false>(os, c3t3,
+        all_vertices, all_cells);
     else
-      Mesh_3::output_to_medit<C3T3,true,true>(os,c3t3);
+      CGAL::SMDS_3::output_to_medit<C3T3,true,true>(os, c3t3,
+        all_vertices, all_cells);
   }
   else
   {
     if ( show_patches )
-      Mesh_3::output_to_medit<C3T3,false,false>(os,c3t3);
+      CGAL::SMDS_3::output_to_medit<C3T3,false,false>(os, c3t3,
+        all_vertices, all_cells);
     else
-      Mesh_3::output_to_medit<C3T3,false,true>(os,c3t3);
+      CGAL::SMDS_3::output_to_medit<C3T3,false,true>(os, c3t3,
+        all_vertices, all_cells);
   }
 }
 
-
-template<typename T3>
-void write_MEDIT(std::ostream& os, const T3& t3)
+/**
+ * @ingroup PkgSMDS3IOFunctions
+ * @brief outputs a mesh complex to the medit (`.mesh`) file format.
+ *      See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
+ * @tparam T3 can be instantiated with any 3D triangulation of \cgal provided that its
+ *  vertex and cell base class are models of the concepts `SimplicialMeshVertexBase_3`
+ * and `SimplicialMeshCellBase_3`, respectively.
+ * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+ *
+ * @param os the output stream
+ * @param t3 the triangulation
+ * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
+ *
+ * \cgalNamedParamsBegin
+ * \cgalParamNBegin{all_cells}
+ *   \cgalParamDescription{If `true`, all the cells in `t3` are written in `os`,
+ *        whether they belong to the complex or not.
+ *        Otherwise, only the cells `c` for which
+ *        `c->subdomain_index() != Subdomain_index()` are written.}
+ *   \cgalParamType{Boolean}
+ *   \cgalParamDefault{`true`}
+ *   \cgalParamExtra{This parameter must be set to `true` for the file to be readable by `read_MEDIT()`.}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{all_vertices}
+ *   \cgalParamDescription{If `true`, all the finite vertices in `t3` are written in `os`.
+ *                         Otherwise, only the vertices that belong to a cell `c` for which
+ *                         `c->subdomain_index() != Subdomain_index()` are written}
+ *   \cgalParamType{Boolean}
+ *   \cgalParamDefault{`true`}
+ *   \cgalParamExtra{If `all_cells` is `true`, the value of this parameter is ignored and
+                     all vertices are written in `os`. It must be
+ *                   set to `true` for the file to be readable by `read_MEDIT()`.}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{rebind_labels}
+ *  \cgalParamDescription{If `true`, labels of cells are rebinded into `[1..nb_of_labels]`}
+ *  \cgalParamType{Boolean}
+ *  \cgalParamDefault{`false`}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{show_patches}
+ *  \cgalParamDescription{If `true`, patches are labeled with different labels than
+ *                        cells. If `false`, each surface facet is written twice,
+ *                        using the label of each adjacent cell.}
+ *  \cgalParamType{Boolean}
+ *  \cgalParamDefault{`true`}
+ * \cgalParamNEnd
+ * \cgalNamedParamsEnd
+ * \see \ref IOStreamMedit
+ */
+template<typename T3, typename NamedParameters = parameters::Default_named_parameters>
+void write_MEDIT(std::ostream& os,
+                 const T3& t3,
+                 const NamedParameters& np = parameters::default_values())
 {
   CGAL::Mesh_complex_3_in_triangulation_3<T3, int, int> c3t3;
   c3t3.triangulation() = t3;
   c3t3.rescan_after_load_of_triangulation();
-  output_to_medit(os, c3t3);
+
+  using parameters::get_parameter;
+  using parameters::choose_parameter;
+
+  bool rebind = choose_parameter(get_parameter(np, internal_np::rebind_labels), false);;
+  bool show_patches = choose_parameter(get_parameter(np, internal_np::show_patches), true);
+  bool all_c = choose_parameter(get_parameter(np, internal_np::all_cells), true);
+  bool all_v = all_c || choose_parameter(get_parameter(np, internal_np::all_vertices), true);
+
+  output_to_medit(os, c3t3, rebind, show_patches, all_v, all_c);
 }
 
+/**
+ * @ingroup PkgSMDS3IOFunctions
+ * @brief outputs a mesh complex to the medit (`.mesh`) file format.
+ *      See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
+ * @tparam T3 can be instantiated with any 3D triangulation of \cgal provided that its
+ *  vertex and cell base class are models of the concepts `MeshVertexBase_3` and `MeshCellBase_3`, respectively.
+ * @tparam CornerIndex is the type of the indices for corners
+ * @tparam CurveIndex is the type of the indices for curves
+ * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+
+ * @param os the output stream
+ * @param c3t3 the mesh complex
+ * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
+ *
+ * \cgalNamedParamsBegin
+ * \cgalParamNBegin{all_cells}
+ *   \cgalParamDescription{If `true`, all the cells in `t3` are written in `os`,
+ *        whether they belong to the complex or not.
+ *        Otherwise, only the cells `c` for which
+ *        `c->subdomain_index() != Subdomain_index()` are written.}
+ *   \cgalParamType{Boolean}
+ *   \cgalParamDefault{`true`}
+ *   \cgalParamExtra{If the complex does not form a topological sphere,
+ *        this parameter must be set to `true` for the file to be readable by `read_MEDIT()`.
+ *        Otherwise the underlying triangulation data structure will not be valid.}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{all_vertices}
+ *   \cgalParamDescription{If `true`, all the vertices in `t3` are written in `os`.
+ *                         Otherwise, only the vertices that belong to a cell `c` for which
+ *                         `c->subdomain_index() != Subdomain_index()` are written}
+ *   \cgalParamType{Boolean}
+ *   \cgalParamDefault{`true`}
+ *   \cgalParamExtra{If `all_cells` is `true`, the value of this parameter is ignored
+          and all vertices are written in `os`. If the complex does not
+          form a topological sphere, it must be
+ *        set to `true` for the file to be readable by `read_MEDIT()`.
+ *        Otherwise the underlying triangulation data structure will not be valid.}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{rebind_labels}
+ *  \cgalParamDescription{If `true`, labels of cells are rebinded into `[1..nb_of_labels]`}
+ *  \cgalParamType{Boolean}
+ *  \cgalParamDefault{`false`}
+ * \cgalParamNEnd
+ *
+ * \cgalParamNBegin{show_patches}
+ *  \cgalParamDescription{If `true`, patches are labeled with different labels than
+ *                        cells. If `false`, each surface facet is written twice,
+ *                        using the label of each adjacent cell.}
+ *  \cgalParamType{Boolean}
+ *  \cgalParamDefault{`true`}
+ * \cgalParamNEnd
+ * \cgalNamedParamsEnd
+ *
+ * \see \ref IOStreamMedit
+ */
+template<typename T3,
+         typename CornerIndex,
+         typename CurveIndex,
+         typename NamedParameters = parameters::Default_named_parameters>
+void write_MEDIT(std::ostream& os,
+  const CGAL::Mesh_complex_3_in_triangulation_3<T3, CornerIndex, CurveIndex>& c3t3,
+  const NamedParameters& np = parameters::default_values())
+{
+  return write_MEDIT(os, c3t3.triangulation(), np);
+}
+
+/**
+ * @ingroup PkgSMDS3IOFunctions
+ * @brief reads a mesh complex written in the medit (`.mesh`) file format.
+ *   See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
+ * @tparam T3 can be instantiated with any 3D triangulation of \cgal provided that its
+ *  vertex and cell base class are models of the concepts `MeshVertexBase_3` and `MeshCellBase_3`,
+ *  respectively.
+ *
+ * @param in the input stream
+ * @param t3 the triangulation
+ *
+ * @returns `true` if the connectivity of the triangulation could be built consistently
+ * from \p in,
+ * and `false` if the triangulation is empty, or if the connectivity
+ * of \p t3 could not be built.
+ * If `false` is returned, \p t3 is empty when the function returns.
+ *
+ * This function reads the data about vertices, surface facets, and
+ * triangulation cells from `in`, and builds a valid `T3` from it.
+ *
+ * Note that a valid 3D triangulation of \cgal must have a valid
+ * data structure (see `TriangulationDataStructure_3 `),
+ * positively oriented cells,
+ * and cover the geometric convex hull of all points in `t3`.
+ */
 template<typename T3>
 bool read_MEDIT(std::istream& in, T3& t3)
 {
   CGAL_assertion(!(!in));
-  return CGAL::build_triangulation_from_file<T3, true>(in, t3);
+  bool b = CGAL::SMDS_3::build_triangulation_from_file(in, t3);
+  if(!b)
+    t3.clear();
+  return b;
 }
 
 } // namespace IO
diff --git a/Mesh_3/include/CGAL/IO/File_tetgen.h b/SMDS_3/include/CGAL/IO/File_tetgen.h
similarity index 88%
rename from Mesh_3/include/CGAL/IO/File_tetgen.h
rename to SMDS_3/include/CGAL/IO/File_tetgen.h
index 03fad2e7998..e35246a38a9 100644
--- a/Mesh_3/include/CGAL/IO/File_tetgen.h
+++ b/SMDS_3/include/CGAL/IO/File_tetgen.h
@@ -13,7 +13,7 @@
 #ifndef CGAL_IO_FILE_TETGEN_H
 #define CGAL_IO_FILE_TETGEN_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/Time_stamper.h>
 #include <CGAL/IO/File_medit.h>
@@ -25,7 +25,7 @@
 
 namespace CGAL {
 
-namespace Mesh_3 {
+namespace SMDS_3 {
 
 template <class C3T3, bool rebind, bool no_patch>
 void
@@ -185,10 +185,22 @@ output_to_tetgen(std::string filename,
   //-------------------------------------------------------
 } // end output_to_tetgen(...)
 
-} // end namespace Mesh_3
+} // end namespace SMDS_3
 
 namespace IO {
 
+
+/**
+ * \ingroup PkgSMDS3ExportFunctions
+ * @brief exports a mesh complex to tetgen format
+ * @param filename the path to the output files, without the extension.
+ * @param c3t3 the mesh complex
+ * @param rebind if true, labels of cells are rebinded into [1..nb_of_labels]
+ * @param show_patches if true, patches are labeled with different labels than
+ * cells. If false, each surface facet is written twice, using the label of
+ * each adjacent cell.
+ * \see \ref IOStreamTetgen
+ */
 template <class C3T3>
 void
 output_to_tetgen(std::string filename,
@@ -199,16 +211,16 @@ output_to_tetgen(std::string filename,
   if ( rebind )
   {
     if ( show_patches )
-      Mesh_3::output_to_tetgen<C3T3,true,false>(filename,c3t3);
+      SMDS_3::output_to_tetgen<C3T3,true,false>(filename,c3t3);
     else
-      Mesh_3::output_to_tetgen<C3T3,true,true>(filename,c3t3);
+      SMDS_3::output_to_tetgen<C3T3,true,true>(filename,c3t3);
   }
   else
   {
     if ( show_patches )
-      Mesh_3::output_to_tetgen<C3T3,false,false>(filename,c3t3);
+      SMDS_3::output_to_tetgen<C3T3,false,false>(filename,c3t3);
     else
-      Mesh_3::output_to_tetgen<C3T3,false,true>(filename,c3t3);
+      SMDS_3::output_to_tetgen<C3T3,false,true>(filename,c3t3);
   }
 }
 
diff --git a/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h b/SMDS_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
similarity index 94%
rename from Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
rename to SMDS_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
index 84bc4f100f7..85819305e56 100644
--- a/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
+++ b/SMDS_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
@@ -14,7 +14,7 @@
 #ifndef CGAL_IO_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
 #define CGAL_IO_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #ifndef CGAL_NO_DEPRECATED_CODE
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
diff --git a/Mesh_3/include/CGAL/IO/output_to_vtu.h b/SMDS_3/include/CGAL/IO/output_to_vtu.h
similarity index 95%
rename from Mesh_3/include/CGAL/IO/output_to_vtu.h
rename to SMDS_3/include/CGAL/IO/output_to_vtu.h
index d553ddfdfed..e78f1b680a2 100644
--- a/Mesh_3/include/CGAL/IO/output_to_vtu.h
+++ b/SMDS_3/include/CGAL/IO/output_to_vtu.h
@@ -14,7 +14,7 @@
 #ifndef CGAL_OUTPUT_TO_VTU_H
 #define CGAL_OUTPUT_TO_VTU_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/assertions.h>
 #include <CGAL/IO/io.h>
@@ -351,7 +351,19 @@ void output_to_vtu_with_attributes(std::ostream& os,
 
 } // namespace internal
 
-//public API
+//! \ingroup PkgSMDS3ExportFunctions
+//!
+//! \brief exports a tetrahedral mesh complex using the `UnstructuredGrid` XML format.
+//!
+//! \tparam C3T3 a model of `MeshComplexWithFeatures_3InTriangulation_3`.
+//!
+//! \param os the stream used for writing
+//! \param c3t3 the mesh complex
+//! \param mode decides if the data should be written in binary (`IO::BINARY`)
+//!   or in ASCII (`IO::ASCII`).
+//!  If the mode is binary, then the stream `os` must be opened in binary mode.
+//! \see \ref IOStreamVTK
+//!
 template <class C3T3>
 void output_to_vtu(std::ostream& os,
                const C3T3& c3t3,
diff --git a/SMDS_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h b/SMDS_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
new file mode 100644
index 00000000000..3ab95555707
--- /dev/null
+++ b/SMDS_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
@@ -0,0 +1,2100 @@
+// Copyright (c) 2009-2014 INRIA Sophia-Antipolis (France).
+// Copyright (c) 2010-2013 GeometryFactory Sarl (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)     : Stephane Tayeb, Clement Jamin
+//
+//******************************************************************************
+// File Description :
+//******************************************************************************
+
+#ifndef CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
+#define CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/SMDS_3/Mesh_complex_3_in_triangulation_3_fwd.h>
+#include <CGAL/disable_warnings.h>
+#include <CGAL/iterator.h>
+#include <CGAL/SMDS_3/utilities.h>
+#include <CGAL/SMDS_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h>
+#include <CGAL/Time_stamper.h>
+#include <CGAL/Bbox_3.h>
+#include <CGAL/Union_find.h>
+#include <CGAL/SMDS_3/io_signature.h>
+
+#include <CGAL/IO/File_medit.h>
+#include <CGAL/IO/File_maya.h>
+
+#include <boost/bimap/bimap.hpp>
+#include <boost/bimap/multiset_of.hpp>
+#include <CGAL/boost/iterator/transform_iterator.hpp>
+#include <boost/iterator/iterator_adaptor.hpp>
+#include <boost/mpl/if.hpp>
+#include <boost/unordered_map.hpp>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/functional/hash.hpp>
+
+#include <iostream>
+#include <fstream>
+
+
+#ifdef CGAL_LINKED_WITH_TBB
+#include <atomic>
+#include <tbb/concurrent_hash_map.h>
+
+namespace CGAL {
+  template < class DSC, bool Const >
+  std::size_t tbb_hasher(const CGAL::internal::CC_iterator<DSC, Const>& it)
+  {
+    return CGAL::internal::hash_value(it);
+  }
+
+  // As Marc Glisse pointed out the TBB hash of a std::pair is
+  // simplistic and leads to the
+  // TBB Warning: Performance is not optimal because the hash function
+  //              produces bad randomness in lower bits in class
+  //              tbb::interface5::concurrent_hash_map
+  template < class DSC, bool Const >
+  std::size_t tbb_hasher(const std::pair<CGAL::internal::CC_iterator<DSC, Const>,
+                                         CGAL::internal::CC_iterator<DSC, Const> >& p)
+  {
+    return boost::hash<std::pair<CGAL::internal::CC_iterator<DSC, Const>,
+                                 CGAL::internal::CC_iterator<DSC, Const> > >()(p);
+  }
+
+  struct Hash_compare_for_TBB {
+    template < class DSC, bool Const >
+    std::size_t hash(const std::pair<CGAL::internal::CC_iterator<DSC, Const>,
+                                     CGAL::internal::CC_iterator<DSC, Const> >& p) const
+    {
+      return tbb_hasher(p);
+    }
+    template < class DSC, bool Const >
+    std::size_t operator()(const CGAL::internal::CC_iterator<DSC, Const>& it)
+    {
+      return CGAL::internal::hash_value(it);
+    }
+    template <typename T>
+    bool equal(const T& v1, const T& v2) const {
+      return v1 == v2;
+    }
+  };
+}//end namespace CGAL
+#endif
+
+namespace CGAL {
+
+  namespace SMDS_3 {
+
+    namespace details {
+
+      template <typename Tr>
+      class C3t3_helper_class
+      {
+      protected:
+        typedef typename Tr::Vertex_handle Vertex_handle;
+        typedef typename Tr::Cell_handle   Cell_handle;
+        typedef typename Tr::Facet         Facet;
+        typedef typename Tr::Edge          Edge;
+
+        typedef std::pair<Vertex_handle, Vertex_handle> Pair_of_vertices;
+
+        // computes and returns an ordered pair of Vertex
+        Pair_of_vertices
+        make_ordered_pair(const Vertex_handle vh1, const Vertex_handle vh2) const {
+          if (vh1 < vh2) {
+            return std::make_pair(vh1, vh2);
+          }
+          else {
+            return std::make_pair(vh2, vh1);
+          }
+        }
+        // same from an Edge
+        Pair_of_vertices
+        make_ordered_pair(const Edge e) const {
+          return make_ordered_pair(e.first->vertex(e.second),
+            e.first->vertex(e.third));
+        }
+        Facet canonical_facet(Cell_handle c, int i) const {
+          Cell_handle c2 = c->neighbor(i);
+          return (c2 < c) ? std::make_pair(c2, c2->index(c)) : std::make_pair(c, i);
+        }
+      }; // end class template C3t3_helper_class
+
+    } // end namespace SMDS_3::details
+  } //end namesapce SMDS_3
+
+/*!
+  \ingroup PkgSMDS3Classes
+
+  \brief A data structure to represent and maintain a 3D complex embedded
+  in a 3D triangulation.
+
+  The class `Mesh_complex_3_in_triangulation_3` implements a data structure
+  to store the 3D restricted Delaunay triangulation used by a mesh
+  generation process.
+
+  This class is a model of the concept
+  `MeshComplexWithFeatures_3InTriangulation_3`.
+
+  \tparam Tr can be instantiated with any 3D
+  triangulation of \cgal provided that its
+  vertex and cell base class are models of the concepts
+  `SimplicialMeshVertexBase_3` and `SimplicialMeshCellBase_3`, respectively.
+
+  \tparam  CornerIndex Type of indices for corners (i.e.\f$ 0\f$--dimensional features)
+  of the discretized geometric domain.
+  It must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and
+  `LessThanComparable`.
+  It must match the `Corner_index` of the model
+  of the `MeshDomainWithFeatures_3` concept when used for mesh generation.
+
+  \tparam CurveIndex Type of indices for curves (i.e. \f$ 1\f$-dimensional features)
+  of the discretized geometric domain.
+  It must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and
+  `LessThanComparable`. The default constructed value must be the value for an edge which
+  does not approximate a 1-dimensional feature of the geometric domain.
+  It must match the `Curve_index` types of the model
+  of the `MeshDomainWithFeatures_3` concept when used for mesh generation.
+
+  Those two last template parameters default to `int`, so that they can be ignored
+  if the domain used for mesh generation does not include 0 and 1-dimensionnal features (i.e
+  is only a model of the concept `MeshDomain_3`).
+
+  \cgalModels `MeshComplexWithFeatures_3InTriangulation_3`
+
+  \sa \link make_mesh_3() `CGAL::make_mesh_3()`\endlink
+  \sa \link refine_mesh_3() `CGAL::refine_mesh_3()`\endlink
+  \sa `MeshComplex_3InTriangulation_3`
+  \sa `MeshComplexWithFeatures_3InTriangulation_3`
+  \sa `SimplicialMeshCellBase_3`,
+  \sa `SimplicialMeshVertexBase_3`
+
+*/
+template <typename Tr,
+          typename CornerIndex,
+          typename CurveIndex>
+class Mesh_complex_3_in_triangulation_3
+#ifndef DOXYGEN_RUNNING
+  : public CGAL::SMDS_3::details::C3t3_helper_class<Tr>
+  , public CGAL::SMDS_3::internal::Debug_messages_tools
+#endif
+{
+public:
+  typedef typename Tr::Concurrency_tag                   Concurrency_tag;
+
+private:
+  typedef Mesh_complex_3_in_triangulation_3<
+    Tr,CornerIndex,CurveIndex>                            Self;
+  typedef SMDS_3::details::C3t3_helper_class<Tr>           Base;
+  typedef CGAL::Hash_handles_with_or_without_timestamps   Hash_fct;
+
+public:
+
+#ifndef CGAL_NO_DEPRECATED_CODE
+  typedef CurveIndex Curve_segment_index;
+#endif
+
+/// \name Types
+/// @{
+  typedef Tr                                            Triangulation;
+  typedef typename Tr::size_type                        size_type;
+  typedef typename Tr::Point                            Point;
+  typedef typename Tr::Edge                             Edge;
+  typedef typename Tr::Facet                            Facet;
+  typedef typename Tr::Vertex_handle                    Vertex_handle;
+  typedef typename Tr::Cell_handle                      Cell_handle;
+  /*!
+  Index type.
+  */
+  typedef typename Tr::Vertex::Index Index;
+  /*!
+  Surface index type.
+  */
+  typedef typename Tr::Cell::Surface_patch_index Surface_patch_index;
+  /*!
+  Subdomain index type.
+  */
+  typedef typename Tr::Cell::Subdomain_index Subdomain_index;
+  /*!
+  Corner index type.
+  */
+  typedef CornerIndex Corner_index;
+  /*!
+  Curve index type.
+  */
+  typedef CurveIndex Curve_index;
+/// @}
+
+
+private:
+  // Type to store the edges:
+  //  - a set of std::pair<Vertex_handle,Vertex_handle> (ordered at insertion)
+  //  - which allows fast lookup from one Vertex_handle
+  //  - each element of the set has an associated info (Curve_index) value
+  typedef boost::bimaps::bimap<
+    boost::bimaps::multiset_of<Vertex_handle>,
+    boost::bimaps::multiset_of<Vertex_handle>,
+    boost::bimaps::set_of_relation<>,
+    boost::bimaps::with_info<Curve_index> >           Edge_map;
+
+  typedef typename Edge_map::value_type               Internal_edge;
+
+  // Type to store the corners
+  typedef boost::unordered_map<Vertex_handle,
+                               Corner_index,
+                               Hash_fct>              Corner_map;
+
+  // Type to store far vertices
+  typedef std::vector<Vertex_handle>                  Far_vertices_vec;
+
+public:
+  enum Face_status {
+    NOT_IN_COMPLEX = 0,
+    ISOLATED = 1, // - An ISOLATED edge is a marked edge,
+                  //   without any incident facets.
+    BOUNDARY,     // - An edge is on BOUNDARY if it has only
+                  //   one incident facet.
+                  // - A vertex is on BOUNDARY if all its
+                  //   incident edges are REGULAR or on
+                  //   BOUNDARY, at least one is on
+                  //   BOUNDARY, and the incident facets
+                  //   form only one connected component.
+    REGULAR,      // - A facet that is in the complex is
+                  //   REGULAR.
+                  // - An edge is REGULAR if it has
+                  //   exactly two incident facets.
+                  // - A vertex is REGULAR if all it
+                  //   incident edges are REGULAR, and the
+                  //   incident facets form only one
+                  //   connected component.
+    SINGULAR      // - SINGULAR is for all other cases.
+  };
+
+/// \name Creation
+/// @{
+   /**
+   * @brief Constructor
+   * builds an empty 3D complex.
+   */
+  Mesh_complex_3_in_triangulation_3();
+  /**
+   * Copy constructor
+   */
+  Mesh_complex_3_in_triangulation_3(const Self& rhs);
+
+  /**
+   * Move constructor
+   */
+  Mesh_complex_3_in_triangulation_3(Self&& rhs);
+
+  /**
+  * Assignement operator, also serves as move-assignement
+  */
+  Self& operator=(Self rhs)
+  {
+    swap(rhs);
+    return *this;
+  }
+
+  /**
+   * swaps `this` and `rhs`
+   */
+  void swap(Self& rhs)
+  {
+    Swap_elements<Concurrency_tag> swapper;
+    swapper(rhs.number_of_facets_, number_of_facets_);
+    tr_.swap(rhs.tr_);
+    swapper(rhs.number_of_cells_, number_of_cells_);
+
+    edges_.swap(rhs.edges_);
+    corners_.swap(rhs.corners_);
+    far_vertices_.swap(rhs.far_vertices_);
+  }
+
+/// @}
+
+/// \name Access Functions
+/// @{
+  /// returns a const reference to the triangulation
+  const Triangulation& triangulation() const { return tr_; }
+/// @}
+
+/// \name Non const access
+/// @{
+    /// returns a reference to the triangulation
+  Triangulation& triangulation() { return tr_; }
+/// @}
+
+
+/// \name Modifiers
+/// @{
+  /**
+   * clears data of the complex
+   */
+  void clear()
+  {
+    number_of_cells_ = 0;
+    number_of_facets_ = 0;
+    clear_manifold_info();
+    tr_.clear();
+    edges_.clear();
+    corners_.clear();
+    far_vertices_.clear();
+  }
+
+  /** adds cell \p cell to the 3D complex, with subdomain index \p index
+  */
+  void add_to_complex(const Cell_handle& cell, const Subdomain_index& index)
+  {
+    CGAL_precondition(!(index == Subdomain_index()));
+
+    if (!is_in_complex(cell))
+    {
+      set_subdomain_index(cell, index);
+      ++number_of_cells_;
+    }
+  }
+  /** adds facet \p facet to the 2D complex, with surface index \p index
+  */
+  void add_to_complex(const Facet& facet, const Surface_patch_index& index)
+  {
+    add_to_complex(facet.first, facet.second, index);
+  }
+  /** adds facet(\p cell, \p i) to the 2D complex, with surface index \p index
+  */
+  void add_to_complex(const Cell_handle& cell,
+                      const int i,
+                      const Surface_patch_index& index);
+
+  /** adds edge \p e to complex, with curve index \p index
+   */
+  void add_to_complex(const Edge& e,
+                      const Curve_index& index)
+  {
+    add_to_complex(e.first->vertex(e.second),
+                   e.first->vertex(e.third),
+                   index);
+  }
+
+  /**
+   * adds edge (\p v1, \p v2) to the 1D complex, with `Curve_index` \p index
+   */
+  void add_to_complex(const Vertex_handle& v1,
+                      const Vertex_handle& v2,
+                      const Curve_index& index)
+  {
+    add_to_complex(make_internal_edge(v1,v2), index);
+  }
+
+  /**
+   * marks vertex \p v as a corner of the complex
+   */
+  void add_to_complex(const Vertex_handle& v, const Corner_index& index)
+  {
+    v->set_dimension(0);
+    corners_.insert(std::make_pair(v,index));
+  }
+
+  /** removes cell \p cell from the 3D complex
+  */
+  void remove_from_complex(const Cell_handle& cell)
+  {
+    if (is_in_complex(cell))
+    {
+      set_subdomain_index(cell, Subdomain_index());
+      --number_of_cells_;
+    }
+  }
+  /** removes facet \p facet from the 2D complex
+  */
+  void remove_from_complex(const Facet& facet);
+
+  /** removes facet(\p cell, \p i) from the 2D complex
+  */
+  void remove_from_complex(const Cell_handle& c, const int i) {
+    remove_from_complex(Facet(c, i));
+  }
+  /**
+   * removes edge \p e from the 1D complex
+   */
+  void remove_from_complex(const Edge& e)
+  {
+    remove_from_complex(e.first->vertex(e.second), e.first->vertex(e.third));
+  }
+
+  /**
+   * removes edge (v1,v2) from the 1D complex
+   */
+  void remove_from_complex(const Vertex_handle& v1, const Vertex_handle& v2)
+  {
+    remove_from_complex(make_internal_edge(v1,v2));
+  }
+
+  /**
+   * removes vertex \p v from the complex
+   */
+  void remove_from_complex(const Vertex_handle& v)
+  {
+    corners_.erase(v);
+    v->set_dimension(-1);
+  }
+
+  /** sets the index of vertex \p vertex to \p index
+  */
+  void set_index(const Vertex_handle& vertex, const Index& index) const
+  {
+    vertex->set_index(index);
+  }
+  /** sets the surface index of facet \p facet to \p index
+  */
+  void set_surface_patch_index(const Facet& f, const Surface_patch_index& index)
+  {
+    set_surface_patch_index(f.first, f.second, index);
+  }
+  /** sets the surface index of facet(\p cell, \p i) to \p index
+  */
+  void set_surface_patch_index(const Cell_handle& cell,
+    const int i,
+    const Surface_patch_index& index) const
+  {
+    cell->set_surface_patch_index(i, index);
+  }
+  /** sets the subdomain index of cell \p cell to \p index
+  */
+  void set_subdomain_index(const Cell_handle& cell,
+    const Subdomain_index& index) const
+  {
+    cell->set_subdomain_index(index);
+  }
+  /** sets the dimension of vertex \p vertex to \p dimension
+  */
+  void set_dimension(const Vertex_handle& vertex, int dimension) const
+  {
+    vertex->set_dimension(dimension);
+  }
+/// @}
+
+/// \name Queries on the identifier of the face complex including triangulation cells, facets, and vertices.
+/// @{
+  /** returns the index of vertex \p v
+  */
+  Index index(const Vertex_handle& v) const { return v->index(); }
+
+  /** returns the subdomain index of cell \p cell
+  */
+  Subdomain_index subdomain_index(const Cell_handle& cell) const
+  {
+    return cell->subdomain_index();
+  }
+  /** returns the surface index of facet \p f
+  */
+  Surface_patch_index surface_patch_index(const Facet& f) const
+  {
+    return surface_patch_index(f.first, f.second);
+  }
+
+  /** returns the surface index of facet(\p cell, \p i)
+  */
+  Surface_patch_index surface_patch_index(const Cell_handle& cell,
+                                          const int i) const
+  {
+    return cell->surface_patch_index(i);
+  }
+  /** returns the dimension of the lowest dimensional face of the input 3D
+  * complex that contains the vertex
+  */
+  int in_dimension(const Vertex_handle& v) const { return v->in_dimension(); }
+
+  /**
+  * returns the curve index of edge \p e
+  */
+  Curve_index curve_index(const Edge& e) const
+  {
+    return curve_index(e.first->vertex(e.second),
+                       e.first->vertex(e.third));
+  }
+
+  /**
+  * returns the curve index of the edge formed by \p v1 and \p v2
+  */
+  Curve_index curve_index(const Vertex_handle& v1,
+                          const Vertex_handle& v2) const
+  {
+    return curve_index(make_internal_edge(v1, v2));
+  }
+
+  /**
+   * returns the corner index of vertex \p v
+   */
+  Corner_index corner_index(const Vertex_handle& v) const
+  {
+    typename Corner_map::const_iterator it = corners_.find(v);
+    if (corners_.end() != it) { return it->second; }
+    return Corner_index();
+  }
+/// @}
+
+#ifndef CGAL_NO_DEPRECATED_CODE
+  CGAL_DEPRECATED
+    Curve_index curve_segment_index(const Edge& e) const
+  {
+    return curve_index(e);
+  }
+
+  CGAL_DEPRECATED
+    Curve_index curve_segment_index(const Vertex_handle& v1,
+      const Vertex_handle& v2) const
+  {
+    return curve_index(v1, v2);
+  }
+#endif // CGAL_NO_DEPRECATED_CODE
+
+  std::size_t number_of_far_points() const
+  {
+    return far_vertices_.size();
+  }
+
+  void add_far_point(const Point &p)
+  {
+    far_vertices_.push_back(triangulation().insert(p));
+  }
+
+  void add_far_point(Vertex_handle vh)
+  {
+    far_vertices_.push_back(vh);
+  }
+
+
+  void remove_isolated_vertex(Vertex_handle v)
+  {
+    Triangulation& tr = triangulation();
+
+    std::vector<Cell_handle> new_cells;
+    new_cells.reserve(32);
+    tr.remove_and_give_new_cells(v, std::back_inserter(new_cells));
+
+    typename std::vector<Cell_handle>::iterator nc_it = new_cells.begin();
+    typename std::vector<Cell_handle>::iterator nc_it_end = new_cells.end();
+    for (; nc_it != nc_it_end; ++nc_it)
+    {
+      Cell_handle c = *nc_it;
+      for (int i = 0; i < 4; ++i)
+      {
+        Facet mirror_facet = tr.mirror_facet(std::make_pair(c, i));
+        if (is_in_complex(mirror_facet))
+        {
+          set_surface_patch_index(c, i,
+            surface_patch_index(mirror_facet));
+          c->set_facet_surface_center(i,
+            mirror_facet.first->get_facet_surface_center(mirror_facet.second));
+        }
+      }
+      /*int i_inf;
+      if (c->has_vertex(tr.infinite_vertex(), i_inf))
+      {
+        Facet mirror_facet = tr.mirror_facet(std::make_pair(c, i_inf));
+        if (is_in_complex(mirror_facet))
+        {
+          set_surface_patch_index(c, i_inf,
+                                  surface_patch_index(mirror_facet));
+        }
+      }*/
+    }
+  }
+
+  void remove_far_points()
+  {
+    //triangulation().remove(far_vertices_.begin(), far_vertices_.end());
+    typename Far_vertices_vec::const_iterator it = far_vertices_.begin();
+    typename Far_vertices_vec::const_iterator it_end = far_vertices_.end();
+    for (; it != it_end; ++it)
+    {
+      remove_isolated_vertex(*it);
+    }
+    far_vertices_.clear();
+  }
+
+  /*!
+    The tetrahedral mesh generation algorithm implemented in
+    \link make_mesh_3() `CGAL::make_mesh_3()`\endlink
+    and \link refine_mesh_3() `CGAL::refine_mesh_3()`\endlink
+    does not guarantee that all the points inserted
+    by the algorithm are actually present in the final mesh.
+
+    In most cases, all points are used, but if the geometry of the object
+    has small features compared to the size of the simplices (triangles and tetrahedra),
+    it might be that the Delaunay facets that are selected in the restricted Delaunay
+    triangulation miss some vertices of the triangulation.
+    The concurrent version of the tetrahedral mesh generation algorithm
+    also inserts a small set of auxiliary vertices that belong to the triangulation
+    but are isolated from the complex at the end of the meshing process.
+
+    This function removes these so-called \em isolated vertices, that belong to the
+    triangulation but not to any cell of the `C3T3`, from the triangulation.
+  */
+  void remove_isolated_vertices()
+  {
+    Triangulation& tr = triangulation();
+    for (Vertex_handle v : tr.finite_vertex_handles())
+      v->set_meshing_info(0);
+
+    for (Cell_handle c : this->cells_in_complex())
+    {
+      for (int i = 0; i < 4; ++i)
+      {
+        Vertex_handle vi = c->vertex(i);
+        vi->set_meshing_info(vi->meshing_info() + 1);
+      }
+    }
+
+    for (Facet f :this->facets_in_complex())
+    {
+          for (int i = 1; i < 4; ++i)
+      {
+        Vertex_handle vi = f.first->vertex((f.second + i) % 4);
+        vi->set_meshing_info(vi->meshing_info() + 1);
+      }
+    }
+
+    std::vector<Vertex_handle> isolated;
+    for (Vertex_handle v : tr.finite_vertex_handles())
+    {
+      if (v->meshing_info() == 0.)
+        isolated.push_back(v);
+    }
+
+#ifdef CGAL_MESH_3_VERBOSE
+    std::cout << "Remove " << isolated.size() << " isolated vertices...";
+    std::cout.flush();
+#endif
+
+    CGAL_assertion(far_vertices_.size() <= isolated.size());
+    far_vertices_.clear();
+
+    for (Vertex_handle v : isolated)
+      remove_isolated_vertex(v);
+
+#ifdef CGAL_MESH_3_VERBOSE
+    std::cout << "\nRemove " << isolated.size() << " isolated vertices done." << std::endl;
+#endif
+  }
+
+  void rescan_after_load_of_triangulation();
+
+/// \name Queries on the faces of the embedded complex
+/// @{
+  /**
+  * returns the number of cells which belong to the 3D complex
+  */
+  size_type number_of_cells_in_complex() const { return number_of_cells_; }
+  /**
+  * returns the number of cells which belong to the 3D complex
+  */
+  size_type number_of_cells() const
+  {
+    return number_of_cells_in_complex();
+  }
+  /**
+  * returns the number of surface facets of the complex
+  */
+  size_type number_of_facets_in_complex() const { return number_of_facets_; }
+  /**
+  * returns the number of surface facets of the complex
+  */
+  size_type number_of_facets() const
+  {
+    return number_of_facets_in_complex();
+  }
+  /**
+   * returns the number of edges of the complex
+   */
+  size_type number_of_edges_in_complex() const
+  {
+    return edges_.size();
+  }
+  /**
+   * returns the number of edges of the complex
+   */
+  size_type number_of_edges() const
+  {
+    return edges_.size();
+  }
+  /**
+   * returns the number of corners of the complex
+   */
+  size_type number_of_vertices_in_complex() const
+  {
+    return corners_.size();
+  }
+  /**
+   * returns the number of corners of the complex
+   */
+  size_type number_of_corners() const
+  {
+    return corners_.size();
+  }
+  /**
+  * returns \c true if cell \p cell belongs to the 3D complex
+  */
+  bool is_in_complex(const Cell_handle& cell) const
+  {
+    return !(subdomain_index(cell) == Subdomain_index());
+  }
+  /** returns true if facet \p facet belongs to the 2D complex
+  */
+  bool is_in_complex(const Facet& facet) const
+  {
+    return is_in_complex(facet.first, facet.second);
+  }
+
+  /** returns true if facet (\p cell, \p i) belongs to the 2D complex
+  */
+  bool is_in_complex(const Cell_handle& cell, const int i) const
+  {
+    return (cell->is_facet_on_surface(i));
+  }
+  /**
+   * returns true if edge \p e belongs to the 1D complex
+   */
+  bool is_in_complex(const Edge& e) const
+  {
+    return is_in_complex(e.first->vertex(e.second), e.first->vertex(e.third));
+  }
+
+  /**
+   * returns true if edge (v1,v2) belongs to the 1D complex
+   */
+  bool is_in_complex(const Vertex_handle& v1, const Vertex_handle& v2) const
+  {
+    return is_in_complex(make_internal_edge(v1,v2));
+  }
+
+  /**
+   * returns true if \p v is a 0-dimensionnal feature in the complex
+   */
+  bool is_in_complex(const Vertex_handle& v) const
+  {
+    return (corners_.find(v) != corners_.end());
+  }
+/// @}
+
+
+  /// \name I/O Functions
+  /// @{
+  /**
+   * outputs the outer boundary of the entire domain, with facets oriented outward.
+   */
+  std::ostream& output_boundary_to_off(std::ostream& out) const
+  {
+    internal::output_boundary_of_c3t3_to_off(*this, 0, out, false);
+    return out;
+  }
+
+  /**
+   * outputs the outer boundary of the selected subdomain, with facets oriented outward.
+   */
+  std::ostream& output_boundary_to_off(std::ostream& out, Subdomain_index subdomain) const
+  {
+    output_boundary_of_c3t3_to_off(*this, subdomain, out);
+    return out;
+  }
+
+  /**
+   * outputs the surface facets, with a consistent orientation at the interface of two subdomains.
+   */
+  std::ostream& output_facets_in_complex_to_off(std::ostream& out) const
+  {
+    internal::output_facets_in_complex_to_off(*this, out);
+    return out;
+  }
+
+  /*!
+  outputs the mesh to `os`
+  in Medit format.
+  */
+#ifdef DOXYGEN_RUNNING
+  void output_to_medit(std::ostream& os) const
+#else
+  void output_to_medit(std::ostream& os,
+                       bool rebind = true,
+                       bool show_patches = false) const
+#endif
+  {
+    // Call global function
+    bool all_vertices = true;
+    bool all_cells = false;
+    CGAL::IO::output_to_medit(os, *this, rebind, show_patches,
+      all_vertices, all_cells);
+  }
+
+  void output_to_maya(std::ostream& os, bool surfaceOnly = true) const
+  {
+    // Call global function
+    CGAL::IO::output_to_maya(os, *this, surfaceOnly);
+  }
+
+  /// @}
+
+  /**
+   * fills \p out with incident edges (1-dimensional features of \p v).
+   * OutputIterator value type is std::pair<Vertex_handle,Curve_index>
+   * \pre v->in_dimension() < 2
+   */
+  template <typename OutputIterator>
+  OutputIterator
+  adjacent_vertices_in_complex(const Vertex_handle& v, OutputIterator out) const;
+
+  // -----------------------------------
+  // Undocumented
+  // -----------------------------------
+
+  bool is_valid(bool verbose = false) const;
+
+  // -----------------------------------
+  // Complex traversal
+  // -----------------------------------
+private:
+  /**
+ * @class Cell_not_in_complex
+ * @brief A class to filter cells which do not belong to the complex
+ */
+  class Cell_not_in_complex
+  {
+    const Self* r_self_;
+    Subdomain_index index_;//needed by SWIG, should be const Subdomain_index
+  public:
+    Cell_not_in_complex() {}//needed by SWIG
+    Cell_not_in_complex(const Self& self,
+      const Subdomain_index& index = Subdomain_index())
+      : r_self_(&self)
+      , index_(index) { }
+
+    bool operator()(Cell_handle ch) const
+    {
+      if (index_ == Subdomain_index()) { return !r_self_->is_in_complex(ch); }
+      else { return !(r_self_->subdomain_index(ch) == index_); }
+    }
+  }; // end class Cell_not_in_complex
+
+  typedef SMDS_3::internal::Iterator_not_in_complex<Self> Iterator_not_in_complex;
+
+  class Facet_iterator_not_in_complex
+  {
+    const Self* c3t3_;
+    Surface_patch_index index_; //need by SWIG: should be const Surface_patch_index
+  public:
+    Facet_iterator_not_in_complex() {} //need by SWIG
+    Facet_iterator_not_in_complex(const Self& c3t3,
+      const Surface_patch_index& index = Surface_patch_index())
+      : c3t3_(&c3t3)
+      , index_(index) { }
+
+    template <typename Iterator>
+    bool operator()(Iterator it) const
+    {
+      if (index_ == Surface_patch_index()) { return !c3t3_->is_in_complex(*it); }
+      else { return !(c3t3_->surface_patch_index(*it) == index_); }
+    }
+  };
+
+  class Edge_iterator_not_in_complex
+  {
+    const Self& c3t3_;
+    const Curve_index index_;
+  public:
+    Edge_iterator_not_in_complex(const Self& c3t3,
+                                 const Curve_index& index = Curve_index())
+    : c3t3_(c3t3)
+    , index_(index) { }
+
+    template <typename Iterator>
+    bool operator()(Iterator it) const
+    {
+      if ( index_ == Curve_index() ) { return ! c3t3_.is_in_complex(*it); }
+      else { return c3t3_.curve_index(*it) != index_;  }
+    }
+  };
+
+  class Vertex_iterator_not_in_complex
+  {
+    const Self& c3t3_;
+    const Corner_index index_;
+  public:
+    Vertex_iterator_not_in_complex(const Self& c3t3,
+                                   const Corner_index& index = Corner_index())
+    : c3t3_(c3t3)
+    , index_(index) { }
+
+    template <typename ItMap>
+    bool operator()(const ItMap it) const
+    {
+      if ( index_ == Corner_index() ) { return false; }
+      else { return it->second != index_;  }
+    }
+  };
+
+  // Filtered iterator
+  typedef Filter_iterator<
+    typename Corner_map::const_iterator,
+    Vertex_iterator_not_in_complex >            Vertex_map_filter_iterator;
+
+  // Iterator type to get the first element of pair
+  typedef boost::transform_iterator <
+    SMDS_3::internal::First_of<typename Vertex_map_filter_iterator::value_type>,
+    Vertex_map_filter_iterator >                Vertex_map_iterator_first;
+
+  // Iterator type to remove a level of referencing
+  class Vertex_map_iterator_first_dereference
+    : public boost::iterator_adaptor <
+        Vertex_map_iterator_first_dereference,
+        Vertex_map_iterator_first,
+        typename Vertex_map_iterator_first::value_type::value_type,
+        boost::use_default,
+        typename Vertex_map_iterator_first::value_type::reference >
+  {
+    typedef Vertex_map_iterator_first_dereference Self;
+    typedef boost::iterator_adaptor <
+        Vertex_map_iterator_first_dereference,
+        Vertex_map_iterator_first,
+        typename Vertex_map_iterator_first::value_type::value_type,
+        boost::use_default,
+        typename Vertex_map_iterator_first::value_type::reference > iterator_adaptor_;
+  public:
+    typedef typename  Vertex_map_iterator_first::reference  pointer;
+    typedef typename iterator_adaptor_::reference           reference;
+
+    Vertex_map_iterator_first_dereference() : Self::iterator_adaptor_() { }
+
+    template < typename Iterator >
+    Vertex_map_iterator_first_dereference(Iterator i)
+      : Self::iterator_adaptor_(typename Self::iterator_adaptor_::base_type(i))
+    { }
+
+    pointer operator->() const { return *(this->base()); }
+    reference operator*() const { return **(this->base()); }
+
+    operator Vertex_handle() { return Vertex_handle(*(this->base())); }
+  };
+
+public:
+/// \name Traversal of the complex
+/// @{
+#ifdef DOXYGEN_RUNNING
+  /// Iterator type to visit the cells of the 3D complex
+  typedef unspecified_type Cells_in_complex_iterator;
+  /// Iterator type to visit the facets of the 2D complex
+  typedef unspecified_type Facets_in_complex_iterator;
+  /// Iterator type to visit the edges of the 1D complex
+  typedef unspecified_type Edges_in_complex_iterator;
+  /// Iterator type to visit the vertices of the 0D complex
+  typedef unspecified_type Vertices_in_complex_iterator;
+
+  /// Range type for iterating over all cells of the 3D complex,
+  /// with a nested type iterator that has as value type `Cell_handle`.
+  typedef Iterator_range<unspecified_type> Cells_in_complex;
+  /// Range type for iterating over all facets of the 2D complex,
+  /// with a nested type iterator that has as value type `Facet`.
+  typedef Iterator_range<unspecified_type> Facets_in_complex;
+  /// Range type for iterating over all cells of the 1D complex,
+  /// with a nested type iterator that has as value type `Edge`.
+  typedef Iterator_range<unspecified_type> Edges_in_complex;
+  /// Range type for iterating over all vertices of the 0D complex,
+  /// with a nested type iterator that has as value type `Vertex_handle`.
+  typedef Iterator_range<unspecified_type> Vertices_in_complex;
+
+#else
+  typedef Filter_iterator<
+    typename Triangulation::Finite_edges_iterator,
+    Edge_iterator_not_in_complex >              Edges_in_complex_iterator;
+  typedef Vertex_map_iterator_first_dereference Vertices_in_complex_iterator;
+  typedef Filter_iterator<
+    typename Triangulation::Finite_facets_iterator,
+    Facet_iterator_not_in_complex >               Facets_in_complex_iterator;
+
+  /**
+ * @class Cells_in_complex_iterator
+ * @brief Iterator type to visit the cells of the triangulation that belong
+ * to the 3D complex
+ *
+ * This class is useful to ensure that Cells_in_complex_iterator is convertible
+ * to Cell_handle
+ */
+  class Cells_in_complex_iterator :
+    public Filter_iterator<typename Triangulation::Finite_cells_iterator,
+                           Cell_not_in_complex>
+  {
+  private:
+    typedef typename Triangulation::Finite_cells_iterator Tr_iterator;
+    typedef Filter_iterator<typename Triangulation::Finite_cells_iterator,
+      Cell_not_in_complex> Base;
+    typedef Cells_in_complex_iterator Self;
+
+  public:
+    Cells_in_complex_iterator() : Base() { }
+    Cells_in_complex_iterator(Base i) : Base(i) { }
+
+    Self& operator++() { Base::operator++(); return *this; }
+    Self& operator--() { Base::operator--(); return *this; }
+    Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
+    Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
+
+    operator Cell_handle() const { return Cell_handle(this->base()); }
+  }; // end class Cells_in_complex_iterator
+
+  typedef Iterator_range<Prevent_deref<Vertices_in_complex_iterator> > Vertices_in_complex;
+  typedef Iterator_range<Edges_in_complex_iterator>                    Edges_in_complex;
+  typedef Iterator_range<Facets_in_complex_iterator>                   Facets_in_complex;
+  typedef Iterator_range<Prevent_deref<Cells_in_complex_iterator> >    Cells_in_complex;
+
+#endif
+
+/// \name Iterators
+/// @{
+
+  /// returns a \c Cells_in_complex_iterator to the first cell of the 3D complex
+  Cells_in_complex_iterator cells_in_complex_begin() const
+  {
+    return CGAL::filter_iterator(tr_.finite_cells_end(),
+                                 Cell_not_in_complex(*this),
+                                 tr_.finite_cells_begin());
+  }
+
+  /// returns a \c Cells_in_complex_iterator to the first cell of the 3D complex
+  Cells_in_complex_iterator cells_in_complex_begin(const Subdomain_index& index) const
+  {
+    return CGAL::filter_iterator(tr_.finite_cells_end(),
+                                 Cell_not_in_complex(*this, index),
+                                 tr_.finite_cells_begin());
+  }
+
+  /// returns the past-the-end iterator for the cells of the 3D complex
+  Cells_in_complex_iterator cells_in_complex_end() const
+  {
+    return CGAL::filter_iterator(tr_.finite_cells_end(),
+                                 Cell_not_in_complex(*this));
+  }
+
+  /// returns a `Facets_in_complex_iterator` to the first facet of the 2D complex
+  Facets_in_complex_iterator facets_in_complex_begin() const
+  {
+    return CGAL::filter_iterator(tr_.finite_facets_end(),
+                                 Facet_iterator_not_in_complex(*this),
+                                 tr_.finite_facets_begin());
+  }
+
+  /// returns a `Facets_in_complex_iterator` to the first facet of the 2D complex
+  Facets_in_complex_iterator
+    facets_in_complex_begin(const Surface_patch_index& index) const
+  {
+    return CGAL::filter_iterator(tr_.finite_facets_end(),
+      Facet_iterator_not_in_complex(*this, index),
+      tr_.finite_facets_begin());
+  }
+
+  /// returns past-the-end iterator on facet of the 2D complex
+  Facets_in_complex_iterator facets_in_complex_end(const Surface_patch_index = Surface_patch_index()) const
+  {
+    return CGAL::filter_iterator(tr_.finite_facets_end(),
+      Facet_iterator_not_in_complex(*this));
+  }
+
+  /// returns a `Edges_in_complex_iterator` to the first edge of the 1D complex
+  Edges_in_complex_iterator edges_in_complex_begin() const
+  {
+    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
+                                 Edge_iterator_not_in_complex(*this),
+                                 this->triangulation().finite_edges_begin());
+  }
+
+  /// returns a `Edges_in_complex_iterator` to the first edge of the 1D complex
+  Edges_in_complex_iterator
+  edges_in_complex_begin(const Curve_index& index) const
+  {
+    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
+                                 Edge_iterator_not_in_complex(*this,index),
+                                 this->triangulation().finite_edges_begin());
+  }
+
+  /// returns past-the-end iterator on edges of the 1D complex
+  Edges_in_complex_iterator edges_in_complex_end(const Curve_index& = Curve_index()) const
+  {
+    return CGAL::filter_iterator(this->triangulation().finite_edges_end(),
+                                 Edge_iterator_not_in_complex(*this));
+  }
+
+  /// returns a `Vertices_in_complex_iterator` to the first vertex of the 0D complex
+  Vertices_in_complex_iterator vertices_in_complex_begin() const
+  {
+    return CGAL::filter_iterator(corners_.end(),
+                                 Vertex_iterator_not_in_complex(*this),
+                                 corners_.begin());
+  }
+
+  /// returns a `Vertices_in_complex_iterator` to the first vertex of the 0D complex
+  Vertices_in_complex_iterator
+  vertices_in_complex_begin(const Corner_index& index) const
+  {
+    return CGAL::filter_iterator(corners_.end(),
+                                 Vertex_iterator_not_in_complex(*this,index),
+                                 corners_.begin());
+  }
+
+  /// returns past-the-end iterator on vertices of the 0D complex
+  Vertices_in_complex_iterator vertices_in_complex_end() const
+  {
+    return CGAL::filter_iterator(corners_.end(),
+                                 Vertex_iterator_not_in_complex(*this));
+  }
+
+  /*!
+    returns a range of iterators over vertices of the 0D complex
+    \note The value type of `Vertices_in_complex::iterator` is `Vertex_handle`.
+  */
+  Vertices_in_complex vertices_in_complex() const
+  {
+    return make_prevent_deref_range(vertices_in_complex_begin(),
+                                    vertices_in_complex_end());
+  }
+  /*!
+    returns a range of iterators over the edges of the 1D complex,
+    starting at an arbitrary edge.
+    Returns an empty range when `t.dimension() < 2`.
+  */
+  Edges_in_complex edges_in_complex() const
+  {
+    return Edges_in_complex(edges_in_complex_begin(),
+                            edges_in_complex_end());
+  }
+  /*!
+    returns a range of iterators over the facets of the 2D complex,
+    starting at an arbitrary facet.
+    Returns an empty range when `t.dimension() < 2`.
+  */
+  Facets_in_complex facets_in_complex() const
+  {
+    return Facets_in_complex(facets_in_complex_begin(),
+                             facets_in_complex_end());
+  }
+  /*!
+    returns a range of iterators over cells of the 3D complex.
+    Returns an empty range when `triangulation().number_of_cells() == 0`
+    or complex is empty.
+    \note The value type of `Cells_in_complex::iterator` is `Cell_handle`.
+  */
+  Cells_in_complex cells_in_complex() const
+  {
+    return make_prevent_deref_range(cells_in_complex_begin(),
+                                    cells_in_complex_end());
+  }
+///  @}
+
+public:
+  template <typename Tr2, typename CoI, typename CuI>
+  friend
+  std::istream& operator>>(std::istream& is,
+    Mesh_complex_3_in_triangulation_3<Tr2, CoI, CuI>& c3t3);
+
+  static std::string io_signature()
+  {
+    return Get_io_signature<Tr>()();
+  }
+
+  /**
+   * @cond SKIP_IN_MANUAL
+   * creates an `Internal_edge` object (i.e a pair of ordered `Vertex_handle`)
+   * @endcond
+   */
+  Internal_edge make_internal_edge(const Vertex_handle& v1,
+                                   const Vertex_handle& v2) const
+  {
+    if ( v1 < v2 ) { return Internal_edge(v1,v2); }
+    else { return Internal_edge(v2,v1); }
+  }
+
+  /**
+   * @cond SKIP_IN_MANUAL
+   * returns true if \p edge is in the 1D complex
+   * @endcond
+   */
+  bool is_in_complex(const Internal_edge& edge) const
+  {
+    return (curve_index(edge) != Curve_index() );
+  }
+
+  /**
+   * @cond SKIP_IN_MANUAL
+   * adds edge \p edge to the 1D complex, with curve index `index`
+   * @endcond
+   */
+  void add_to_complex(const Internal_edge& edge, const Curve_index& index)
+  {
+    CGAL_precondition(!is_in_complex(edge));
+#if CGAL_MESH_3_PROTECTION_DEBUG & 1
+    std::cerr << "Add edge ( " << disp_vert(edge.left)
+              << " , " << disp_vert(edge.right) << " ), curve_index=" << index
+              << " to c3t3.\n";
+#endif // CGAL_MESH_3_PROTECTION_DEBUG
+    std::pair<typename Edge_map::iterator, bool> it = edges_.insert(edge);
+    it.first->info = index;
+  }
+
+  /**
+   * @cond SKIP_IN_MANUAL
+   * removes edge \p edge from the 1D complex
+   * @endcond
+   */
+  void remove_from_complex(const Internal_edge& edge)
+  {
+    edges_.erase(edge);
+  }
+
+  /**
+  * @cond SKIP_IN_MANUAL
+  * returns the curve index of edge \p edge
+  * @endcond
+  */
+  Curve_index curve_index(const Internal_edge& edge) const
+  {
+    typename Edge_map::const_iterator it = edges_.find(edge);
+    if ( edges_.end() != it ) { return it->info; }
+    return Curve_index();
+  }
+
+  /// @cond SKIP_IN_MANUAL
+  /// Returns `NOT_IN_COMPLEX`, `BOUNDARY`, `REGULAR`, or `SINGULAR`,
+  /// depending on the number of incident facets in the complex, and the
+  /// number of connected components of its link
+  /// @endcond
+  Face_status face_status(const Vertex_handle v) const
+  {
+    if (!manifold_info_initialized_) init_manifold_info();
+    const std::size_t n = v->cached_number_of_incident_facets();
+
+    if (n == 0) return NOT_IN_COMPLEX;
+
+    //test incident edges for REGULARITY and count BOUNDARY edges
+    typename std::vector<Edge> edges;
+    edges.reserve(64);
+    if (tr_.is_parallel()) {
+      tr_.incident_edges_threadsafe(v, std::back_inserter(edges));
+    }
+    else {
+      tr_.incident_edges(v, std::back_inserter(edges));
+    }
+    int number_of_boundary_incident_edges = 0; // could be a bool
+    for (typename std::vector<Edge>::iterator
+      eit = edges.begin(), end = edges.end();
+      eit != end; eit++)
+    {
+      switch (face_status(*eit))
+      {
+      case NOT_IN_COMPLEX: case REGULAR: break;
+      case BOUNDARY: ++number_of_boundary_incident_edges; break;
+      default:
+#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+        std::cerr << "singular edge...\n";
+        std::cerr << tr_.point(v) << std::endl;
+#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+        return SINGULAR;
+      }
+    }
+
+    // From here all incident edges (in complex) are REGULAR or BOUNDARY.
+    const std::size_t nb_components = union_find_of_incident_facets(v);
+    if (nb_components > 1) {
+#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+      std::cerr << "singular vertex: nb_components=" << nb_components << std::endl;
+      std::cerr << tr_.point(v) << std::endl;
+#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+      return SINGULAR;
+    }
+    else { // REGULAR OR BOUNDARY
+#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+      std::cerr << "regular or boundary: " << tr_.point(v) << std::endl;
+#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+      if (number_of_boundary_incident_edges != 0)
+        return BOUNDARY;
+      else
+        return REGULAR;
+    }
+  }
+
+  /// @cond SKIP_IN_MANUAL
+  /// This function should be called only when incident edges
+  /// are known to be `REGULAR` or `BOUNDARY`
+  /// @endcond
+  bool is_regular_or_boundary_for_vertices(Vertex_handle v) const {
+    return union_find_of_incident_facets(v) == 1;
+  }
+
+  /// @cond SKIP_IN_MANUAL
+  /// Returns `NOT_IN_COMPLEX`, `BOUNDARY`, `REGULAR`, or `SINGULAR`,
+  /// depending on the number of incident facets in the complex
+  /// @endcond
+  Face_status face_status(const Edge& edge) const
+  {
+    if (!manifold_info_initialized_) init_manifold_info();
+
+#ifdef CGAL_LINKED_WITH_TBB
+    typename Edge_facet_counter::const_accessor accessor;
+    if (!edge_facet_counter_.find(accessor,
+      this->make_ordered_pair(edge)))
+      return NOT_IN_COMPLEX;
+    switch (accessor->second)
+#else // not CGAL_LINKED_WITH_TBB
+    switch (edge_facet_counter_[this->make_ordered_pair(edge)])
+#endif // not CGAL_LINKED_WITH_TBB
+    {
+    case 0: return NOT_IN_COMPLEX;
+    case 1: return BOUNDARY;
+    case 2: return REGULAR;
+    default: return SINGULAR;
+    }
+  }
+
+  /// Returns true if the vertex \p v has is incident to at least a facet
+  /// of the complex
+  bool has_incident_facets_in_complex(const Vertex_handle& v) const
+  {
+    if (!manifold_info_initialized_) init_manifold_info();
+    return v->cached_number_of_incident_facets() > 0;
+  }
+
+ /**
+  * @cond SKIP_IN_MANUAL
+  * @brief inserts \p [first,last[ in the triangulation (with dimension 2)
+  * @param first the iterator on the first point to insert
+  * @param last the iterator past the last point to insert
+  *
+  * InputIterator value type must be \c std::pair<Tr::Point,Index>
+  * @endcond
+  */
+  template <typename InputIterator>
+  void insert_surface_points(InputIterator first, InputIterator last)
+  {
+    typename Tr::Geom_traits::Construct_weighted_point_3 cwp =
+      tr_.geom_traits().construct_weighted_point_3_object();
+
+    while (first != last)
+    {
+      Vertex_handle vertex = tr_.insert(cwp((*first).first));
+      vertex->set_index((*first).second);
+      vertex->set_dimension(2);
+      ++first;
+    }
+  }
+
+  /**
+  * @cond SKIP_IN_MANUAL
+  * @brief inserts \p [first,last[ in the triangulation (with dimension 2 and
+  * index \p default_index)
+  * @param first the iterator on the first point to insert
+  * @param last the iterator past the last point to insert
+  * @param default_index the index to be used to insert points
+  *
+  * InputIterator value type must be \c Tr::Point
+  * @endcond
+  */
+  template <typename InputIterator>
+  void insert_surface_points(InputIterator first,
+                             InputIterator last,
+                             const Index& default_index)
+  {
+    typename Tr::Geom_traits::Construct_weighted_point_3 cwp =
+      tr_.geom_traits().construct_weighted_point_3_object();
+
+    while (first != last)
+    {
+      Vertex_handle vertex = tr_.insert(cwp(*first));
+      vertex->set_index(default_index);
+      vertex->set_dimension(2);
+      ++first;
+    }
+  }
+
+  void clear_cells_and_facets_from_c3t3() {
+    for (typename Tr::Finite_cells_iterator
+      cit = this->triangulation().finite_cells_begin(),
+      end = this->triangulation().finite_cells_end();
+      cit != end; ++cit)
+    {
+      set_subdomain_index(cit, Subdomain_index());
+    }
+    this->number_of_cells_ = 0;
+    for (typename Tr::Finite_facets_iterator
+      fit = this->triangulation().finite_facets_begin(),
+      end = this->triangulation().finite_facets_end();
+      fit != end; ++fit)
+    {
+      Facet facet = *fit;
+      set_surface_patch_index(facet.first, facet.second, Surface_patch_index());
+      if (this->triangulation().dimension() > 2) {
+        Facet mirror = tr_.mirror_facet(facet);
+        set_surface_patch_index(mirror.first, mirror.second, Surface_patch_index());
+      }
+    }
+    this->number_of_facets_ = 0;
+    clear_manifold_info();
+  }
+
+  void clear_manifold_info() {
+    edge_facet_counter_.clear();
+    manifold_info_initialized_ = false;
+  }
+
+  /** @cond SKIP_IN_MANUAL
+  * Returns bbox
+  * @endcond
+  */
+  Bbox_3 bbox() const;
+
+private:
+  // Sequential: non-atomic
+  // "dummy" is here to allow the specialization (see below)
+  // See http://groups.google.com/group/comp.lang.c++.moderated/browse_thread/thread/285ab1eec49e1cb6
+  template<typename Concurrency_tag2, typename dummy = void>
+  struct Number_of_elements
+  {
+    typedef size_type type;
+  };
+
+  template<typename Concurrency_tag2, typename dummy = void>
+  struct Init_number_of_elements
+  {
+    template<typename T>
+    void operator()(T& a, const T& b)
+    {
+      a = b;
+    }
+    template<typename T>
+    void operator()(T& a)
+    {
+      a = 0;
+    }
+  };
+
+  template<typename Concurrency_tag2, typename dummy = void>
+  struct Swap_elements
+  {
+    template<typename T>
+    void operator()(T& a, T& b)
+    {
+      std::swap(a, b);
+    }
+  };
+#ifdef CGAL_LINKED_WITH_TBB
+  // Parallel: atomic
+  template<typename dummy>
+  struct Number_of_elements<Parallel_tag, dummy>
+  {
+    typedef std::atomic<size_type> type;
+  };
+
+  template<typename dummy>
+  struct Init_number_of_elements<Parallel_tag, dummy>
+  {
+    template<typename T>
+    void operator()(T& a, const T& b)
+    {
+      a = b.load();
+    }
+    template<typename T>
+    void operator()(T& a)
+    {
+      a = 0;
+    }
+  };
+
+  template<typename dummy>
+  struct Swap_elements<Parallel_tag, dummy>
+  {
+    template<typename T>
+    void operator()(T& a, T& b)
+    {
+      T tmp;
+      tmp.exchange(a);
+      a.exchange(b);
+      b.exchange(tmp);
+    }
+  };
+#endif // CGAL_LINKED_WITH_TBB
+
+private:
+  void init_manifold_info() const
+  {
+    for (typename Tr::All_vertices_iterator
+      vit = triangulation().finite_vertices_begin(),
+      end = triangulation().finite_vertices_end();
+      vit != end; ++vit)
+    {
+      vit->set_c2t3_cache(0, (std::numeric_limits<size_type>::max)());
+    }
+
+    edge_facet_counter_.clear();
+
+    for (typename Tr::Finite_facets_iterator
+      fit = triangulation().finite_facets_begin(),
+      end = triangulation().finite_facets_end();
+      fit != end; ++fit)
+    {
+      if (is_in_complex(*fit)) {
+        const Cell_handle cell = fit->first;
+        const int i = fit->second;
+        for (int j = 0; j < 3; ++j)
+        {
+          const int edge_index_va = tr_.vertex_triple_index(i, j);
+          const int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j + 1));
+          const Vertex_handle edge_va = cell->vertex(edge_index_va);
+          const Vertex_handle edge_vb = cell->vertex(edge_index_vb);
+#ifndef CGAL_LINKED_WITH_TBB
+          ++edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
+#else // CGAL_LINKED_WITH_TBB
+          {
+            typename Edge_facet_counter::accessor accessor;
+            edge_facet_counter_.insert(accessor,
+              this->make_ordered_pair(edge_va, edge_vb));
+            ++accessor->second;
+          }
+#endif // CGAL_LINKED_WITH_TBB
+
+          const std::size_t n = edge_va->cached_number_of_incident_facets();
+          edge_va->set_c2t3_cache(n + 1, (std::numeric_limits<size_type>::max)());
+        }
+      }
+    }
+    manifold_info_initialized_ = true;
+  }
+
+  /// Extract the subset `F` of facets of the complex incident to `v` and
+  /// return the number of connected component of the adjacency graph of `F`.
+  std::size_t union_find_of_incident_facets(const Vertex_handle v) const
+  {
+    if (v->is_c2t3_cache_valid())
+    {
+      const std::size_t n = v->cached_number_of_components();
+      if (n != (std::numeric_limits<size_type>::max)()) return n;
+    }
+
+    Union_find<Facet> facets;
+    { // fill the union find
+      std::vector<Facet> non_filtered_facets;
+      if (tr_.is_parallel()) {
+        tr_.incident_facets_threadsafe(v, std::back_inserter(non_filtered_facets));
+      }
+      else {
+        tr_.incident_facets(v, std::back_inserter(non_filtered_facets));
+      }
+
+      for (typename std::vector<Facet>::iterator
+        fit = non_filtered_facets.begin(),
+        end = non_filtered_facets.end();
+        fit != end; ++fit)
+      {
+        if (is_in_complex(*fit)) facets.push_back(*fit);
+      }
+    }
+
+    typedef boost::unordered_map<Vertex_handle,
+                                 typename Union_find<Facet>::handle,
+                                 Hash_fct>    Vertex_set_map;
+    typedef typename Vertex_set_map::iterator Vertex_set_map_iterator;
+
+    Vertex_set_map vsmap;
+
+    for (typename Union_find<Facet>::iterator
+         it = facets.begin(), end = facets.end();
+         it != end; ++it)
+    {
+      const Cell_handle& ch = (*it).first;
+      const int& i = (*it).second;
+      for (int j = 0; j < 3; ++j) {
+        const Vertex_handle w = ch->vertex(tr_.vertex_triple_index(i, j));
+        if (w != v) {
+          Vertex_set_map_iterator vsm_it = vsmap.find(w);
+          if (vsm_it != vsmap.end()) {
+            facets.unify_sets(vsm_it->second, it);
+          }
+          else {
+            vsmap.insert(std::make_pair(w, it));
+          }
+        }
+      }
+    }
+    const std::size_t nb_components = facets.number_of_sets();
+
+    const std::size_t n = v->cached_number_of_incident_facets();
+    v->set_c2t3_cache(n, nb_components);
+    return nb_components;
+  }
+
+public:
+  // -----------------------------------
+  // Backward Compatibility
+  // -----------------------------------
+#ifndef DOXYGEN_RUNNING
+#ifndef CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
+  typedef Surface_patch_index   Surface_index;
+
+  void set_surface_index(const Facet& f, const Surface_index& index)
+  {
+    set_surface_patch_index(f, index);
+  }
+
+  void set_surface_index(const Cell_handle& c, const int i, const Surface_index& index)
+  {
+    set_surface_patch_index(c, i, index);
+  }
+
+  Surface_index surface_index(const Facet& f) const
+  {
+    return surface_patch_index(f);
+  }
+
+  Surface_index surface_index(const Cell_handle& c, const int i) const
+  {
+    return surface_patch_index(c, i);
+  }
+#endif // CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
+
+#ifndef CGAL_MESH_3_NO_DEPRECATED_C3T3_ITERATORS
+  typedef Facets_in_complex_iterator  Facet_iterator;
+  typedef Cells_in_complex_iterator   Cell_iterator;
+
+  Facet_iterator facets_begin() const
+  {
+    return facets_in_complex_begin();
+  }
+
+  Facet_iterator facets_end() const
+  {
+    return facets_in_complex_end();
+  }
+
+  Cell_iterator cells_begin() const
+  {
+    return cells_in_complex_begin();
+  }
+
+  Cell_iterator cells_end() const
+  {
+    return cells_in_complex_end();
+  }
+#endif // CGAL_MESH_3_NO_DEPRECATED_C3T3_ITERATORS
+#endif // DOXYGEN_RUNNING
+  // -----------------------------------
+  // End backward Compatibility
+  // -----------------------------------
+
+
+private:
+  // Private data members
+  Triangulation tr_;
+
+  typedef typename Base::Pair_of_vertices Pair_of_vertices;
+#ifdef CGAL_LINKED_WITH_TBB
+  typedef tbb::concurrent_hash_map<Pair_of_vertices, int,
+                                   Hash_compare_for_TBB> Edge_facet_counter;
+#else // not CGAL_LINKED_WITH_TBB
+  typedef std::map<Pair_of_vertices, int> Edge_facet_counter;
+#endif // not CGAL_LINKED_WITH_TBB
+
+  mutable Edge_facet_counter edge_facet_counter_;
+
+  typename Number_of_elements<Concurrency_tag>::type number_of_facets_;
+  typename Number_of_elements<Concurrency_tag>::type number_of_cells_;
+
+  mutable bool manifold_info_initialized_;
+
+  Edge_map edges_;
+  Corner_map corners_;
+  Far_vertices_vec far_vertices_;
+};
+
+template <typename Tr, typename CI_, typename CSI_>
+Mesh_complex_3_in_triangulation_3<Tr, CI_, CSI_>::
+Mesh_complex_3_in_triangulation_3()
+  : Base()
+  , tr_()
+  , edge_facet_counter_() //TODO: parallel!
+  , manifold_info_initialized_(false) //TODO: parallel!
+{
+  // We don't put it in the initialization list because
+  // std::atomic has no contructors
+  number_of_facets_ = 0;
+  number_of_cells_ = 0;
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
+Mesh_complex_3_in_triangulation_3(const Self& rhs)
+  : Base(rhs)
+  , tr_(rhs.tr_)
+  , edge_facet_counter_(rhs.edge_facet_counter_)
+  , manifold_info_initialized_(rhs.manifold_info_initialized_)
+  , edges_()
+  , corners_()
+{
+  Init_number_of_elements<Concurrency_tag> init;
+  init(number_of_facets_, rhs.number_of_facets_);
+  init(number_of_cells_, rhs.number_of_cells_);
+
+  // Copy edges
+  for ( typename Edge_map::const_iterator it = rhs.edges_.begin(),
+       end = rhs.edges_.end() ; it != end ; ++it )
+  {
+    const Vertex_handle& va = it->right;
+    const Vertex_handle& vb = it->left;
+
+    Vertex_handle new_va;
+    this->triangulation().is_vertex(rhs.triangulation().point(va), new_va);
+
+    Vertex_handle new_vb;
+    this->triangulation().is_vertex(rhs.triangulation().point(vb), new_vb);
+
+    this->add_to_complex(make_internal_edge(new_va,new_vb), it->info);
+  }
+
+  // Copy corners
+  for ( typename Corner_map::const_iterator it = rhs.corners_.begin(),
+       end = rhs.corners_.end() ; it != end ; ++it )
+  {
+    Vertex_handle new_v;
+    this->triangulation().is_vertex(rhs.triangulation().point(it->first), new_v);
+    this->add_to_complex(new_v, it->second);
+  }
+
+  // Parse vertices to identify far vertices
+  if (rhs.far_vertices_.size() > 0)
+  {
+    Triangulation &tr = triangulation();
+    typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin();
+    for(typename Tr::Finite_vertices_iterator end = tr.finite_vertices_end();
+        vit != end ; ++vit)
+    {
+      if (vit->in_dimension() == -1)
+        far_vertices_.push_back(vit);
+    }
+    CGAL_assertion(far_vertices_.size() == rhs.far_vertices_.size());
+  }
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+Mesh_complex_3_in_triangulation_3<Tr, CI_, CSI_>::
+Mesh_complex_3_in_triangulation_3(Self&& rhs)
+  : Base()
+  , tr_(std::move(rhs.tr_))
+  , edge_facet_counter_(std::move(rhs.edge_facet_counter_))
+  , manifold_info_initialized_(std::exchange(rhs.manifold_info_initialized_, false))
+  , edges_(std::move(rhs.edges_))
+  , corners_(std::move(rhs.corners_))
+  , far_vertices_(std::move(rhs.far_vertices_))
+{
+  Init_number_of_elements<Concurrency_tag> init;
+  init(number_of_facets_, rhs.number_of_facets_);
+  init(number_of_cells_, rhs.number_of_cells_);
+  init(rhs.number_of_facets_); // set to 0
+  init(rhs.number_of_cells_); // set to 0
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+template <typename OutputIterator>
+OutputIterator
+Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
+adjacent_vertices_in_complex(const Vertex_handle& v, OutputIterator out) const
+{
+  CGAL_precondition(v->in_dimension() < 2);
+
+  typedef typename Edge_map::right_const_iterator Rcit;
+  typedef typename Edge_map::left_const_iterator Lcit;
+
+  // Add edges containing v is on the left
+  std::pair<Rcit,Rcit> range_right = edges_.right.equal_range(v);
+  for ( Rcit rit = range_right.first ; rit != range_right.second ; ++rit )
+  {
+    *out++ = std::make_pair(rit->second, rit->info);
+  }
+
+  // Add edges containing v on the right
+  std::pair<Lcit,Lcit> range_left = edges_.left.equal_range(v);
+  for ( Lcit lit = range_left.first ; lit != range_left.second ; ++lit )
+  {
+    *out++ = std::make_pair(lit->second, lit->info);
+  }
+
+  return out;
+}
+
+
+template <typename Tr, typename CI_, typename CSI_>
+bool
+Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
+is_valid(bool verbose) const
+{
+  typedef typename Tr::Weighted_point                         Weighted_point;
+  typedef boost::unordered_map<Vertex_handle, int, Hash_fct>  Vertex_map;
+
+  Vertex_map vertex_map;
+
+  // Fill map counting neighbor number for each vertex of an edge
+  for ( typename Edge_map::const_iterator it = edges_.begin(),
+       end = edges_.end() ; it != end ; ++it )
+  {
+    const Vertex_handle& v1 = it->right;
+    if ( vertex_map.find(v1) == vertex_map.end() ) { vertex_map[v1] = 1; }
+    else { vertex_map[v1] += 1; }
+
+    const Vertex_handle& v2 = it->left;
+    if ( vertex_map.find(v2) == vertex_map.end() ) { vertex_map[v2] = 1; }
+    else { vertex_map[v2] += 1; }
+  }
+
+  // Verify that each vertex has 2 neighbors if it's not a corner
+  for ( typename Vertex_map::iterator vit = vertex_map.begin(),
+       vend = vertex_map.end() ; vit != vend ; ++vit )
+  {
+    if ( vit->first->in_dimension() != 0 && vit->second != 2 )
+    {
+      if(verbose)
+        std::cerr << "Validity error: vertex " << (void*)(&*vit->first)
+                  << " (" << this->triangulation().point(vit->first) << ") "
+                  << "is not a corner (dimension " << vit->first->in_dimension()
+                  << ") but has " << vit->second << " neighbor(s)!\n";
+      return false;
+    }
+  }
+
+  // Verify that balls of each edge intersect
+  for ( typename Edge_map::const_iterator it = edges_.begin(),
+       end = edges_.end() ; it != end ; ++it )
+  {
+    typename Tr::Geom_traits::Compute_weight_3 cw =
+      this->triangulation().geom_traits().compute_weight_3_object();
+    typename Tr::Geom_traits::Construct_point_3 cp =
+      this->triangulation().geom_traits().construct_point_3_object();
+    typename Tr::Geom_traits::Construct_sphere_3 sphere =
+      this->triangulation().geom_traits().construct_sphere_3_object();
+    typename Tr::Geom_traits::Do_intersect_3 do_intersect =
+      this->triangulation().geom_traits().do_intersect_3_object();
+
+    const Weighted_point& itrwp = this->triangulation().point(it->right);
+    const Weighted_point& itlwp = this->triangulation().point(it->left);
+
+    if ( ! do_intersect(sphere(cp(itrwp), cw(itrwp)), sphere(cp(itlwp), cw(itlwp))) )
+    {
+      std::cerr << "Points p[" << disp_vert(it->right) << "], dim=" << it->right->in_dimension()
+                << " and q[" << disp_vert(it->left) << "], dim=" << it->left->in_dimension()
+                << " form an edge but do not intersect !\n";
+      return false;
+    }
+  }
+
+  return true;
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+void
+Mesh_complex_3_in_triangulation_3<Tr, CI_, CSI_>::
+add_to_complex(const Cell_handle& cell,
+               const int i,
+               const Surface_patch_index& index)
+{
+  CGAL_precondition(!(index == Surface_patch_index()));
+
+  if (!is_in_complex(cell, i))
+  {
+    Facet mirror = tr_.mirror_facet(std::make_pair(cell, i));
+    set_surface_patch_index(cell, i, index);
+    set_surface_patch_index(mirror.first, mirror.second, index);
+    ++number_of_facets_;
+    if (manifold_info_initialized_) {
+      for (int j = 0; j < 3; ++j)
+      {
+        int edge_index_va = tr_.vertex_triple_index(i, j);
+        int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j + 1));
+        Vertex_handle edge_va = cell->vertex(edge_index_va);
+        Vertex_handle edge_vb = cell->vertex(edge_index_vb);
+#ifdef CGAL_LINKED_WITH_TBB
+        {
+          typename Edge_facet_counter::accessor accessor;
+          edge_facet_counter_.insert(accessor,
+            this->make_ordered_pair(edge_va, edge_vb));
+          ++accessor->second;
+        }
+#else // not CGAL_LINKED_WITH_TBB
+        ++edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
+#endif // not CGAL_LINKED_WITH_TBB
+
+        const std::size_t n = edge_va->cached_number_of_incident_facets();
+        const std::size_t m = edge_va->cached_number_of_components();
+        edge_va->set_c2t3_cache(n + 1, m);
+      }
+      const int dimension_plus_1 = tr_.dimension() + 1;
+      // update c2t3 for vertices of f
+      for (int j = 0; j < dimension_plus_1; j++) {
+        if (j != i) {
+#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+          if (cell->vertex(j)->is_c2t3_cache_valid())
+            std::cerr << "(" << tr_.point(cell, j) << ")->invalidate_c2t3_cache()\n";
+#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+          cell->vertex(j)->invalidate_c2t3_cache();
+        }
+      }
+    }
+  }
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+void
+Mesh_complex_3_in_triangulation_3<Tr, CI_, CSI_>::
+remove_from_complex(const Facet& facet)
+{
+  if (is_in_complex(facet))
+  {
+    Facet mirror = tr_.mirror_facet(facet);
+    set_surface_patch_index(facet.first, facet.second, Surface_patch_index());
+    set_surface_patch_index(mirror.first, mirror.second, Surface_patch_index());
+    --number_of_facets_;
+    if (manifold_info_initialized_) {
+      const Cell_handle cell = facet.first;
+      const int i = facet.second;
+      for (int j = 0; j < 3; ++j)
+      {
+        const int edge_index_va = tr_.vertex_triple_index(i, j);
+        const int edge_index_vb = tr_.vertex_triple_index(i, (j == 2) ? 0 : (j + 1));
+        const Vertex_handle edge_va = cell->vertex(edge_index_va);
+        const Vertex_handle edge_vb = cell->vertex(edge_index_vb);
+#ifdef CGAL_LINKED_WITH_TBB
+        {
+          typename Edge_facet_counter::accessor accessor;
+          edge_facet_counter_.insert(accessor,
+            this->make_ordered_pair(edge_va, edge_vb));
+          --accessor->second;
+        }
+#else // not CGAL_LINKED_WITH_TBB
+        --edge_facet_counter_[this->make_ordered_pair(edge_va, edge_vb)];
+#endif // not CGAL_LINKED_WITH_TBB
+
+        const std::size_t n = edge_va->cached_number_of_incident_facets();
+        CGAL_assertion(n > 0);
+        const std::size_t m = edge_va->cached_number_of_components();
+        edge_va->set_c2t3_cache(n - 1, m);
+      }
+      const int dimension_plus_1 = tr_.dimension() + 1;
+      // update c2t3 for vertices of f
+      for (int j = 0; j < dimension_plus_1; j++) {
+        if (j != facet.second) {
+#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+          if (cell->vertex(j)->is_c2t3_cache_valid())
+            std::cerr << "(" << tr_.point(cell, j) << ")->invalidate_c2t3_cache()\n";
+#endif // CGAL_MESHES_DEBUG_REFINEMENT_POINTS
+          cell->vertex(j)->invalidate_c2t3_cache();
+        }
+      }
+    }
+  }
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+Bbox_3
+Mesh_complex_3_in_triangulation_3<Tr, CI_, CSI_>::
+bbox() const
+{
+  if (0 == triangulation().number_of_vertices())
+  {
+    return Bbox_3();
+  }
+
+  typename Tr::Finite_vertices_iterator vit = tr_.finite_vertices_begin();
+  Bbox_3 result = tr_.point(vit++).bbox();
+
+  for (typename Tr::Finite_vertices_iterator end = tr_.finite_vertices_end();
+    vit != end; ++vit)
+  {
+    result = result + tr_.point(vit).bbox();
+  }
+
+  return result;
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+void
+Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_>::
+rescan_after_load_of_triangulation()
+{
+  corners_.clear();
+  for(typename Tr::Finite_vertices_iterator
+        vit = this->triangulation().finite_vertices_begin(),
+        end = this->triangulation().finite_vertices_end();
+      vit != end; ++vit)
+  {
+    if ( vit->in_dimension() == 0 ) {
+      add_to_complex(vit, Corner_index(1));
+    }
+  }
+
+  this->number_of_facets_ = 0;
+  for (typename Tr::Finite_facets_iterator
+    fit = this->triangulation().finite_facets_begin(),
+    end = this->triangulation().finite_facets_end();
+    fit != end; ++fit)
+  {
+    if (this->is_in_complex(*fit)) {
+      ++this->number_of_facets_;
+    }
+  }
+
+  this->number_of_cells_ = 0;
+  for (typename Tr::Finite_cells_iterator
+    cit = this->triangulation().finite_cells_begin(),
+    end = this->triangulation().finite_cells_end();
+    cit != end; ++cit)
+  {
+    if (this->is_in_complex(cit)) {
+      ++this->number_of_cells_;
+    }
+  }
+}
+
+template <typename Tr, typename CI_, typename CSI_>
+std::ostream &
+operator<< (std::ostream& os,
+            const Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_> &c3t3)
+{
+  // TODO: implement edge saving
+  return os << c3t3.triangulation();
+}
+
+
+template <typename Tr, typename CI_, typename CSI_>
+std::istream &
+operator>> (std::istream& is,
+            Mesh_complex_3_in_triangulation_3<Tr,CI_,CSI_> &c3t3)
+{
+  // TODO: implement edge loading
+  c3t3.clear();
+  is >> c3t3.triangulation();
+
+  if (!is) {
+    c3t3.clear();
+    return is;
+  }
+
+  c3t3.rescan_after_load_of_triangulation();
+  return is;
+}
+
+} //namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif // CGAL_MESH_COMPLEX_3_IN_TRIANGULATION_3_H
diff --git a/SMDS_3/include/CGAL/SMDS_3/Dump_c3t3.h b/SMDS_3/include/CGAL/SMDS_3/Dump_c3t3.h
new file mode 100644
index 00000000000..ebb78341db1
--- /dev/null
+++ b/SMDS_3/include/CGAL/SMDS_3/Dump_c3t3.h
@@ -0,0 +1,137 @@
+// Copyright (c) 2012  GeometryFactory Sarl (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)     : Laurent Rineau
+
+#ifndef CGAL_SMDS_3_DUMP_C3T3_H
+#define CGAL_SMDS_3_DUMP_C3T3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/disable_warnings.h>
+
+#include <CGAL/SMDS_3/io_signature.h>
+#include <CGAL/IO/File_medit.h>
+
+#include <CGAL/is_streamable.h>
+
+#include <fstream>
+#include <string>
+
+namespace CGAL {
+
+template <typename C3t3,
+          bool is_streamable =
+            is_streamable<typename C3t3::Triangulation::Vertex>::value &&
+            is_streamable<typename C3t3::Triangulation::Cell>::value
+            &&
+            (is_streamable<typename C3t3::Surface_patch_index>::value ||
+             Output_rep<typename C3t3::Surface_patch_index>::is_specialized)
+            &&
+            (is_streamable<typename C3t3::Subdomain_index>::value ||
+             Output_rep<typename C3t3::Subdomain_index>::is_specialized)
+          >
+struct Dump_c3t3 {
+  void dump_c3t3(const C3t3& c3t3, std::string prefix) const
+  {
+    std::clog<<"======dump c3t3===== to: " << prefix << std::endl;
+    std::ofstream medit_file((prefix+".mesh").c_str());
+    medit_file.precision(17);
+    CGAL::IO::output_to_medit(medit_file, c3t3, false /*rebind*/, true /*show_patches*/);
+    medit_file.close();
+
+    std::string bin_filename = prefix;
+    bin_filename += ".binary.cgal";
+    std::ofstream bin_file(bin_filename.c_str(),
+                           std::ios_base::binary | std::ios_base::out);
+    std::string signature = CGAL::Get_io_signature<C3t3>()();
+    CGAL_assertion(signature != std::string());
+    bin_file << "binary CGAL c3t3 " << signature << "\n";
+    CGAL::IO::set_binary_mode(bin_file);
+    bin_file << c3t3;
+  }
+}; // end struct template Dump_c3t3<C3t3, bool>
+
+template <typename C3t3>
+struct Dump_c3t3<C3t3, false>
+{
+  void dump_c3t3(const C3t3&, std::string) {
+    std::cerr << "Warning " << __FILE__ << ":" << __LINE__ << "\n"
+              << "  the c3t3 object of following type:\n"
+              << typeid(C3t3).name() << std::endl
+              << "  cannot be dumped because some types are not streamable:\n";
+    if(!is_streamable<typename C3t3::Triangulation::Vertex>::value) {
+      std::cerr << "     - C3t3::Triangulation::Vertex is not streamble\n";
+      std::cerr << "       "
+                << typeid(typename C3t3::Triangulation::Vertex).name()
+                << "\n";
+    }
+
+    if(!is_streamable<typename C3t3::Triangulation::Cell>::value) {
+      std::cerr << "     - C3t3::Triangulation::Cell is not streamble\n";
+      std::cerr << "       "
+                << typeid(typename C3t3::Triangulation::Cell).name()
+                << "\n";
+    }
+
+    if(!is_streamable<typename C3t3::Surface_patch_index>::value &&
+       !CGAL::Output_rep<typename C3t3::Surface_patch_index>::is_specialized)
+    {
+      std::cerr << "     - C3t3::Surface_patch_index is not streamable\n";
+      std::cerr << "       "
+                << typeid(typename C3t3::Surface_patch_index).name()
+                << "\n";
+    }
+    if(!is_streamable<typename C3t3::Subdomain_index>::value &&
+       !CGAL::Output_rep<typename C3t3::Subdomain_index>::is_specialized)
+    {
+      std::cerr << "     - C3t3::Subdomain_index is not streamable\n";
+      std::cerr << "       "
+                << typeid(typename C3t3::Subdomain_index).name()
+                << "\n";
+    }
+  }
+}; // end struct template specialization Dump_c3t3<C3t3, false>
+
+template <typename C3t3>
+void dump_c3t3_edges(const C3t3& c3t3, std::string prefix)
+{
+  typename C3t3::Triangulation::Geom_traits::Construct_point_3 cp =
+    c3t3.triangulation().geom_traits().construct_point_3_object();
+
+  std::ofstream file((prefix+".polylines.txt").c_str());
+  file.precision(17);
+  for(typename C3t3::Edges_in_complex_iterator
+        edge_it = c3t3.edges_in_complex_begin(),
+        end     = c3t3.edges_in_complex_end();
+      edge_it != end; ++edge_it)
+  {
+    const typename C3t3::Triangulation::Cell_handle c = edge_it->first;
+    const int i = edge_it->second;
+    const int j = edge_it->third;
+    const typename C3t3::Triangulation::Weighted_point& ei = c3t3.triangulation().point(c, i);
+    const typename C3t3::Triangulation::Weighted_point& ej = c3t3.triangulation().point(c, j);
+    file << "2 " << cp(ei) << " "  << cp(ej) << "\n";
+  }
+}
+template <typename C3t3>
+void dump_c3t3(const C3t3& c3t3, std::string prefix)
+{
+  if(!prefix.empty()) {
+    Dump_c3t3<C3t3> dump;
+    dump.dump_c3t3(c3t3, prefix);
+  }
+}
+
+} // end namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif // CGAL_SMDS_3_DUMP_C3T3_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/Has_features.h b/SMDS_3/include/CGAL/SMDS_3/Has_features.h
similarity index 96%
rename from Mesh_3/include/CGAL/Mesh_3/Has_features.h
rename to SMDS_3/include/CGAL/SMDS_3/Has_features.h
index 94d9b02de4b..e2c322fc0f6 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Has_features.h
+++ b/SMDS_3/include/CGAL/SMDS_3/Has_features.h
@@ -13,7 +13,7 @@
 #ifndef CGAL_MESH_3_HAS_FEATURES_H
 #define CGAL_MESH_3_HAS_FEATURES_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 
 #include <boost/mpl/has_xxx.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h b/SMDS_3/include/CGAL/SMDS_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h
similarity index 81%
rename from Mesh_3/include/CGAL/Mesh_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h
rename to SMDS_3/include/CGAL/SMDS_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h
index 93f5b70d430..77b0d8b0004 100644
--- a/Mesh_3/include/CGAL/Mesh_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h
+++ b/SMDS_3/include/CGAL/SMDS_3/internal/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h
@@ -12,7 +12,7 @@
 #ifndef CGAL_INTERNAL_MESH_3_BOUNDARY_OF_SUDDOMAIN_OF_COMPLEX_3_IN_TRIANGULATION_3_TO_OFF_H
 #define CGAL_INTERNAL_MESH_3_BOUNDARY_OF_SUDDOMAIN_OF_COMPLEX_3_IN_TRIANGULATION_3_TO_OFF_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -58,11 +58,14 @@ output_boundary_of_c3t3_to_off(const C3T3& c3t3,
 {
   typedef typename C3T3::Triangulation::Geom_traits::Point_3             Point;
   typedef std::vector<std::size_t>                                       Face;
+  typedef typename C3T3::Surface_patch_index                             Surface_patch_index;
 
   std::vector<Point> points;
   std::vector<Face> faces;
+  std::vector<Surface_patch_index> patches;
 
-  CGAL::Mesh_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, sd_index, points, faces, normals_point_outside_of_the_subdomain);
+  CGAL::SMDS_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, sd_index, points, faces,
+        patches, normals_point_outside_of_the_subdomain);
 
   return output_polygon_soup_to_off(points, faces, out);
 }
@@ -73,12 +76,14 @@ output_facets_in_complex_to_off(const C3T3& c3t3,
                                 std::ostream& out)
 {
   typedef typename C3T3::Triangulation::Geom_traits::Point_3             Point;
+  typedef typename C3T3::Surface_patch_index                             Surface_patch_index;
   typedef std::vector<std::size_t>                                       Face;
 
   std::vector<Point> points;
   std::vector<Face> faces;
+  std::vector<Surface_patch_index> patches;
 
-  CGAL::Mesh_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, points, faces);
+  CGAL::SMDS_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, points, faces, patches);
 
   return output_polygon_soup_to_off(points, faces, out);
 }
diff --git a/Mesh_3/include/CGAL/Mesh_3/internal/Handle_IO_for_pair_of_int.h b/SMDS_3/include/CGAL/SMDS_3/internal/Handle_IO_for_pair_of_int.h
similarity index 97%
rename from Mesh_3/include/CGAL/Mesh_3/internal/Handle_IO_for_pair_of_int.h
rename to SMDS_3/include/CGAL/SMDS_3/internal/Handle_IO_for_pair_of_int.h
index b8b9c0c6182..cd3c8f135a9 100644
--- a/Mesh_3/include/CGAL/Mesh_3/internal/Handle_IO_for_pair_of_int.h
+++ b/SMDS_3/include/CGAL/SMDS_3/internal/Handle_IO_for_pair_of_int.h
@@ -13,12 +13,12 @@
 #ifndef CGAL_INTERNAL_MESH_3_INTERNAL_HANDLE_IO_FOR_PAIR_OF_INT_H
 #define CGAL_INTERNAL_MESH_3_INTERNAL_HANDLE_IO_FOR_PAIR_OF_INT_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/disable_warnings.h>
 
 #include <utility>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <ostream>
 #include <istream>
 #include <boost/variant.hpp>
diff --git a/SMDS_3/include/CGAL/SMDS_3/internal/SMDS_3_helper.h b/SMDS_3/include/CGAL/SMDS_3/internal/SMDS_3_helper.h
new file mode 100644
index 00000000000..86a631dd5cf
--- /dev/null
+++ b/SMDS_3/include/CGAL/SMDS_3/internal/SMDS_3_helper.h
@@ -0,0 +1,68 @@
+// Copyright (c) 2021 GeometryFactory
+// 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)     : Jane Tournois
+
+#ifndef CGAL_INTERNAL_SMDS_3_HELPERS_H
+#define CGAL_INTERNAL_SMDS_3_HELPERS_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/enum.h>
+
+#include <vector>
+#include <array>
+
+namespace CGAL {
+namespace SMDS_3 {
+namespace internal {
+
+  template<typename Triangulation>
+  bool is_convex(const Triangulation& tr)
+  {
+    typedef typename Triangulation::Vertex_handle        Vertex_handle;
+    typedef typename Triangulation::Cell_handle          Cell_handle;
+    typedef typename Triangulation::Geom_traits::Point_3 Point_3;
+    typename Triangulation::Geom_traits::Construct_point_3 cp
+      = tr.geom_traits().construct_point_3_object();
+    typename Triangulation::Geom_traits::Orientation_3 orientation =
+      tr.geom_traits().orientation_3_object();
+
+    std::vector<Cell_handle> infcells;
+    tr.incident_cells(tr.infinite_vertex(), std::back_inserter(infcells));
+    for (Cell_handle c : infcells)
+    {
+      const Cell_handle neigh = c->neighbor(c->index(tr.infinite_vertex()));
+      const int i = neigh->index(c);
+
+      const std::array<Point_3, 3> pfacet = { cp(neigh->vertex((i + 1) % 4)->point()),
+                                              cp(neigh->vertex((i + 2) % 4)->point()),
+                                              cp(neigh->vertex((i + 3) % 4)->point())};
+      const CGAL::Orientation o = orientation(
+          pfacet[0], pfacet[1], pfacet[2], cp(neigh->vertex(i)->point()));
+
+      for (Vertex_handle v : tr.finite_vertex_handles())
+      {
+        if (c->has_vertex(v))
+          continue;
+        if (o != orientation(pfacet[0], pfacet[1], pfacet[2],
+                             cp(neigh->vertex(i)->point())))
+          return false;
+      }
+    }
+
+    return true;
+  }
+
+} // end namespace internal
+} // end namespace SMDS_3
+} // end namespace CGAL
+
+#endif // CGAL_INTERNAL_SMDS_3_HELPERS_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/internal/indices_management.h b/SMDS_3/include/CGAL/SMDS_3/internal/indices_management.h
similarity index 99%
rename from Mesh_3/include/CGAL/Mesh_3/internal/indices_management.h
rename to SMDS_3/include/CGAL/SMDS_3/internal/indices_management.h
index a4b05a9cc61..b98528cace4 100644
--- a/Mesh_3/include/CGAL/Mesh_3/internal/indices_management.h
+++ b/SMDS_3/include/CGAL/SMDS_3/internal/indices_management.h
@@ -18,7 +18,7 @@
 #ifndef CGAL_INTERNAL_MESH_3_INDICES_MANAGEMENT_H
 #define CGAL_INTERNAL_MESH_3_INDICES_MANAGEMENT_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 
 #include <boost/type_traits/is_same.hpp>
@@ -26,7 +26,7 @@
 #include <boost/variant/variant.hpp>
 #include <boost/variant/get.hpp>
 #include <boost/variant/apply_visitor.hpp>
-#include <CGAL/Mesh_3/Has_features.h>
+#include <CGAL/SMDS_3/Has_features.h>
 #include <CGAL/IO/io.h>
 
 #include <tuple>
diff --git a/SMDS_3/include/CGAL/SMDS_3/io_signature.h b/SMDS_3/include/CGAL/SMDS_3/io_signature.h
new file mode 100644
index 00000000000..ba50d850123
--- /dev/null
+++ b/SMDS_3/include/CGAL/SMDS_3/io_signature.h
@@ -0,0 +1,363 @@
+// Copyright (c) 2006  INRIA Sophia-Antipolis (France).
+// Copyright (c) 2011  GeometryFactory Sarl (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)     : Laurent RINEAU
+
+#ifndef CGAL_SMDS_3_IO_SIGNATURE_H
+#define CGAL_SMDS_3_IO_SIGNATURE_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#define CGAL_MESH_3_IO_H // the old include macro, tested by other files
+
+#include <CGAL/Point_3.h>
+#include <CGAL/Weighted_point_3.h>
+#include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/Triangulation_vertex_base_3.h>
+#include <CGAL/Triangulation_vertex_base_with_info_3.h>
+#include <CGAL/Triangulation_cell_base_3.h>
+#include <CGAL/Triangulation_cell_base_with_info_3.h>
+#include <CGAL/Regular_triangulation_3.h>
+#include <CGAL/Regular_triangulation_cell_base_3.h>
+#include <CGAL/Regular_triangulation_cell_base_with_weighted_circumcenter_3.h>
+
+#ifdef CGAL_PERIODIC_3_MESH_3_CONFIG_H
+#include <CGAL/Periodic_3_triangulation_3.h>
+#include <CGAL/Periodic_3_regular_triangulation_3.h>
+#endif
+
+#include <boost/variant.hpp>
+#include <boost/tuple/tuple.hpp>
+#include <utility>
+
+namespace CGAL {
+
+// SFINAE test
+template <typename T, typename U>
+class has_io_signature
+{
+private:
+  template <U> struct helper;
+  template <typename V> static char check(helper<&V::io_signature> *);
+  template <typename V> static char (&check(...))[2];
+
+public:
+  enum { value = (sizeof(check<T>(0)) == sizeof(char)) };
+};
+
+template <class T, bool has_io_signature>
+struct Get_io_signature_aux
+{
+  std::string operator() () const
+  {
+    return T::io_signature();
+  }
+}; // end struct template Get_io_signature_aux
+
+template <class T>
+struct Get_io_signature_aux<T, false>
+{
+  std::string operator()() const
+  {
+    std::cerr << "Type without signature: " << typeid(T).name() << std::endl;
+    return std::string();
+  }
+}; // end template partial specialization Get_io_signature_aux<T, false>
+
+
+template <class T>
+struct Get_io_signature
+  : public Get_io_signature_aux<
+  T,
+  (has_io_signature<T, std::string (T::*)() >::value ||
+   has_io_signature<T, std::string (T::*)() const >::value ||
+   has_io_signature<T, std::string (*)() >::value )  // signature for
+                                                     // static mem func
+  >
+{
+};
+
+template <>
+struct Get_io_signature<int>
+{
+  std::string operator()() {
+    return "i";
+  }
+};
+
+template <>
+struct Get_io_signature<unsigned int>
+{
+  std::string operator()() {
+    return "ui";
+  }
+};
+
+template <>
+struct Get_io_signature<char>
+{
+  std::string operator()() {
+    return "c";
+  }
+};
+
+template <>
+struct Get_io_signature<unsigned char>
+{
+  std::string operator()() {
+    return "uc";
+  }
+};
+
+template <>
+struct Get_io_signature<signed char>
+{
+  std::string operator()() {
+    return "sc";
+  }
+};
+
+template <>
+struct Get_io_signature<short int>
+{
+  std::string operator()() {
+    return "s";
+  }
+};
+
+template <>
+struct Get_io_signature<unsigned short int>
+{
+  std::string operator()() {
+    return "us";
+  }
+};
+
+template <>
+struct Get_io_signature<double>
+{
+  std::string operator()() {
+    return "d";
+  }
+};
+
+template <typename T, typename U>
+struct Get_io_signature<boost::variant<T,U> >
+{
+    std::string operator()() {
+      return std::string("boost::variant<") +
+        Get_io_signature<T>()() + "," +
+        Get_io_signature<U>()() + ">";
+  }
+};
+
+template <typename T, typename U>
+struct Get_io_signature<std::pair<T,U> >
+{
+    std::string operator()() {
+      return std::string("std::pair<") +
+        Get_io_signature<T>()() + "," +
+        Get_io_signature<U>()() + ">";
+  }
+};
+
+template <typename T, typename U>
+struct Get_io_signature<boost::tuple<T,U> >
+{
+    std::string operator()() {
+      return std::string("std::pair<") +
+        Get_io_signature<T>()() + "," +
+        Get_io_signature<U>()() + ">";
+  }
+};
+
+template <typename T, typename U, typename V>
+struct Get_io_signature<boost::variant<T,U,V> >
+{
+    std::string operator()() {
+      return std::string("boost::variant<") +
+        Get_io_signature<T>()() + "," +
+        Get_io_signature<U>()() + "," +
+        Get_io_signature<V>()() + ">";
+  }
+};
+
+template <typename T, typename U,
+          typename V, typename W>
+struct Get_io_signature<boost::variant<T,U,V,W> >
+{
+    std::string operator()() {
+      return std::string("boost::variant<") +
+        Get_io_signature<T>()() + "," +
+        Get_io_signature<U>()() + "," +
+        Get_io_signature<V>()() + "," +
+        Get_io_signature<W>()() + ">";
+  }
+};
+
+template <class Kernel>
+struct Get_io_signature<Point_3<Kernel> >
+{
+  std::string operator()() {
+    return "Point_3";
+  }
+};
+
+template <class K>
+struct Get_io_signature<Weighted_point_3<K> >
+{
+  std::string operator()() {
+    return std::string("Weighted_point<") + Get_io_signature<Point_3<K> >()() + ">";
+  }
+};
+
+#ifdef CGAL_TRIANGULATION_3_H
+template <class Gt, class Tds>
+struct
+Get_io_signature<Triangulation_3<Gt, Tds > >
+{
+  std::string operator()() {
+    return std::string("Triangulation_3(") +
+      Get_io_signature<typename Tds::Vertex::Point>()() +
+      ",Vb(" + Get_io_signature<typename Tds::Vertex>()() +
+      "),Cb(" + Get_io_signature<typename Tds::Cell>()() +
+      "))";
+  }
+};
+#endif
+
+#ifdef CGAL_DELAUNAY_TRIANGULATION_3_H
+template <class Gt, class Tds>
+struct
+Get_io_signature<Delaunay_triangulation_3<Gt, Tds> >
+{
+  std::string operator()() {
+    return Get_io_signature<Triangulation_3<Gt, Tds> >()();
+  }
+};
+#endif
+
+#ifdef CGAL_REGULAR_TRIANGULATION_3_H
+template <class Gt, class Tds>
+struct
+Get_io_signature<Regular_triangulation_3<Gt, Tds> >
+{
+  std::string operator()() {
+    return Get_io_signature<Triangulation_3<Gt, Tds> >()();
+  }
+};
+#endif
+
+#ifdef CGAL_PERIODIC_3_TRIANGULATION_3_H
+template <class Gt, class Tds>
+struct
+Get_io_signature<Periodic_3_triangulation_3<Gt, Tds> >
+{
+  std::string operator()() {
+    return std::string("Periodic_3_triangulation_3(") +
+      Get_io_signature<typename Tds::Vertex::Point>()() +
+      ",Vb(" + Get_io_signature<typename Tds::Vertex>()() +
+      "),Cb(" + Get_io_signature<typename Tds::Cell>()() +
+      "))";
+  }
+};
+#endif
+
+#ifdef CGAL_PERIODIC_3_REGULAR_TRIANGULATION_3_H
+template <class Gt, class Tds>
+struct
+Get_io_signature<Periodic_3_regular_triangulation_3<Gt, Tds> >
+{
+  std::string operator()() {
+    return Get_io_signature<Periodic_3_triangulation_3<Gt, Tds> >()();
+  }
+};
+#endif
+
+#ifdef CGAL_TRIANGULATION_VERTEX_BASE_3_H
+template <class Gt, class Vb>
+struct Get_io_signature<Triangulation_vertex_base_3<Gt, Vb> >
+{
+  std::string operator()() {
+    return "Tvb_3";
+  }
+};
+#endif
+
+#ifdef CGAL_REGULAR_TRIANGULATION_VERTEX_BASE_3_H
+template <class Gt, class Vb>
+struct Get_io_signature<Regular_triangulation_vertex_base_3<Gt, Vb> >
+{
+  // identical to Triangulation_vertex_base_3
+  std::string operator()() {
+    return "Tvb_3";
+  }
+};
+#endif
+
+#ifdef CGAL_TRIANGULATION_VERTEX_BASE_WITH_INFO_3_H
+template <class Info, class Gt, class Vb>
+struct
+Get_io_signature<Triangulation_vertex_base_with_info_3<Info, Gt, Vb> >
+{
+  std::string operator()() {
+    return Get_io_signature<Vb>()();
+  }
+};
+#endif
+
+#ifdef CGAL_TRIANGULATION_CELL_BASE_3_H
+template <class Gt, class Cb>
+struct
+Get_io_signature<Triangulation_cell_base_3<Gt, Cb> >
+{
+  std::string operator()() {
+    return "Tcb_3";
+  }
+};
+#endif
+
+#ifdef CGAL_TRIANGULATION_CELL_BASE_WITH_INFO_3_H
+template <class Info, class Gt, class Cb>
+struct
+Get_io_signature<Triangulation_cell_base_with_info_3<Info, Gt, Cb> >
+{
+  std::string operator()() {
+    return Get_io_signature<Cb>()();
+  }
+};
+#endif
+
+#ifdef CGAL_REGULAR_TRIANGULATION_CELL_BASE_3_H
+template <class Gt, class Cb, class Container>
+struct
+Get_io_signature<Regular_triangulation_cell_base_3<Gt, Cb, Container> >
+{
+  std::string operator()() {
+    return "RTcb_3";
+  }
+};
+#endif
+
+#ifdef CGAL_REGULAR_TRIANGULATION_CELL_BASE_WITH_CIRCUMCENTER_3_H
+template <class Gt, class Cb>
+struct
+Get_io_signature<Regular_triangulation_cell_base_with_weighted_circumcenter_3<Gt, Cb> >
+{
+  std::string operator()() {
+    return "RTWWCcb_3";
+  }
+};
+#endif
+
+} // end namespace CGAL
+
+
+#endif // CGAL_SMDS_3_IO_SIGNATURE_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/tet_soup_to_c3t3.h b/SMDS_3/include/CGAL/SMDS_3/tet_soup_to_c3t3.h
similarity index 57%
rename from Mesh_3/include/CGAL/Mesh_3/tet_soup_to_c3t3.h
rename to SMDS_3/include/CGAL/SMDS_3/tet_soup_to_c3t3.h
index 5c2f6d69a08..812bc87214c 100644
--- a/Mesh_3/include/CGAL/Mesh_3/tet_soup_to_c3t3.h
+++ b/SMDS_3/include/CGAL/SMDS_3/tet_soup_to_c3t3.h
@@ -14,10 +14,10 @@
 //
 //******************************************************************************
 
-#ifndef CGAL_MESH_3_TET_SOUP_TO_C3T3_H
-#define CGAL_MESH_3_TET_SOUP_TO_C3T3_H
+#ifndef CGAL_SMDS_3_TET_SOUP_TO_C3T3_H
+#define CGAL_SMDS_3_TET_SOUP_TO_C3T3_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/disable_warnings.h>
 #include <CGAL/assertions.h>
@@ -32,7 +32,8 @@
 
 namespace CGAL
 {
-
+namespace SMDS_3
+{
 template<typename Vh>
 std::array<Vh, 3> make_ordered_vertex_array(const Vh vh0, const Vh vh1, const Vh vh2)
 {
@@ -43,12 +44,13 @@ std::array<Vh, 3> make_ordered_vertex_array(const Vh vh0, const Vh vh1, const Vh
   return ft;
 }
 
-template<class Tr>
+template<class Tr, typename PointRange>
 void build_vertices(Tr& tr,
-                    const std::vector<typename Tr::Point>& points,
+                    const PointRange& points,
                     std::vector<typename Tr::Vertex_handle>& vertex_handle_vector)
 {
   typedef typename Tr::Vertex_handle            Vertex_handle;
+  typedef typename Tr::Point                          Point;
 
   vertex_handle_vector[0] = tr.tds().create_vertex(); // creates the infinite vertex
   tr.set_infinite_vertex(vertex_handle_vector[0]);
@@ -58,7 +60,7 @@ void build_vertices(Tr& tr,
   {
     Vertex_handle vh = tr.tds().create_vertex();
     vertex_handle_vector[i+1] = vh;
-    vh->set_point(points[i]);
+    vh->set_point(Point(points[i]));
   }
 }
 
@@ -66,7 +68,8 @@ template<class Tr>
 bool add_facet_to_incident_cells_map(const typename Tr::Cell_handle c, int i,
     boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
                          std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map,
-    const bool verbose)
+    const bool verbose,
+    const bool allow_non_manifold)
 {
   typedef typename Tr::Vertex_handle                                Vertex_handle;
   typedef typename Tr::Cell_handle                                  Cell_handle;
@@ -74,8 +77,10 @@ bool add_facet_to_incident_cells_map(const typename Tr::Cell_handle c, int i,
   typedef std::pair<Cell_handle, int>                               Incident_cell;
   typedef boost::unordered_map<Facet_vvv, std::vector<Incident_cell> > Incident_cells_map;
 
+  bool success = true;
+
   // the opposite vertex of f in c is i
-  Facet_vvv f = make_ordered_vertex_array(c->vertex((i + 1) % 4),
+  Facet_vvv f = CGAL::SMDS_3::make_ordered_vertex_array(c->vertex((i + 1) % 4),
                                           c->vertex((i + 2) % 4),
                                           c->vertex((i + 3) % 4));
   CGAL_precondition(f[0] != f[1] && f[1] != f[2]);
@@ -92,47 +97,50 @@ bool add_facet_to_incident_cells_map(const typename Tr::Cell_handle c, int i,
     {
       if(verbose)
         std::cout << "Error in add_facet_to_incident_cells_map" << std::endl;
-      return false;
+      if(!allow_non_manifold)
+        success = false;
     }
     is_insert_successful.first->second.push_back(e);
   }
-  return true;
+  return success;
 }
 
-template<class Tr>
+template<class Tr, typename CellRange, typename SubdomainsRange, typename FacetPatchMap>
 bool build_finite_cells(Tr& tr,
-    const std::vector<std::array<int,5> >& finite_cells,
+    const CellRange& finite_cells,
+    const SubdomainsRange& subdomains,
     const std::vector<typename Tr::Vertex_handle>& vertex_handle_vector,
     boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
                         std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map,
-    const std::map<std::array<int,3>, typename Tr::Cell::Surface_patch_index>& border_facets,
+    const FacetPatchMap& border_facets,
     const bool verbose,
-                        bool replace_domain_0 = false)
+    const bool replace_domain_0)
 {
-  typedef std::array<int, 5>              Tet_with_ref; // 4 ids + 1 reference
-
   typedef typename Tr::Vertex_handle                            Vertex_handle;
   typedef typename Tr::Cell_handle                              Cell_handle;
   typedef typename Tr::Cell::Surface_patch_index                Surface_patch_index;
 
+  bool success = true;
+
   CGAL_assertion_code(
     typename Tr::Geom_traits::Construct_point_3 cp =
       tr.geom_traits().construct_point_3_object();
+    typename Tr::Geom_traits::Orientation_3 orientation =
+      tr.geom_traits().orientation_3_object();
   )
-  int max_domain = 0;
+  typename SubdomainsRange::value_type max_domain = 0;
   if(replace_domain_0)
   {
     for(std::size_t i=0; i<finite_cells.size(); ++i)
     {
-      const Tet_with_ref& tet = finite_cells[i];
-      if(tet[4] > max_domain)
-        max_domain=tet[4];
+      if(subdomains[i] > max_domain)
+        max_domain = subdomains[i];
     }
   }
   // build the finite cells
   for(std::size_t i=0; i<finite_cells.size(); ++i)
   {
-    const Tet_with_ref& tet = finite_cells[i];
+    const auto& tet = finite_cells[i];
     std::array<Vertex_handle, 4> vs;
 
     for(int j=0; j<4; ++j)
@@ -145,16 +153,17 @@ bool build_finite_cells(Tr& tr,
     }
 
     // this assertion also tests for degeneracy
-    CGAL_assertion(CGAL::orientation(cp(tr.point(vs[0])), cp(tr.point(vs[1])),
-                                     cp(tr.point(vs[2])), cp(tr.point(vs[3])))
+    CGAL_assertion(orientation(cp(tr.point(vs[0])), cp(tr.point(vs[1])),
+                               cp(tr.point(vs[2])), cp(tr.point(vs[3])))
                      == POSITIVE);
 
     Cell_handle c = tr.tds().create_cell(vs[0], vs[1], vs[2], vs[3]);
-    c->set_subdomain_index(tet[4]); // the cell's info keeps the reference of the tetrahedron
-    if(replace_domain_0 && tet[4] == 0)
+    c->set_subdomain_index(subdomains[i]); // the cell's info keeps the reference of the tetrahedron
+    if(replace_domain_0 && subdomains[i] == 0)
     {
       c->set_subdomain_index(max_domain+1); // the cell's info keeps the reference of the tetrahedron
     }
+
     // assign cells to vertices
     for(int j=0; j<4; ++j)
     {
@@ -165,8 +174,9 @@ bool build_finite_cells(Tr& tr,
     // build the map used for adjacency later
     for(int j=0; j<4; ++j)
     {
-      if(!add_facet_to_incident_cells_map<Tr>(c, j, incident_cells_map, verbose))
-        return false;
+      if(!CGAL::SMDS_3::add_facet_to_incident_cells_map<Tr>(c, j, incident_cells_map, verbose, false))
+          //do not allow non-manifold in the finite cells case
+        success = false;
       if(border_facets.size() != 0)
       {
         std::array<int,3> facet;
@@ -185,8 +195,7 @@ bool build_finite_cells(Tr& tr,
           ++k;
         } while(f[0] != n0);
 
-        typename std::map<std::array<int,3>, Surface_patch_index>::const_iterator
-          it = border_facets.find(f);
+        typename FacetPatchMap::const_iterator it = border_facets.find(f);
         if(it != border_facets.end())
         {
           c->set_surface_patch_index(j, it->second);
@@ -206,7 +215,7 @@ bool build_finite_cells(Tr& tr,
       }
     }
   }
-  return true;
+  return success;
 }
 
 template<class Tr>
@@ -214,14 +223,15 @@ bool add_infinite_facets_to_incident_cells_map(typename Tr::Cell_handle c,
      int inf_vert_pos,
      boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
                           std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map,
-     const bool verbose)
+     const bool verbose,
+     const bool allow_non_manifold)
 {
   int l = (inf_vert_pos + 1) % 4;
-  bool b1 = add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose);
+  bool b1 = CGAL::SMDS_3::add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose, allow_non_manifold);
   l = (inf_vert_pos + 2) % 4;
-  bool b2 = add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose);
+  bool b2 = CGAL::SMDS_3::add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose, allow_non_manifold);
   l = (inf_vert_pos + 3) % 4;
-  bool b3 = add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose);
+  bool b3 = CGAL::SMDS_3::add_facet_to_incident_cells_map<Tr>(c, l, incident_cells_map, verbose, allow_non_manifold);
   return b1 && b2 && b3;
 }
 
@@ -229,7 +239,8 @@ template<class Tr>
 bool build_infinite_cells(Tr& tr,
   boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
                        std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map,
-  const bool verbose)
+  const bool verbose,
+  const bool allow_non_manifold)
 {
   typedef typename Tr::Vertex_handle                               Vertex_handle;
   typedef typename Tr::Cell_handle                                 Cell_handle;
@@ -237,6 +248,8 @@ bool build_infinite_cells(Tr& tr,
   typedef std::pair<Cell_handle, int>                              Incident_cell;
   typedef boost::unordered_map<Facet_vvv, std::vector<Incident_cell> > Incident_cells_map;
 
+  bool success = true;
+
   std::vector<Cell_handle> infinite_cells;
 
   // check the incident cells map for facets who only have one incident cell
@@ -287,7 +300,7 @@ bool build_infinite_cells(Tr& tr,
   {
     for (int i = 1; i < 4; ++i)
     {
-      std::array<Vertex_handle, 3> vs = make_ordered_vertex_array(c->vertex((i + 1) % 4),
+      std::array<Vertex_handle, 3> vs = CGAL::SMDS_3::make_ordered_vertex_array(c->vertex((i + 1) % 4),
         c->vertex((i + 2) % 4),
         c->vertex((i + 3) % 4));
       if (facets.find(vs) == facets.end())
@@ -297,52 +310,93 @@ bool build_infinite_cells(Tr& tr,
     }
   }
   for (auto fp : facets)
-    CGAL_assertion(fp.second == 2);
+  {
+    if (fp.second != 2)
+    {
+      std::cout << "Warning : non manifold edge" << std::endl;
+      std::cout << "fp.second = " << fp.second << std::endl;
+      std::cout << fp.first[0]->point() << " "
+        << fp.first[1]->point() << " "
+        << fp.first[2]->point() << std::endl;
+      success = false;
+    }
+//    CGAL_assertion(fp.second == 2);
+  }
 #endif
 
   // add the facets to the incident cells map
   for (const Cell_handle& c : infinite_cells)
-    if(!add_infinite_facets_to_incident_cells_map<Tr>(c, 0, incident_cells_map, verbose))
-      return false;
+    if(!CGAL::SMDS_3::add_infinite_facets_to_incident_cells_map<Tr>(c,
+                                                                    0,
+                                                                    incident_cells_map,
+                                                                    verbose,
+                                                                    allow_non_manifold))
+      success = false;
 
-  return true;
+  return success;
+}
+
+template<typename Tr>
+bool has_infinite_vertex(const std::array<typename Tr::Vertex_handle, 3>& v,
+                         const Tr& tr)
+{
+  for (auto vh : v)
+  {
+    if (tr.infinite_vertex() == vh)
+      return true;
+  }
+  return false;
 }
 
 template<class Tr>
 bool assign_neighbors(Tr& tr,
   const boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
-                             std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map)
+                             std::vector<std::pair<typename Tr::Cell_handle, int> > >& incident_cells_map,
+  const bool allow_non_manifold)
 {
   typedef typename Tr::Cell_handle                                   Cell_handle;
   typedef std::pair<Cell_handle, int>                                Incident_cell;
   typedef boost::unordered_map<std::array<typename Tr::Vertex_handle, 3>,
                                std::vector<Incident_cell> >          Incident_cells_map;
 
+  bool success = true;
+
   typename Incident_cells_map::const_iterator icit = incident_cells_map.begin();
   for(; icit!=incident_cells_map.end(); ++icit)
   {
     const std::vector<Incident_cell>& adjacent_cells = icit->second;
-    if(adjacent_cells.size() != 2)
-      return false;
+    if (adjacent_cells.size() == 2)
+    {
+      Cell_handle c0 = adjacent_cells[0].first;
+      int i0 = adjacent_cells[0].second;
+      Cell_handle c1 = adjacent_cells[1].first;
+      int i1 = adjacent_cells[1].second;
 
-    Cell_handle c0 = adjacent_cells[0].first;
-    int i0 = adjacent_cells[0].second;
-    Cell_handle c1 = adjacent_cells[1].first;
-    int i1 = adjacent_cells[1].second;
-
-    tr.tds().set_adjacency(c0, i0, c1, i1);
+      tr.tds().set_adjacency(c0, i0, c1, i1);
+    }
+    else if(allow_non_manifold)// if (adjacent_cells.size() == 4)
+    {
+      CGAL_assertion_code(const auto& v = icit->first);
+      CGAL_assertion(has_infinite_vertex(v, tr));
+      success = false;
+    }
   }
-  return true;
+  return success;
 }
 
-template<class Tr, bool c3t3_loader_failed>
-bool build_triangulation(Tr& tr,
-                         const std::vector<typename Tr::Point>& points,
-                         const std::vector<std::array<int,5> >& finite_cells,
-                         const std::map<std::array<int,3>, typename Tr::Cell::Surface_patch_index>& border_facets,
-                         std::vector<typename Tr::Vertex_handle>& vertex_handle_vector,
-                         const bool verbose = false,
-                         bool replace_domain_0 = false)
+template<class Tr,
+         typename PointRange,
+         typename CellRange,
+         typename FacetPatchMap>
+bool build_triangulation_impl(Tr& tr,
+    const PointRange& points,
+    const CellRange& finite_cells,
+    const std::vector<typename Tr::Cell::Subdomain_index>& subdomains,
+    const FacetPatchMap& border_facets,
+    std::vector<typename Tr::Vertex_handle>& vertex_handle_vector,
+    const bool verbose,// = false,
+    const bool replace_domain_0,// = false,
+    const bool allow_non_manifold) // = false
 {
   typedef typename Tr::Vertex_handle            Vertex_handle;
   typedef typename Tr::Cell_handle              Cell_handle;
@@ -352,6 +406,8 @@ bool build_triangulation(Tr& tr,
   typedef std::pair<Cell_handle, int>                   Incident_cell;
   typedef boost::unordered_map<Facet_vvv, std::vector<Incident_cell> >  Incident_cells_map;
 
+  bool success = true;
+
   Incident_cells_map incident_cells_map;
   vertex_handle_vector.resize(points.size() + 1); // id to vertex_handle
                                         //index 0 is for infinite vertex
@@ -373,14 +429,23 @@ bool build_triangulation(Tr& tr,
   }
   if (!finite_cells.empty())
   {
-    if(!build_finite_cells<Tr>(tr, finite_cells, vertex_handle_vector, incident_cells_map,
-                           border_facets, verbose, replace_domain_0))
-      return false;
-    if(!build_infinite_cells<Tr>(tr, incident_cells_map, verbose))
-      return false;
+    if (!CGAL::SMDS_3::build_finite_cells<Tr>(tr, finite_cells, subdomains, vertex_handle_vector, incident_cells_map,
+                                border_facets, verbose, replace_domain_0))
+    {
+      if(verbose) std::cout << "build_finite_cells went wrong" << std::endl;
+      success = false;
+    }
+    if (!CGAL::SMDS_3::build_infinite_cells<Tr>(tr, incident_cells_map, verbose, allow_non_manifold))
+    {
+      if(verbose) std::cout << "build_infinite_cells went wrong" << std::endl;
+      success = false;
+    }
     tr.tds().set_dimension(3);
-    if (!assign_neighbors<Tr>(tr, incident_cells_map))
-      return false;
+    if (!CGAL::SMDS_3::assign_neighbors<Tr>(tr, incident_cells_map, allow_non_manifold))
+    {
+      if(verbose) std::cout << "assign_neighbors went wrong" << std::endl;
+      success = false;
+    }
     if (verbose)
     {
       std::cout << "built triangulation : " << std::endl;
@@ -390,25 +455,92 @@ bool build_triangulation(Tr& tr,
   if(verbose)
     std::cout << tr.number_of_vertices() << " vertices" << std::endl;
 
-  if(c3t3_loader_failed)
-    return true;
-  else
-    return tr.tds().is_valid();
+  return success;// tr.tds().is_valid();
+              //TDS not valid when cells do not cover the convex hull of vertices
 }
 
-template<class Tr, bool c3t3_loader_failed>
+template<class Tr,
+         typename PointRange,
+         typename CellRange,
+         typename FacetPatchMap>
+bool build_triangulation_one_subdomain(Tr& tr,
+    const PointRange& points,
+    const CellRange& finite_cells,
+    const typename Tr::Cell::Subdomain_index& subdomain,
+    const FacetPatchMap& border_facets,
+    std::vector<typename Tr::Vertex_handle>& vertex_handle_vector,
+    const bool verbose,// = false,
+    const bool replace_domain_0,// = false
+    const bool allow_non_manifold)// = false
+{
+  std::vector<typename Tr::Cell::Subdomain_index> subdomains(finite_cells.size(), subdomain);
+  return build_triangulation_impl(tr, points, finite_cells, subdomains,
+                                  border_facets, vertex_handle_vector,
+                                  verbose, replace_domain_0,
+                                  allow_non_manifold);
+}
+
+template<class Tr,
+         typename PointRange,
+         typename CellRange,
+         typename FacetPatchMap>
+bool build_triangulation_one_subdomain(Tr& tr,
+    const PointRange& points,
+    const CellRange& finite_cells,
+    const typename Tr::Cell::Subdomain_index& subdomain,
+    const FacetPatchMap& border_facets,
+    const bool verbose,// = false,
+    const bool replace_domain_0,// = false
+    const bool allow_non_manifold)//= false
+{
+  std::vector<typename Tr::Cell::Subdomain_index> subdomains(finite_cells.size(), subdomain);
+  std::vector<typename Tr::Vertex_handle> vertex_handle_vector;
+  return build_triangulation_impl(tr, points, finite_cells, subdomains,
+                                  border_facets, vertex_handle_vector,
+                                  verbose, replace_domain_0,
+                                  allow_non_manifold);
+}
+
+template<class Tr,
+         typename PointRange,
+         typename CellRange,
+         typename SubdomainsRange,
+         typename FacetPatchMap>
+bool build_triangulation_with_subdomains_range(Tr& tr,
+    const PointRange& points,
+    const CellRange& finite_cells,
+    const SubdomainsRange& subdomains,
+    const FacetPatchMap& border_facets,
+    const bool verbose,// = false
+    const bool replace_domain_0,// = false,
+    const bool allow_non_manifold)
+{
+  std::vector<typename Tr::Vertex_handle> vertex_handle_vector;
+  std::vector<typename Tr::Cell::Subdomain_index> subdomains_vector(
+      subdomains.begin(), subdomains.end());
+  return build_triangulation_impl(tr, points, finite_cells, subdomains_vector, border_facets,
+                                  vertex_handle_vector,
+                                  verbose, replace_domain_0,
+                                  allow_non_manifold);
+}
+
+template<class Tr>
 bool build_triangulation_from_file(std::istream& is,
                                    Tr& tr,
-                                   bool replace_domain_0)
+                                   const bool verbose,
+                                   const bool replace_domain_0,
+                                   const bool allow_non_manifold)
 {
-  typedef typename Tr::Point                                  Point_3;
+  using Point_3 = typename Tr::Point;
+  using Subdomain_index = typename Tr::Cell::Subdomain_index;
 
-  typedef std::array<int, 3> Facet; // 3 = id
-  typedef std::array<int, 5> Tet_with_ref; // first 4 = id, fifth = reference
+  using Facet        = std::array<int, 3>; // 3 = id
+  using Tet_with_ref = std::array<int, 4>; // 4 = id
 
   std::vector<Tet_with_ref> finite_cells;
+  std::vector<Subdomain_index> subdomains;
   std::vector<Point_3> points;
-  std::map<Facet, typename Tr::Cell::Surface_patch_index> border_facets;
+  boost::unordered_map<Facet, typename Tr::Cell::Surface_patch_index> border_facets;
 
   // grab the vertices
   int dim;
@@ -420,9 +552,25 @@ bool build_triangulation_from_file(std::istream& is,
 
   CGAL_assertion(dim == 3);
 
-  std::cout << "Reading .mesh file..." << std::endl;
+  if(verbose)
+    std::cout << "Reading .mesh file..." << std::endl;
+
+  bool dont_replace_domain_0 = false;
+
   while(is >> word && word != "End")
   {
+    if (word.at(0) == '#')
+    {
+      is >> word;
+      if (word == "End")
+        break;
+      else if (word == "CGAL::Mesh_complex_3_in_triangulation_3")
+      {
+        dont_replace_domain_0 = true;//with CGAL meshes, domain 0 should be kept
+        continue;
+      }
+      //else skip other comments
+    }
     if(word == "Vertices")
     {
       is >> nv;
@@ -473,33 +621,33 @@ bool build_triangulation_from_file(std::istream& is,
         t[1] = n1 - 1;
         t[2] = n2 - 1;
         t[3] = n3 - 1;
-        t[4] = reference;
         finite_cells.push_back(t);
+        subdomains.push_back(reference);
       }
     }
   }
 
-  std::cout << points.size() << " points" << std::endl;
-  std::cout << border_facets.size() << " border facets" << std::endl;
-  std::cout << finite_cells.size() << " cells" << std::endl;
+  if (verbose)
+  {
+    std::cout << points.size() << " points" << std::endl;
+    std::cout << border_facets.size() << " border facets" << std::endl;
+    std::cout << finite_cells.size() << " cells" << std::endl;
+  }
 
   if(finite_cells.empty())
     return false;
+  CGAL_assertion(finite_cells.size() == subdomains.size());
 
-  std::vector<typename Tr::Vertex_handle> vertices(points.size() + 1);
-  bool is_well_built = build_triangulation<Tr, c3t3_loader_failed>(tr,
-    points, finite_cells, border_facets, vertices, false, replace_domain_0);
-  return is_well_built;
+  return build_triangulation_with_subdomains_range(tr,
+                      points, finite_cells, subdomains, border_facets,
+                      verbose,
+                      replace_domain_0 && !dont_replace_domain_0,
+                      allow_non_manifold);
 }
 
-template<class Tr, bool c3t3_loader_failed>
-bool build_triangulation_from_file(std::istream& is,
-                                   Tr& tr)
-{
-  return build_triangulation_from_file<Tr, c3t3_loader_failed>(is, tr, false);
-}
+}  // namespace SMDS_3
 }  // namespace CGAL
 
 #include <CGAL/enable_warnings.h>
 
-#endif // CGAL_MESH_3_TET_SOUP_TO_C3T3_H
+#endif // CGAL_SMDS_3_TET_SOUP_TO_C3T3_H
diff --git a/Mesh_3/include/CGAL/Mesh_3/utilities.h b/SMDS_3/include/CGAL/SMDS_3/utilities.h
similarity index 93%
rename from Mesh_3/include/CGAL/Mesh_3/utilities.h
rename to SMDS_3/include/CGAL/SMDS_3/utilities.h
index 5e49f7a617e..369bfc9df03 100644
--- a/Mesh_3/include/CGAL/Mesh_3/utilities.h
+++ b/SMDS_3/include/CGAL/SMDS_3/utilities.h
@@ -14,10 +14,10 @@
 // File Description :
 //******************************************************************************
 
-#ifndef CGAL_MESH_3_UTILITIES_H
-#define CGAL_MESH_3_UTILITIES_H
+#ifndef CGAL_SMDS_3_UTILITIES_H
+#define CGAL_SMDS_3_UTILITIES_H
 
-#include <CGAL/license/Triangulation_3.h>
+#include <CGAL/license/SMDS_3.h>
 
 #include <CGAL/Has_timestamp.h>
 #include <iterator>
@@ -25,7 +25,7 @@
 #include <sstream>
 
 namespace CGAL {
-namespace Mesh_3 {
+namespace SMDS_3 {
 namespace internal {
 
 struct Debug_messages_tools {
@@ -115,7 +115,7 @@ public:
 
 
 } // end namespace internal
-} // end namespace Mesh_3
+} // end namespace SMDS_3
 } //namespace CGAL
 
-#endif // CGAL_MESH_3_UTILITIES_H
+#endif // CGAL_SMDS_3_UTILITIES_H
diff --git a/SMDS_3/include/CGAL/Simplicial_mesh_cell_base_3.h b/SMDS_3/include/CGAL/Simplicial_mesh_cell_base_3.h
new file mode 100644
index 00000000000..15a4b1fd3eb
--- /dev/null
+++ b/SMDS_3/include/CGAL/Simplicial_mesh_cell_base_3.h
@@ -0,0 +1,391 @@
+// Copyright (c) 2006-2007  INRIA Sophia-Antipolis (France).
+// Copyright (c) 2008,2011 GeometryFactory Sarl (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)     : Laurent Rineau, Stephane Tayeb, Andreas Fabri, Jane Tournois
+
+
+#ifndef CGAL_SIMPLICIAL_MESH_CELL_BASE_3_H
+#define CGAL_SIMPLICIAL_MESH_CELL_BASE_3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/array.h>
+#include <CGAL/assertions.h>
+#include <CGAL/basic.h>
+#include <CGAL/triangulation_assertions.h>
+#include <CGAL/TDS_3/internal/Dummy_tds_3.h>
+#include <CGAL/tags.h>
+#include <CGAL/Has_timestamp.h>
+
+#include <CGAL/Triangulation_cell_base_3.h>
+#include <CGAL/SMDS_3/io_signature.h>
+
+#ifdef CGAL_LINKED_WITH_TBB
+# include <atomic>
+#endif
+
+namespace CGAL {
+
+// Class Simplicial_mesh_cell_3
+// Cell base class used for tetrahedral remeshing
+// Adds information to Cb about the cell of the input complex containing it
+template< class Subdomain_index_,
+          class Surface_patch_index_,
+          class TDS>
+class Simplicial_mesh_cell_3
+{
+public:
+  using Triangulation_data_structure = TDS;
+  using Vertex_handle = typename TDS::Vertex_handle;
+  using Cell_handle = typename TDS::Cell_handle;
+  using Vertex = typename TDS::Vertex;
+  using Cell = typename TDS::Cell;
+  using TDS_data = typename TDS::Cell_data;
+
+  // Index Type
+  using Subdomain_index = Subdomain_index_;
+  using Surface_patch_index = Surface_patch_index_;
+
+public:
+  // Constructors
+  Simplicial_mesh_cell_3()
+    : time_stamp_(std::size_t(-1))
+  {}
+
+  Simplicial_mesh_cell_3(const Simplicial_mesh_cell_3& rhs)
+    : N(rhs.N)
+    , V(rhs.V)
+    , time_stamp_(rhs.time_stamp_)
+    , subdomain_index_(rhs.subdomain_index_)
+  {
+    for(int i=0; i <4; i++){
+      surface_index_table_[i] = rhs.surface_index_table_[i];
+    }
+  }
+
+  Simplicial_mesh_cell_3(Vertex_handle v0,
+                         Vertex_handle v1,
+                         Vertex_handle v2,
+                         Vertex_handle v3)
+    : V(CGAL::make_array(v0, v1, v2, v3))
+  {
+  }
+
+  Simplicial_mesh_cell_3(Vertex_handle v0,
+                         Vertex_handle v1,
+                         Vertex_handle v2,
+                         Vertex_handle v3,
+                         Cell_handle n0,
+                         Cell_handle n1,
+                         Cell_handle n2,
+                         Cell_handle n3)
+    : N(CGAL::make_array(n0, n1, n2, n3))
+    , V(CGAL::make_array(v0, v1, v2, v3))
+  {
+  }
+
+  // ACCESS FUNCTIONS
+  Vertex_handle vertex(int i) const
+  {
+    CGAL_triangulation_precondition( i >= 0 && i <= 3 );
+    return V[i];
+  }
+
+  bool has_vertex(Vertex_handle v) const
+  {
+    return (V[0] == v) || (V[1] == v) || (V[2]== v) || (V[3]== v);
+  }
+
+  bool has_vertex(Vertex_handle v, int & i) const
+  {
+    if (v == V[0]) { i = 0; return true; }
+    if (v == V[1]) { i = 1; return true; }
+    if (v == V[2]) { i = 2; return true; }
+    if (v == V[3]) { i = 3; return true; }
+    return false;
+  }
+
+  int index(Vertex_handle v) const
+  {
+    if (v == V[0]) { return 0; }
+    if (v == V[1]) { return 1; }
+    if (v == V[2]) { return 2; }
+    CGAL_triangulation_assertion( v == V[3] );
+    return 3;
+  }
+
+  Cell_handle neighbor(int i) const
+  {
+    CGAL_triangulation_precondition( i >= 0 && i <= 3);
+    return N[i];
+  }
+
+  bool has_neighbor(Cell_handle n) const
+  {
+    return (N[0] == n) || (N[1] == n) || (N[2] == n) || (N[3] == n);
+  }
+
+  bool has_neighbor(Cell_handle n, int & i) const
+  {
+    if(n == N[0]){ i = 0; return true; }
+    if(n == N[1]){ i = 1; return true; }
+    if(n == N[2]){ i = 2; return true; }
+    if(n == N[3]){ i = 3; return true; }
+    return false;
+  }
+
+  int index(Cell_handle n) const
+  {
+    if (n == N[0]) return 0;
+    if (n == N[1]) return 1;
+    if (n == N[2]) return 2;
+    CGAL_triangulation_assertion( n == N[3] );
+    return 3;
+  }
+
+  // SETTING
+  void set_neighbor(int i, Cell_handle n)
+  {
+    CGAL_triangulation_precondition( i >= 0 && i <= 3);
+    CGAL_triangulation_precondition( this != n.operator->() );
+    N[i] = n;
+  }
+
+  void set_neighbors()
+  {
+    N[0] = N[1] = N[2] = N[3] = Cell_handle();
+  }
+
+  void set_neighbors(Cell_handle n0, Cell_handle n1,
+                     Cell_handle n2, Cell_handle n3)
+  {
+    CGAL_triangulation_precondition( this != n0.operator->() );
+    CGAL_triangulation_precondition( this != n1.operator->() );
+    CGAL_triangulation_precondition( this != n2.operator->() );
+    CGAL_triangulation_precondition( this != n3.operator->() );
+    N[0] = n0;
+    N[1] = n1;
+    N[2] = n2;
+    N[3] = n3;
+  }
+
+  // CHECKING
+
+  // the following trivial is_valid allows
+  // the user of derived cell base classes
+  // to add their own purpose checking
+  bool is_valid(bool = false, int = 0) const
+  { return true; }
+
+  // For use by Compact_container.
+  void * for_compact_container() const { return N[0].for_compact_container(); }
+  void for_compact_container(void *p) { N[0].for_compact_container(p); }
+
+  // TDS internal data access functions.
+        TDS_data& tds_data()       { return _tds_data; }
+  const TDS_data& tds_data() const { return _tds_data; }
+
+  // We must override the functions that modify the vertices.
+  // And if the point inside a vertex is modified, we fail,
+  // but there's not much we can do for this now.
+  void set_vertex(int i, Vertex_handle v)
+  {
+    CGAL_triangulation_precondition( i >= 0 && i <= 3);
+    V[i] = v;
+  }
+
+  void set_vertices()
+  {
+    V[0] = V[1] = V[2] = V[3] = Vertex_handle();
+  }
+
+  void set_vertices(Vertex_handle v0, Vertex_handle v1,
+                    Vertex_handle v2, Vertex_handle v3)
+  {
+    V[0] = v0;
+    V[1] = v1;
+    V[2] = v2;
+    V[3] = v3;
+  }
+
+  // Returns the index of the cell of the input complex that contains the cell
+  Subdomain_index subdomain_index() const { return subdomain_index_; }
+
+  // Sets the index of the cell of the input complex that contains the cell
+  void set_subdomain_index(const Subdomain_index& index)
+  { subdomain_index_ = index; }
+
+  /// Set surface index of \c facet to \c index
+  void set_surface_patch_index(const int facet, const Surface_patch_index& index)
+  {
+    CGAL_precondition(facet>=0 && facet<4);
+    surface_index_table_[facet] = index;
+  }
+
+  /// Returns surface index of facet \c facet
+  Surface_patch_index surface_patch_index(const int facet) const
+  {
+    CGAL_precondition(facet>=0 && facet<4);
+    return surface_index_table_[facet];
+  }
+
+  /// Returns true if facet lies on a surface patch
+  bool is_facet_on_surface(const int facet) const
+  {
+    CGAL_precondition(facet>=0 && facet<4);
+    return ( !( Surface_patch_index() == surface_index_table_[facet] ));
+  }
+
+  // -----------------------------------
+  // Backward Compatibility
+  // -----------------------------------
+#ifndef CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
+  typedef Surface_patch_index   Surface_index;
+
+  void set_surface_index(const int facet, const Surface_index& index)
+  { set_surface_patch_index(facet,index); }
+
+  /// Returns surface index of facet \c facet
+  Surface_index surface_index(const int facet) const
+  { return surface_patch_index(facet); }
+#endif // CGAL_MESH_3_NO_DEPRECATED_SURFACE_INDEX
+  // -----------------------------------
+  // End backward Compatibility
+  // -----------------------------------
+
+  static
+  std::string io_signature()
+  {
+    return
+      Get_io_signature<Subdomain_index>()()
+      + "+(" + Get_io_signature<Surface_patch_index>()() + ")[4]";
+  }
+
+  /// For the determinism of Compact_container iterators
+  ///@{
+  typedef Tag_true Has_timestamp;
+
+  std::size_t time_stamp() const {
+    return time_stamp_;
+  }
+  void set_time_stamp(const std::size_t& ts) {
+    time_stamp_ = ts;
+  }
+  ///@}
+
+private:
+
+  /// Stores surface_index for each facet of the cell
+  std::array<Surface_patch_index, 4> surface_index_table_ = {};
+
+  std::array<Cell_handle, 4> N;
+  std::array<Vertex_handle, 4> V;
+
+  std::size_t time_stamp_;
+
+  // The index of the cell of the input complex that contains me
+  Subdomain_index subdomain_index_ = {};
+
+  TDS_data      _tds_data;
+
+public:
+
+  friend std::istream& operator>>(std::istream &is, Simplicial_mesh_cell_3 &c)
+  {
+    Subdomain_index index;
+    if(IO::is_ascii(is))
+      is >> index;
+    else
+      read(is, index);
+    if(is) {
+      c.set_subdomain_index(index);
+      for(int i = 0; i < 4; ++i)
+        {
+          Surface_patch_index i2;
+          if(IO::is_ascii(is))
+            is >> IO::iformat(i2);
+          else
+            {
+              read(is, i2);
+            }
+          c.set_surface_patch_index(i, i2);
+        }
+    }
+    return is;
+  }
+
+  friend
+  std::ostream& operator<<(std::ostream &os, const Simplicial_mesh_cell_3&c)
+  {
+    if(IO::is_ascii(os))
+      os << c.subdomain_index();
+    else
+      write(os, c.subdomain_index());
+    for(int i = 0; i < 4; ++i)
+      {
+        if(IO::is_ascii(os))
+          os << ' ' << IO::oformat(c.surface_patch_index(i));
+        else
+          write(os, c.surface_patch_index(i));
+      }
+    return os;
+  }
+
+};  // end class Simplicial_mesh_cell_3
+
+/*!
+\ingroup PkgSMDS3Classes
+
+The class `Simplicial_mesh_cell_base_3`
+is a model of the concept `SimplicialMeshCellBase_3`.
+It is designed to serve as cell base class for.3D simplicial mesh data structures.
+It stores and gives access to data about the complex the cell belongs to, such as the
+subdomain it belongs to or surface it takes part to.
+
+\tparam Subdomain_index Type of indices for subdomains of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must match the label
+of the exterior of the domain (which contains at least the unbounded component).
+ It must match the `Subdomain_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
+
+\tparam Surface_patch_index Type of indices for surface patches (boundaries and interfaces)
+of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must be the index value
+assigned to a non surface facet.
+ It must match the `Surface_patch_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
+
+\cgalModels `SimplicialMeshCellBase_3`
+
+\sa `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>`
+\sa \link Mesh_cell_base_3 `CGAL::Mesh_cell_base_3`\endlink
+\sa `MeshDomain_3`
+\sa `MeshDomainWithFeatures_3`
+*/
+template <typename Subdomain_index,
+          typename Surface_patch_index>
+class Simplicial_mesh_cell_base_3
+{
+public:
+  template <typename TDS2>
+  struct Rebind_TDS
+  {
+    typedef Simplicial_mesh_cell_3<Subdomain_index,
+                                   Surface_patch_index,
+                                   TDS2> Other;
+  };
+};
+
+}  // end namespace CGAL
+
+
+#endif // CGAL_SIMPLICIAL_MESH_CELL_BASE_3_H
diff --git a/SMDS_3/include/CGAL/Simplicial_mesh_vertex_base_3.h b/SMDS_3/include/CGAL/Simplicial_mesh_vertex_base_3.h
new file mode 100644
index 00000000000..3f1a9c92d42
--- /dev/null
+++ b/SMDS_3/include/CGAL/Simplicial_mesh_vertex_base_3.h
@@ -0,0 +1,288 @@
+// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
+// Copyright (c) 2011 GeometryFactory Sarl (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)     : Stéphane Tayeb, Andreas Fabri, Jane Tournois
+//
+//******************************************************************************
+// File Description :
+//
+//
+//******************************************************************************
+
+
+#ifndef CGAL_SIMPLICIAL_MESH_VERTEX_BASE_3_H
+#define CGAL_SIMPLICIAL_MESH_VERTEX_BASE_3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/Triangulation_vertex_base_3.h>
+
+#include <CGAL/SMDS_3/internal/indices_management.h>
+#include <CGAL/SMDS_3/io_signature.h>
+#include <CGAL/Has_timestamp.h>
+
+#include <boost/variant.hpp>
+#include <tuple>
+
+namespace CGAL {
+
+//Class Simplicial_mesh_vertex_3
+//Adds information to Vb about the localization of the vertex in regards
+//to the 3D input complex.
+//\cgalModels `SimplicialMeshVertexBase_3`
+template<class GT,
+         typename Subdomain_index,
+         typename Surface_patch_index,
+         typename Curve_index,
+         typename Corner_index,
+         class Vb>
+class Simplicial_mesh_vertex_3
+: public Vb
+{
+private :
+  using Cmvb3_base = Vb;
+
+public:
+  using Vertex_handle = typename Vb::Vertex_handle;
+
+  // Types
+  using Index = boost::variant<Subdomain_index, Surface_patch_index, Curve_index, Corner_index>;
+  using FT = typename GT::FT;
+
+  // Constructor
+  Simplicial_mesh_vertex_3()
+    : Vb()
+    , number_of_incident_facets_(0)
+    , number_of_components_(0)
+    , index_()
+    , dimension_(-1)
+    , cache_validity(false)
+    , time_stamp_(std::size_t(-1))
+  {}
+
+  // Default copy constructor and assignment operator are ok
+
+  // Returns the dimension of the lowest dimensional face of the input 3D
+  // complex that contains the vertex
+  int in_dimension() const {
+    if(dimension_ < -1) return -2-dimension_;
+    else return dimension_;
+  }
+
+  // Sets the dimension of the lowest dimensional face of the input 3D complex
+  // that contains the vertex
+  void set_dimension(const int dimension) {
+    CGAL_assertion(dimension < 4);
+    dimension_ = short(dimension);
+  }
+
+  // Returns the index of the lowest dimensional face of the input 3D complex
+  // that contains the vertex
+  Index index() const { return index_; }
+
+  // Sets the index of the lowest dimensional face of the input 3D complex
+  // that contains the vertex
+  void set_index(const Index& index) { index_ = index; }
+
+  /// For the determinism of Compact_container iterators
+  ///@{
+  typedef Tag_true Has_timestamp;
+
+  std::size_t time_stamp() const {
+    return time_stamp_;
+  }
+  void set_time_stamp(const std::size_t& ts) {
+    time_stamp_ = ts;
+  }
+  ///@}
+
+  bool is_c2t3_cache_valid() const {
+    return cache_validity;
+  }
+
+  void invalidate_c2t3_cache()
+  {
+    cache_validity = false;
+  }
+
+  void set_c2t3_cache(const std::size_t i, const std::size_t j)
+  {
+    number_of_incident_facets_ = i;
+    number_of_components_ = j;
+    cache_validity = true;
+  }
+
+  std::size_t cached_number_of_incident_facets() const
+  {
+    return number_of_incident_facets_;
+  }
+
+  std::size_t cached_number_of_components() const
+  {
+    return number_of_components_;
+  }
+
+  static
+  std::string io_signature()
+  {
+    return
+      Get_io_signature<Vb>()() + "+" +
+      Get_io_signature<int>()() + "+" +
+      Get_io_signature<Index>()();
+  }
+private:
+
+  std::size_t number_of_incident_facets_;
+  std::size_t number_of_components_; // number of components in the adjacency
+  // graph of incident facets (in complex)
+
+
+  // Index of the lowest dimensional face of the input 3D complex
+  // that contains me
+  Index index_;
+
+  // Dimension of the lowest dimensional face of the input 3D complex
+  // that contains me. Negative values are a marker for special vertices.
+  short dimension_;
+  bool cache_validity;
+  std::size_t time_stamp_;
+
+public:
+
+  friend std::istream& operator>>(std::istream &is, Simplicial_mesh_vertex_3& v)
+  {
+    is >> static_cast<Cmvb3_base&>(v);
+    int dimension;
+    if(IO::is_ascii(is)) {
+      is >> dimension;
+
+    } else {
+      CGAL::read(is, dimension);
+    }
+    v.set_dimension(dimension);
+    CGAL_assertion(v.in_dimension() >= -1);
+    CGAL_assertion(v.in_dimension() < 4);
+
+    using Indices_tuple = std::tuple<Subdomain_index,
+                                     Surface_patch_index,
+                                     Curve_index,
+                                     Corner_index>;
+    Index index =
+      Mesh_3::internal::Read_write_index<Indices_tuple,
+                                         Index>()(is, v.in_dimension());
+    v.set_index(index);
+    return is;
+  }
+
+  friend std::ostream& operator<<(std::ostream &os, const Simplicial_mesh_vertex_3& v)
+  {
+    os << static_cast<const Cmvb3_base&>(v);
+    if(IO::is_ascii(os)) {
+      os << " " << v.in_dimension()
+         << " ";
+    } else {
+      CGAL::write(os, v.in_dimension());
+    }
+    using Indices_tuple = std::tuple<Subdomain_index,
+                                     Surface_patch_index,
+                                     Curve_index,
+                                     Corner_index>;
+    Mesh_3::internal::Read_write_index<Indices_tuple,
+                                       Index>()(os,
+                                                v.in_dimension(),
+                                                v.index());
+    return os;
+  }
+};  // end class Simplicial_mesh_vertex_3
+
+
+/*!
+\ingroup PkgSMDS3Classes
+
+The class `Simplicial_mesh_vertex_base_3` is a model of the concept
+`SimplicialMeshVertexBase_3`.
+It is designed to serve as vertex base class for 3D simplicial mesh data structures.
+It stores and gives access to data about the complex the vertex belongs to, such as the
+index of the subcomplex it belongs to.
+
+\tparam Gt is the geometric traits class.
+It must be a model of the concept `TriangulationTraits_3`
+
+\tparam Subdomain_index Type of indices for subdomains of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must match the label
+of the exterior of the domain (which contains at least the unbounded component).
+ It must match the `Subdomain_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
+
+\tparam Surface_patch_index Type of indices for surface patches (boundaries and interfaces)
+of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must be the index value
+assigned to a non surface facet.
+ It must match the `Surface_patch_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
+
+\tparam Curve_index Type of indices for curves (i.e. \f$ 1\f$-dimensional features)
+of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and
+`LessThanComparable`. The default constructed value must be the value for an edge which
+does not approximate a 1-dimensional feature of the geometric domain.
+ It must match the `Curve_index` types of the model
+  of the `MeshDomainWithFeatures_3` concept when used for mesh generation.
+
+\tparam  Corner_index Type of indices for corners (i.e.\f$ 0\f$--dimensional features)
+of the discretized geometric domain.
+It must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible` and
+`LessThanComparable`.
+ It must match the `Corner_index` of the model
+  of the `MeshDomainWithFeatures_3` concept when used for mesh generation.
+
+\tparam Vb is the vertex base class. It has to be a model
+of the concept `TriangulationVertexBase_3` and defaults to
+`Triangulation_vertex_base_3<Gt>`.
+
+\cgalModels `SimplicialMeshVertexBase_3`
+
+\sa `CGAL::Mesh_complex_3_in_triangulation_3`
+\sa \link Mesh_vertex_base_3 `CGAL::Mesh_vertex_base_3`\endlink
+\sa `MeshDomain_3`
+\sa `MeshDomainWithFeatures_3`
+*/
+template<class Gt,
+         typename Subdomain_index,
+         typename Surface_patch_index,
+         typename Curve_index,
+         typename Corner_index,
+         class Vb = Triangulation_vertex_base_3<Gt> >
+struct Simplicial_mesh_vertex_base_3
+{
+  using Triangulation_data_structure = internal::Dummy_tds_3;
+  using Vertex_handle = typename Triangulation_data_structure::Vertex_handle;
+  using Cell_handle = typename Triangulation_data_structure::Cell_handle;
+
+  template < class TDS3 >
+  struct Rebind_TDS {
+    using Vb3 = typename Vb::template Rebind_TDS<TDS3>::Other;
+    using Other = Simplicial_mesh_vertex_3 <Gt,
+      Subdomain_index,
+      Surface_patch_index,
+      Curve_index,
+      Corner_index,
+      Vb3>;
+  };
+};
+
+
+}  // end namespace CGAL
+
+
+
+#endif // CGAL_SIMPLICIAL_MESH_VERTEX_BASE_3_H
diff --git a/SMDS_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h b/SMDS_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h
new file mode 100644
index 00000000000..24db08154f6
--- /dev/null
+++ b/SMDS_3/include/CGAL/facets_in_complex_3_to_triangle_mesh.h
@@ -0,0 +1,239 @@
+// Copyright (c) 2009-2017 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)     : Maxime Gimeno,
+//                 Mael Rouxel-Labbé
+
+#ifndef CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
+#define CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/array.h>
+#include <CGAL/boost/graph/Euler_operations.h>
+#include <CGAL/Cartesian_converter.h>
+#include <CGAL/Kernel_traits.h>
+#include <CGAL/Polygon_mesh_processing/orient_polygon_soup.h>
+#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>
+#include <CGAL/Time_stamper.h>
+
+#include <boost/tuple/tuple.hpp>
+
+#include <algorithm>
+#include <cstddef>
+#include <iterator>
+#include <unordered_map>
+#include <vector>
+
+namespace CGAL {
+
+namespace SMDS_3 {
+
+namespace internal {
+
+template <class Polygon>
+void resize(Polygon& p, std::size_t size)
+{
+  p.resize(size);
+}
+
+template <std::size_t N, class INT>
+void resize(std::array<INT, N>&, std::size_t CGAL_assertion_code(size))
+{
+  CGAL_assertion(size == N);
+}
+
+template<class C3T3, class PointContainer, class FaceContainer, class PatchIndexContainer>
+void facets_in_complex_3_to_triangle_soup(const C3T3& c3t3,
+                                          const typename C3T3::Subdomain_index sd_index,
+                                          PointContainer& points,
+                                          FaceContainer& faces,
+                                          PatchIndexContainer& patches,
+                                          const bool normals_point_outside_of_the_subdomain = true,
+                                          const bool export_all_facets = false)
+{
+  typedef typename PointContainer::value_type                            Point_3;
+  typedef typename FaceContainer::value_type                             Face;
+
+  typedef typename C3T3::Triangulation                                   Tr;
+  typedef typename C3T3::Surface_patch_index                             Surface_patch_index;
+
+  typedef typename Tr::Cell_handle                                       Cell_handle;
+  typedef typename Tr::Weighted_point                                    Weighted_point;
+  typedef typename Tr::Facet                                             Facet;
+
+  typedef std::unordered_map<Point_3, std::size_t>                       PIM;
+
+  typedef typename C3T3::size_type                                       size_type;
+
+  // triangulation point to range point
+  CGAL::Cartesian_converter<typename CGAL::Kernel_traits<typename Tr::Geom_traits::Point_3>::type,
+                            typename CGAL::Kernel_traits<Point_3>::type> t2r;
+
+  size_type nf = c3t3.number_of_facets_in_complex();
+  faces.reserve(faces.size() + nf);
+  patches.reserve(faces.size() + nf);
+  points.reserve(points.size() + nf/2); // approximating Euler
+
+  PIM p_to_ids;
+  std::size_t inum = 0;
+
+  for(Facet fit : c3t3.facets_in_complex())
+  {
+    Cell_handle c = fit.first;
+    int s = fit.second;
+    const Surface_patch_index spi = c->surface_patch_index(s);
+    Face f;
+    resize(f, 3);
+
+    typename C3T3::Subdomain_index cell_sdi = c3t3.subdomain_index(c);
+    typename C3T3::Subdomain_index opp_sdi = c3t3.subdomain_index(c->neighbor(s));
+
+    if(!export_all_facets && cell_sdi != sd_index && opp_sdi != sd_index)
+      continue;
+
+    for(std::size_t i=1; i<4; ++i)
+    {
+      CGAL_assertion_code(typedef typename Tr::Vertex_handle Vertex_handle;)
+      CGAL_assertion_code(Vertex_handle v = c->vertex((s+i)&3);)
+      CGAL_assertion(v != Vertex_handle() && !c3t3.triangulation().is_infinite(v));
+
+      const Weighted_point& wp = c3t3.triangulation().point(c, (s+i)&3);
+      const Point_3& bp = t2r(c3t3.triangulation().geom_traits().construct_point_3_object()(wp));
+
+      auto insertion_res = p_to_ids.emplace(bp, inum);
+      if(insertion_res.second) // new point
+      {
+        points.push_back(bp);
+        ++inum;
+      }
+
+      f[i-1] = insertion_res.first->second;
+    }
+
+    if(export_all_facets)
+    {
+      if((cell_sdi > opp_sdi) == (s%2 == 1))
+        std::swap(f[0], f[1]);
+    }
+    else
+    {
+      if(((cell_sdi == sd_index) == (s%2 == 1)) == normals_point_outside_of_the_subdomain)
+        std::swap(f[0], f[1]);
+    }
+
+    faces.push_back(f);
+    patches.push_back(spi);
+  }
+}
+
+template<class C3T3, class PointContainer, class FaceContainer, class SurfacePatchContainer>
+void facets_in_complex_3_to_triangle_soup(const C3T3& c3t3,
+                                          PointContainer& points,
+                                          FaceContainer& faces,
+                                          SurfacePatchContainer& patches)
+{
+  typedef typename C3T3::Subdomain_index              Subdomain_index;
+  Subdomain_index useless = Subdomain_index();
+  facets_in_complex_3_to_triangle_soup(c3t3, useless, points, faces, patches,
+                                       true/*point outward*/, true /*extract all facets*/);
+}
+
+template <typename Index2FaceMap, typename SurfacePatchRange>
+void set_face_patches(const Index2FaceMap&,
+                      const SurfacePatchRange&,
+                      const internal_np::Param_not_found&)
+{
+  return;
+}
+
+template <typename Index2FaceMap,
+          typename SurfacePatchRange,
+          typename FacePatchMap>
+void set_face_patches(const Index2FaceMap& i2f,
+                      const SurfacePatchRange& patches,
+                      const FacePatchMap& fpmap)
+{
+  for (auto index_and_face : i2f)
+  {
+    put(fpmap, index_and_face.second, patches[index_and_face.first]);
+  }
+}
+
+} // end namespace internal
+
+} // end namespace SMDS_3
+
+  /**
+   * @ingroup PkgSMDS3Functions
+   *
+   * @brief builds a `TriangleMesh` from the surface facets, with a consistent orientation
+   *   at the interface of two subdomains.
+   *
+   * This function exports the surface as a `TriangleMesh` and appends it to `tmesh`, using
+   *   `orient_polygon_soup()`.
+   *
+   * @tparam C3T3 a model of `MeshComplexWithFeatures_3InTriangulation_3`.
+   * @tparam TriangleMesh a model of `MutableFaceGraph` with an internal point property map.
+   *    The point type must be compatible with the one used in `C3T3`.
+   * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   *
+   * @param c3t3 an instance of `C3T3`
+   * @param tmesh an instance of `TriangleMesh`
+   * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
+   *
+   * \cgalNamedParamsBegin
+   *   \cgalParamNBegin{face_patch_map}
+  *     \cgalParamDescription{a property map with the patch id's associated to the faces of `faces(tmesh)`}
+  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%face_descriptor`
+  *                    as key type and the desired property, model of `CopyConstructible`
+  *                    and `LessThanComparable`,
+  *                    and compatible with the `Surface_patch_index` type of `C3T3` as value type.}
+  *     \cgalParamDefault{If not provided, faces patch ids are ignored.}
+  *   \cgalParamNEnd
+  * \cgalNamedParamsEnd
+  */
+  template<class C3T3, class TriangleMesh, typename NamedParameters = parameters::Default_named_parameters>
+  void facets_in_complex_3_to_triangle_mesh(const C3T3& c3t3,
+    TriangleMesh& tmesh,
+    const NamedParameters& np = parameters::default_values())
+  {
+    namespace PMP = CGAL::Polygon_mesh_processing;
+
+    typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type  VertexPointMap;
+    typedef typename boost::property_traits<VertexPointMap>::value_type              Point_3;
+    typedef typename boost::graph_traits<TriangleMesh>::face_descriptor              face_descriptor;
+    typedef typename C3T3::Surface_patch_index                                       Surface_patch_index;
+
+    typedef std::array<std::size_t, 3>                                       Face;
+
+    std::vector<Face> faces;
+    std::vector<Surface_patch_index> patches;
+    std::vector<Point_3> points;
+
+    SMDS_3::internal::facets_in_complex_3_to_triangle_soup(c3t3, points, faces, patches);
+
+    if (!PMP::is_polygon_soup_a_polygon_mesh(faces))
+      PMP::orient_polygon_soup(points, faces);
+    CGAL_postcondition(PMP::is_polygon_soup_a_polygon_mesh(faces));
+
+    std::unordered_map<std::size_t, face_descriptor> i2f;
+    PMP::polygon_soup_to_polygon_mesh(points, faces, tmesh,
+      CGAL::parameters::polygon_to_face_output_iterator(std::inserter(i2f, i2f.end())));
+
+    using parameters::get_parameter;
+    SMDS_3::internal::set_face_patches(i2f,
+                                      patches,
+                                      get_parameter(np, internal_np::face_patch));
+  }
+
+} // namespace CGAL
+
+#endif // CGAL_FACETS_IN_COMPLEX_3_TO_TRIANGLE_MESH_H
diff --git a/SMDS_3/include/CGAL/tetrahedron_soup_to_triangulation_3.h b/SMDS_3/include/CGAL/tetrahedron_soup_to_triangulation_3.h
new file mode 100644
index 00000000000..5d481acd01e
--- /dev/null
+++ b/SMDS_3/include/CGAL/tetrahedron_soup_to_triangulation_3.h
@@ -0,0 +1,221 @@
+// Copyright (c) 2009-2014 INRIA Sophia-Antipolis (France).
+// Copyright (c) 2010-2013 GeometryFactory Sarl (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, Maxime Gimeno, Jane Tournois
+//
+//******************************************************************************
+// File Description :
+//******************************************************************************
+
+#ifndef CGAL_SMDS_3_TETRAHEDRON_SOUP_TO_C3T3_H
+#define CGAL_SMDS_3_TETRAHEDRON_SOUP_TO_C3T3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/internal/SMDS_3_helper.h>
+#include <CGAL/Named_function_parameters.h>
+#include <CGAL/boost/graph/named_params_helper.h>
+
+#include <vector>
+#include <array>
+#include <boost/unordered_map.hpp>
+
+namespace CGAL {
+
+  /** \ingroup PkgSMDS3Functions
+  * builds a 3D triangulation from a soup of tetrahedra.
+  *
+  * @tparam TetrahedronRange a model of `Range` whose value type is
+  * a `Tetrahedron_3`. The point type of the tetrahedra must be convertible
+  * to `Triangulation::Point`
+  * @tparam Triangulation a 3D triangulation class that has
+  * a vertex base model of `SimplicialMeshVertexBase_3`
+  * and a cell base model of `SimplicialMeshCellBase_3`
+  *
+  * @param tets the set of finite tetrahedra of a valid CGAL triangulation.
+  * Each element in the range is the geometric description of the
+  * corresponding cell in the triangulation.
+  *
+  * @returns the 3D triangulation built from \p tets
+  *
+  * @post the output triangulation must be a triangulation of the convex hull of `tets`
+  *
+  * @sa @ref SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
+  *
+  */
+  template<typename Triangulation, typename TetrahedronRange>
+  Triangulation tetrahedron_soup_to_triangulation_3(const TetrahedronRange& tets)
+  {
+    using Tr    = Triangulation;
+    using Point = typename Tr::Point;
+
+    Triangulation tr;
+    std::vector<Point> points;
+    std::vector<std::array<int, 4> > finite_cells;
+    boost::unordered_map<std::array<int, 3>, typename Tr::Cell::Surface_patch_index> border_facets;
+    boost::unordered_map<Point, int> p2i;
+
+    CGAL_assertion_code(
+      typename Triangulation::Geom_traits::Orientation_3 orientation =
+      tr.geom_traits().orientation_3_object();
+    );
+
+    for (typename TetrahedronRange::value_type tet : tets)
+    {
+      CGAL_assertion(tet.orientation() == CGAL::POSITIVE);
+      std::array<int, 4> cell;
+
+      for (int i = 0; i < 4; ++i)
+      {
+        const Point& pi = tet[i];
+        if (p2i.find(pi) == p2i.end())
+        {
+          points.push_back(pi);
+          int index = static_cast<int>(points.size() - 1);
+          p2i.insert(std::make_pair(pi, index));
+          cell[i] = index;
+        }
+        else
+          cell[i] = p2i.at(pi);
+      }
+
+      CGAL_assertion(orientation(points[cell[0]],
+        points[cell[1]], points[cell[2]], points[cell[3]]) == CGAL::POSITIVE);
+
+      finite_cells.push_back(cell);
+    }
+
+    typename Tr::Cell::Subdomain_index default_si(1);
+    CGAL::SMDS_3::build_triangulation_one_subdomain(tr, points, finite_cells, default_si, border_facets,
+      /*verbose = */false, /*replace_domain_0 = */false, /*allow_non_manifold =*/false);
+
+    CGAL_assertion(CGAL::SMDS_3::internal::is_convex(tr));
+
+    return tr;
+  }
+
+  /** \ingroup PkgSMDS3Functions
+  * builds a 3D triangulation from a soup of tetrahedra.
+  *
+  * @tparam PointRange a model of the concept `RandomAccessContainer`
+  * whose value type is the point type.
+  * The point type must be convertible to `Triangulation::Point`.
+  * @tparam TetrahedronRange a model of the concept `RandomAccessContainer` whose
+  * value type is a model of the concept `RandomAccessContainer` whose value type is `std::size_t`
+  * @tparam Triangulation a 3D triangulation class that has
+  * a vertex base model of `MeshVertexBase_3`
+  * and a cell base model of `MeshCellBase_3`
+  * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+  *
+  * @param points points of the soup of tetrahedra
+  * @param tets the set of finite tetrahedra of a valid CGAL triangulation.
+  * Each element in the range describes a tetrahedron using the indices of the points
+  * in `points`.
+  * It must
+  * describe a non self-intersecting set of tetrahedra, that cover the convex hull of the
+  * corresponding point set. The tetrahedra must form a valid triangulation with each
+  * pair of neighboring cells sharing exactly one triangle. Combinatorial validity and
+  * validity of the geometric embedding are required.
+  *
+  * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
+  *
+  * \cgalNamedParamsBegin
+  *   \cgalParamNBegin{surface_facets}
+  *     \cgalParamDescription{each element in the range describes a surface facet using the indices of points
+  *       in `points` (indices 0 to 2), and the associated `Surface_patch_index` (index 3)}
+  *     \cgalParamType{a class model of `AssociativeContainer`
+  *                    whose key type is model of `RandomAccessContainer` containing `int`
+  *                    and mapped type is `Tr::Cell::Surface_patch_index`}
+  *     \cgalParamDefault{an empty `boost::unordered_map<std::array<int, 3>, typename Tr::Cell::Surface_patch_index>`}
+  *     \cgalParamExtra{to avoid copies of large data sets, this parameter can be passed using `std::cref`}
+  *   \cgalParamNEnd
+  *   \cgalParamNBegin{subdomain_indices}
+  *     \cgalParamDescription{each element in the range gives the
+  *       `Triangulation::Cell::Subdomain_index` corresponding to the tetrahedron (cell)
+  *        of same index in `tets`}
+  *     \cgalParamType{a class model of `RandomAccessContainer` whose value type
+  *                    is `Triangulation::Cell::Subdomain_index`}
+  *     \cgalParamDefault{each finite cell of the output triangulation is
+  *                    set to have `1` as `Subdomain_index`}
+  *     \cgalParamExtra{to avoid copies of large data sets, this parameter can be passed using `std::cref`}
+  *   \cgalParamNEnd
+  *\cond SKIP_IN_MANUAL
+  *   \cgalParamNBegin{allow_non_manifold}
+  *     \cgalParamDescription{allows the construction of a triangulation with non-manifold edges
+  *       and non manifold vertices. The triangulation is invalid if this situation is met,
+  *       so it should be used only in advanced cases, and the triangulation will be hardly usable.}
+  *     \cgalParamType{bool}
+  *     \cgalParamDefault{false}
+  *   \cgalParamNEnd
+  *\endcond
+  * \cgalNamedParamsEnd
+  *
+  * @returns the 3D triangulation built from parameters
+  *
+  * @pre `points` contains each point only once
+  * @post the output triangulation must be a triangulation of the convex hull of `points`
+  * @post `is_valid()` returns `true` for the returned triangulation
+  *
+  * @sa \link polygon_soup_to_polygon_mesh() `CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh()` \endlink
+  * @sa @ref SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
+  *
+  */
+  template<typename Triangulation,
+           typename PointRange,
+           typename TetrahedronRange,
+           typename NamedParameters = parameters::Default_named_parameters>
+  Triangulation tetrahedron_soup_to_triangulation_3(const PointRange& points,
+                                                    const TetrahedronRange& tets,
+                                                    const NamedParameters& np = parameters::default_values())
+  {
+    using parameters::choose_parameter;
+    using parameters::get_parameter;
+    using parameters::get_parameter_reference;
+
+    using Default_facet_map
+      = boost::unordered_map<std::array<int, 3>,
+                             typename Triangulation::Cell::Surface_patch_index>;
+    using Facet_map_ref_type
+      = typename internal_np::Lookup_named_param_def<
+                             internal_np::surface_facets_t,
+                             NamedParameters,
+                             Default_facet_map>::reference;
+    using Subdomains_ref_type
+      = typename internal_np::Lookup_named_param_def<
+                              internal_np::subdomain_indices_t,
+                              NamedParameters,
+                              int>::reference;
+
+    Triangulation tr;
+    Default_facet_map empty_map;
+    const Facet_map_ref_type& facets = choose_parameter(
+          get_parameter_reference(np, internal_np::surface_facets),
+          empty_map);
+    const Subdomains_ref_type& subdomains = choose_parameter(
+          get_parameter_reference(np, internal_np::subdomain_indices),
+          1);
+    const bool non_manifold = choose_parameter(
+          get_parameter(np, internal_np::allow_non_manifold),
+          false);
+
+    CGAL::SMDS_3::build_triangulation_with_subdomains_range(tr, points, tets, subdomains, facets,
+      /*verbose = */false, /*replace_domain_0 = */false, non_manifold);
+
+    CGAL_assertion(CGAL::SMDS_3::internal::is_convex(tr));
+
+    return tr;
+  }
+
+} //namespace CGAL
+
+
+#endif // CGAL_SMDS_3_TETRAHEDRON_SOUP_TO_C3T3_H
diff --git a/SMDS_3/package_info/SMDS_3/copyright b/SMDS_3/package_info/SMDS_3/copyright
new file mode 100644
index 00000000000..8932b3233d2
--- /dev/null
+++ b/SMDS_3/package_info/SMDS_3/copyright
@@ -0,0 +1,2 @@
+INRIA Sophia-Antipolis (France)
+
diff --git a/SMDS_3/package_info/SMDS_3/dependencies b/SMDS_3/package_info/SMDS_3/dependencies
new file mode 100644
index 00000000000..41ea78306d3
--- /dev/null
+++ b/SMDS_3/package_info/SMDS_3/dependencies
@@ -0,0 +1,29 @@
+Algebraic_foundations
+Arithmetic_kernel
+BGL
+Cartesian_kernel
+Circulator
+Distance_2
+Distance_3
+Filtered_kernel
+Hash_map
+Homogeneous_kernel
+Installation
+Intersections_2
+Intersections_3
+Interval_support
+Kernel_23
+Kernel_d
+Modular_arithmetic
+Number_types
+Polygon_mesh_processing
+Profiling_tools
+Property_map
+Random_numbers
+STL_Extension
+Spatial_sorting
+Stream_support
+SMDS_3
+TDS_3
+Triangulation_3
+Union_find
diff --git a/SMDS_3/package_info/SMDS_3/description.txt b/SMDS_3/package_info/SMDS_3/description.txt
new file mode 100644
index 00000000000..75585704c22
--- /dev/null
+++ b/SMDS_3/package_info/SMDS_3/description.txt
@@ -0,0 +1,2 @@
+Package SMDS_3 :
+Simplicial Mesh Data Structures
\ No newline at end of file
diff --git a/SMDS_3/package_info/SMDS_3/license.txt b/SMDS_3/package_info/SMDS_3/license.txt
new file mode 100644
index 00000000000..8bb8efcb72b
--- /dev/null
+++ b/SMDS_3/package_info/SMDS_3/license.txt
@@ -0,0 +1 @@
+GPL (v3 or later)
diff --git a/SMDS_3/package_info/SMDS_3/maintainer b/SMDS_3/package_info/SMDS_3/maintainer
new file mode 100644
index 00000000000..880cb264269
--- /dev/null
+++ b/SMDS_3/package_info/SMDS_3/maintainer
@@ -0,0 +1,2 @@
+Laurent Rineau <laurent.rineau@cgal.org>
+Jane Tournois <jane.tournois@geometryfactory.com>
diff --git a/SMDS_3/test/SMDS_3/CMakeLists.txt b/SMDS_3/test/SMDS_3/CMakeLists.txt
new file mode 100644
index 00000000000..43cea5fc098
--- /dev/null
+++ b/SMDS_3/test/SMDS_3/CMakeLists.txt
@@ -0,0 +1,30 @@
+# Created by the script cgal_create_cmake_script
+# This is the CMake script for compiling a CGAL application.
+
+cmake_minimum_required(VERSION 3.1...3.20)
+project( SMDS_3_Tests )
+
+find_package(CGAL REQUIRED)
+
+# Use Eigen
+find_package(Eigen3 3.1.0 REQUIRED) #(requires 3.1.0 or greater)
+include(CGAL_Eigen3_support)
+
+create_single_source_cgal_program( "test_c3t3.cpp" )
+create_single_source_cgal_program( "test_c3t3_io.cpp" )
+create_single_source_cgal_program( "test_c3t3_with_features.cpp" )
+create_single_source_cgal_program( "test_c3t3_into_facegraph.cpp" )
+create_single_source_cgal_program( "test_c3t3_extract_subdomains_boundaries.cpp" )
+create_single_source_cgal_program( "test_c3t3_io_MEDIT.cpp" )
+create_single_source_cgal_program( "test_simplicial_cb_vb.cpp")
+
+foreach(target
+    test_c3t3
+    test_c3t3_io
+    test_c3t3_with_features
+    test_c3t3_into_facegraph
+    test_c3t3_extract_subdomains_boundaries)
+  if(TARGET ${target})
+    target_link_libraries(${target} PUBLIC CGAL::Eigen3_support)
+  endif()
+endforeach()
diff --git a/Mesh_3/test/Mesh_3/data/c3t3_io-hetero.binary.cgal b/SMDS_3/test/SMDS_3/data/c3t3_io-hetero.binary.cgal
similarity index 100%
rename from Mesh_3/test/Mesh_3/data/c3t3_io-hetero.binary.cgal
rename to SMDS_3/test/SMDS_3/data/c3t3_io-hetero.binary.cgal
diff --git a/Mesh_3/test/Mesh_3/data/c3t3_io-hetero.cgal b/SMDS_3/test/SMDS_3/data/c3t3_io-hetero.cgal
similarity index 100%
rename from Mesh_3/test/Mesh_3/data/c3t3_io-hetero.cgal
rename to SMDS_3/test/SMDS_3/data/c3t3_io-hetero.cgal
diff --git a/Mesh_3/test/Mesh_3/data/c3t3_io-homo.binary.cgal b/SMDS_3/test/SMDS_3/data/c3t3_io-homo.binary.cgal
similarity index 100%
rename from Mesh_3/test/Mesh_3/data/c3t3_io-homo.binary.cgal
rename to SMDS_3/test/SMDS_3/data/c3t3_io-homo.binary.cgal
diff --git a/Mesh_3/test/Mesh_3/data/c3t3_io-homo.cgal b/SMDS_3/test/SMDS_3/data/c3t3_io-homo.cgal
similarity index 100%
rename from Mesh_3/test/Mesh_3/data/c3t3_io-homo.cgal
rename to SMDS_3/test/SMDS_3/data/c3t3_io-homo.cgal
diff --git a/Mesh_3/test/Mesh_3/test_c3t3.cpp b/SMDS_3/test/SMDS_3/test_c3t3.cpp
similarity index 98%
rename from Mesh_3/test/Mesh_3/test_c3t3.cpp
rename to SMDS_3/test/SMDS_3/test_c3t3.cpp
index ffbc80d090a..78835c78fda 100644
--- a/Mesh_3/test/Mesh_3/test_c3t3.cpp
+++ b/SMDS_3/test/SMDS_3/test_c3t3.cpp
@@ -37,10 +37,6 @@ struct Tester
 
   typedef typename CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
   typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
-  typedef CGAL::Mesh_3::Mesh_complex_3_in_triangulation_3_base<Tr,
-    CGAL::Sequential_tag> C3t3_base_sequential;
-  typedef CGAL::Mesh_3::Mesh_complex_3_in_triangulation_3_base<Tr,
-    CGAL::Parallel_tag> C3t3_base_parallel;
 
   typedef typename Tr::Bare_point Bare_point;
   typedef typename Tr::Weighted_point Weighted_point;
@@ -254,7 +250,7 @@ struct Tester
     //-------------------------------------------------------
     std::cout << "Insert 6 points from domain in c3t3_bis, add 1 cell to c3t3_bis\n";
     Polyhedron polyhedron;
-    std::ifstream input("data/sphere.off");
+    std::ifstream input(CGAL::data_file_path("meshes/sphere.off"));
     input >> polyhedron;
     input.close();
     Mesh_domain domain(polyhedron);
@@ -393,7 +389,8 @@ struct Tester
     assert ( c3t3.surface_patch_index(*patch_fit_bis) == surface_patch_index_bis );
 
     std::ofstream out_medit("test-medit.mesh");
-    CGAL::IO::output_to_medit(out_medit, c3t3);
+    CGAL::IO::write_MEDIT(out_medit, c3t3);
+    out_medit.close();
     CGAL::IO::output_to_tetgen("test-tetgen", c3t3);
   }
 };
diff --git a/Mesh_3/test/Mesh_3/test_c3t3_extract_subdomains_boundaries.cpp b/SMDS_3/test/SMDS_3/test_c3t3_extract_subdomains_boundaries.cpp
similarity index 100%
rename from Mesh_3/test/Mesh_3/test_c3t3_extract_subdomains_boundaries.cpp
rename to SMDS_3/test/SMDS_3/test_c3t3_extract_subdomains_boundaries.cpp
diff --git a/Mesh_3/test/Mesh_3/test_c3t3_into_facegraph.cpp b/SMDS_3/test/SMDS_3/test_c3t3_into_facegraph.cpp
similarity index 80%
rename from Mesh_3/test/Mesh_3/test_c3t3_into_facegraph.cpp
rename to SMDS_3/test/SMDS_3/test_c3t3_into_facegraph.cpp
index 05ea8149ca6..b31fbe22f0a 100644
--- a/Mesh_3/test/Mesh_3/test_c3t3_into_facegraph.cpp
+++ b/SMDS_3/test/SMDS_3/test_c3t3_into_facegraph.cpp
@@ -4,7 +4,7 @@
 
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 #include <CGAL/Mesh_3/Robust_intersection_traits_3.h>
 #include <CGAL/Polyhedral_mesh_domain_with_features_3.h>
 
@@ -33,25 +33,23 @@ int main (int argc, char** argv){
                                      Cell_base_with_info>::type               Tr;
 
   typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
-
+  typedef C3t3::Triangulation::Cell_handle            Cell_handle;
 
   // Open file
-  std::ifstream in (argc > 1 ? argv[1] : "data/elephant.mesh",
+  std::ifstream in (argc > 1 ? argv[1] : CGAL::data_file_path("meshes/elephant.mesh"),
                     std::ios_base::in);
   if(!in) {
     std::cerr << "Error! Cannot open file " << argv[1] << std::endl;
     return 1;
   }
   C3t3 c3t3;
-  if(CGAL::build_triangulation_from_file<C3t3::Triangulation, true>(in, c3t3.triangulation()))
+  if(CGAL::SMDS_3::build_triangulation_from_file(in, c3t3.triangulation()))
   {
-    for( C3t3::Triangulation::Finite_cells_iterator
-         cit = c3t3.triangulation().finite_cells_begin();
-         cit != c3t3.triangulation().finite_cells_end();
-         ++cit)
+    for( Cell_handle cit : c3t3.triangulation().finite_cell_handles())
     {
       assert(cit->subdomain_index() >= 0);
-      c3t3.add_to_complex(cit, cit->subdomain_index());
+      if(cit->subdomain_index() > 0)
+        c3t3.add_to_complex(cit, cit->subdomain_index());
       for(int i=0; i < 4; ++i)
       {
         if(cit->surface_patch_index(i)>0)
@@ -64,10 +62,7 @@ int main (int argc, char** argv){
     //if there is no facet in the complex, we add the border facets.
     if(c3t3.number_of_facets_in_complex() == 0)
     {
-      for( C3t3::Triangulation::All_cells_iterator
-           cit = c3t3.triangulation().all_cells_begin();
-           cit != c3t3.triangulation().all_cells_end();
-           ++cit)
+      for( Cell_handle cit : c3t3.triangulation().all_cell_handles())
       {
         if(c3t3.triangulation().is_infinite(cit))
         {
@@ -89,6 +84,7 @@ int main (int argc, char** argv){
 
   std::ofstream out("graph.off");
   out << poly;
+  out.close();
 
   assert(is_valid(poly));
   return EXIT_SUCCESS;
diff --git a/Mesh_3/test/Mesh_3/test_c3t3_io.cpp b/SMDS_3/test/SMDS_3/test_c3t3_io.cpp
similarity index 99%
rename from Mesh_3/test/Mesh_3/test_c3t3_io.cpp
rename to SMDS_3/test/SMDS_3/test_c3t3_io.cpp
index a937d691868..ef8d9e16d7a 100644
--- a/Mesh_3/test/Mesh_3/test_c3t3_io.cpp
+++ b/SMDS_3/test/SMDS_3/test_c3t3_io.cpp
@@ -1,5 +1,5 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Mesh_3/io_signature.h>
+#include <CGAL/SMDS_3/io_signature.h>
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/IO/File_binary_mesh_3.h>
diff --git a/SMDS_3/test/SMDS_3/test_c3t3_io_MEDIT.cpp b/SMDS_3/test/SMDS_3/test_c3t3_io_MEDIT.cpp
new file mode 100644
index 00000000000..cb905e69edc
--- /dev/null
+++ b/SMDS_3/test/SMDS_3/test_c3t3_io_MEDIT.cpp
@@ -0,0 +1,54 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h>
+#include <CGAL/IO/File_medit.h>
+#include <CGAL/Iso_cuboid_3.h>
+
+#include <CGAL/tags.h>
+
+#include <string>
+#include <iostream>
+#include <fstream>
+
+int main()
+{
+  using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+  using Tr = CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3<K>;
+
+  // Open file elephant
+  std::string filename = CGAL::data_file_path("meshes/elephant.mesh");
+  std::ifstream in(filename, std::ios_base::in);
+  if(!in) {
+    std::cerr << "Error! Cannot open file " << filename << std::endl;
+    return 1;
+  }
+  Tr tr;
+  CGAL::IO::read_MEDIT(in, tr);
+  assert(tr.is_valid());
+
+  std::ofstream os("elephant_out.mesh");
+  CGAL::IO::write_MEDIT(os, tr,
+    CGAL::parameters::all_vertices(false).all_cells(true));
+  os.close();
+
+  CGAL::Bbox_3 bb(tr.finite_vertices_begin()->point().bbox());
+  for (auto v : tr.finite_vertex_handles())
+    bb = bb + v->point().bbox();
+
+  CGAL::Iso_cuboid_3<K> isocuboid(bb);
+  for (int i = 0; i < 8; ++i)
+    tr.insert(isocuboid.vertex(i));
+
+  std::ofstream os2("elephant_out_not_all_vertices.mesh");
+  CGAL::IO::write_MEDIT(os2, tr,
+    CGAL::parameters::all_vertices(false));
+  os2.close();
+
+  Tr tr2;
+  std::ifstream is2("elephant_out_not_all_vertices.mesh");
+  CGAL::IO::read_MEDIT(is2, tr2);;
+  is2.close();
+  assert(tr2.is_valid());
+
+  return EXIT_SUCCESS;
+}
diff --git a/Mesh_3/test/Mesh_3/test_c3t3_with_features.cpp b/SMDS_3/test/SMDS_3/test_c3t3_with_features.cpp
similarity index 99%
rename from Mesh_3/test/Mesh_3/test_c3t3_with_features.cpp
rename to SMDS_3/test/SMDS_3/test_c3t3_with_features.cpp
index 6280238c60b..737bfcacb33 100644
--- a/Mesh_3/test/Mesh_3/test_c3t3_with_features.cpp
+++ b/SMDS_3/test/SMDS_3/test_c3t3_with_features.cpp
@@ -18,6 +18,8 @@
 
 #include "test_utilities.h"
 
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+#include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Labeled_mesh_domain_3.h>
 #include <CGAL/Mesh_domain_with_polyline_features_3.h>
 
diff --git a/SMDS_3/test/SMDS_3/test_simplicial_cb_vb.cpp b/SMDS_3/test/SMDS_3/test_simplicial_cb_vb.cpp
new file mode 100644
index 00000000000..4f3531c5fcb
--- /dev/null
+++ b/SMDS_3/test/SMDS_3/test_simplicial_cb_vb.cpp
@@ -0,0 +1,45 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Triangulation_3.h>
+#include <CGAL/Triangulation_data_structure_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/point_generators_3.h>
+
+#include <CGAL/tags.h>
+#include <utility>
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+
+using Subdomain_index = int;
+using Surface_patch_index = std::pair<int, int>;
+using Curve_index = char;
+using Corner_index = short;
+
+using Cb = CGAL::Simplicial_mesh_cell_base_3<Subdomain_index, Surface_patch_index>;
+using Vb = CGAL::Simplicial_mesh_vertex_base_3<K, Subdomain_index, Surface_patch_index,
+                                                  Curve_index, Corner_index>;
+
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb, CGAL::Sequential_tag>;
+using Tr = CGAL::Triangulation_3<K, Tds>;
+
+using C3t3 = CGAL::Mesh_complex_3_in_triangulation_3<Tr>;
+
+int main ()
+{
+  Tr triangulation;
+  auto rng = CGAL::Random_points_on_sphere_3<K::Point_3>(1.);
+  while (triangulation.number_of_vertices() < 100)
+  {
+    triangulation.insert(*rng++);
+  }
+
+  C3t3 c3t3;
+  c3t3.triangulation() = std::move(triangulation);
+
+
+  return EXIT_SUCCESS;
+}
diff --git a/SMDS_3/test/SMDS_3/test_utilities.h b/SMDS_3/test/SMDS_3/test_utilities.h
new file mode 100644
index 00000000000..16797ae26bc
--- /dev/null
+++ b/SMDS_3/test/SMDS_3/test_utilities.h
@@ -0,0 +1,51 @@
+// Copyright (c) 2009 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)     : Stephane Tayeb
+//
+//******************************************************************************
+// File Description :
+//
+//******************************************************************************
+
+#ifndef CGAL_MESH_3_TEST_TEST_UTILITIES_H
+#define CGAL_MESH_3_TEST_TEST_UTILITIES_H
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <CGAL/Mesh_triangulation_3.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+
+#include <CGAL/disable_warnings.h>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K_e_i;
+typedef CGAL::Exact_predicates_exact_constructions_kernel K_e_e;
+
+namespace CGAL {
+namespace details {
+
+template<>
+struct Mesh_geom_traits_generator<K_e_e>
+{
+private:
+  typedef K_e_e Geom_traits;
+
+public:
+  typedef Geom_traits type;
+  typedef type Type;
+};  // end struct Mesh_geom_traits_generator<...>
+
+} // end namespace details
+} // end namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif // CGAL_MESH_3_TEST_TEST_UTILITIES_H
diff --git a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
index cfc54c6631c..184bb2ce429 100644
--- a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
+++ b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
@@ -32,6 +32,8 @@ CGAL_add_named_parameter(face_partition_id_t, face_partition_id, face_partition_
 CGAL_add_named_parameter(vertex_to_vertex_output_iterator_t, vertex_to_vertex_output_iterator, vertex_to_vertex_output_iterator)
 CGAL_add_named_parameter(halfedge_to_halfedge_output_iterator_t, halfedge_to_halfedge_output_iterator, halfedge_to_halfedge_output_iterator)
 CGAL_add_named_parameter(face_to_face_output_iterator_t, face_to_face_output_iterator, face_to_face_output_iterator)
+CGAL_add_named_parameter(point_to_vertex_output_iterator_t, point_to_vertex_output_iterator, point_to_vertex_output_iterator)
+CGAL_add_named_parameter(polygon_to_face_output_iterator_t, polygon_to_face_output_iterator, polygon_to_face_output_iterator)
 
 CGAL_add_named_parameter(vertex_to_vertex_map_t, vertex_to_vertex_map, vertex_to_vertex_map)
 CGAL_add_named_parameter(halfedge_to_halfedge_map_t, halfedge_to_halfedge_map, halfedge_to_halfedge_map)
@@ -214,6 +216,15 @@ CGAL_add_named_parameter(smooth_constrained_edges_t, smooth_constrained_edges, s
 CGAL_add_named_parameter(do_enforce_manifoldness_t, do_enforce_manifoldness, do_enforce_manifoldness)
 CGAL_add_named_parameter(seed_points_t, seed_points, seed_points)
 
+// SMDS_3 parameters
+CGAL_add_named_parameter(surface_facets_t, surface_facets, surface_facets)
+CGAL_add_named_parameter(subdomain_indices_t, subdomain_indices, subdomain_indices)
+CGAL_add_named_parameter(all_vertices_t, all_vertices, all_vertices)
+CGAL_add_named_parameter(all_cells_t, all_cells, all_cells)
+CGAL_add_named_parameter(rebind_labels_t, rebind_labels, rebind_labels)
+CGAL_add_named_parameter(show_patches_t, show_patches, show_patches)
+CGAL_add_named_parameter(allow_non_manifold_t, allow_non_manifold, allow_non_manifold)
+
 // output parameters
 CGAL_add_named_parameter(face_proxy_map_t, face_proxy_map, face_proxy_map)
 CGAL_add_named_parameter(proxies_t, proxies, proxies)
diff --git a/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt b/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt
index 2bc5e41c1a6..4834a83616b 100644
--- a/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt
+++ b/Stream_support/doc/Stream_support/File_formats/Supported_file_formats.txt
@@ -432,8 +432,10 @@ A precise specification of the format is available <a href="http://gun.teipir.gr
 
 The VTK libraries use different file formats to handle data structures, but we only support two:
 - The `VTU` format can be used to store a collection of 3D cells, like tetrahedra,
-  but also points, triangles, lines, etc. In the <a href="https://vtk.org/"> VTK Libraries</a>,
-  it is the format reserved to store `Unstructured Grids`, and in \cgal,
+  but also points, triangles, lines, etc. In the <a href="https://vtk.org/"> VTK Libraries</a>.
+  It is the format reserved to store
+  <a href="https://kitware.github.io/vtk-examples/site/VTKFileFormats/#unstructuredgrid">`Unstructured Grids`</a>,
+  and in \cgal,
   we use it to store triangulations (2D and 3D).
 
 - The `VTP` format can be used to store collections of points, lines, and triangles.
@@ -473,8 +475,8 @@ A precise specification of those formats is available at
 
 The following \cgal data structures can be exported into the `.VTU` file format:
 
-- `CGAL::Mesh_complex_3_in_triangulation_3`, using \link PkgMesh3IOFunctions `CGAL::IO::output_to_vtu()` \endlink
-- `CGAL::Constrained_Delaunay_triangulation_2`, using the function \link PkgMesh2IO `CGAL::IO::write_VTU()` \endlink
+- `CGAL::Mesh_complex_3_in_triangulation_3`, using \link CGAL::IO::output_to_vtu() `CGAL::IO::output_to_vtu()` \endlink
+- `CGAL::Constrained_Delaunay_triangulation_2`, using the function \link CGAL::IO::write_VTU `CGAL::IO::write_VTU()` \endlink
 
 
 \section IOStreamAvizo Avizo File Format
@@ -483,7 +485,7 @@ The AmiraMesh format, using file extension `.am`, is used
 by the <a href="https://www.fei.com/software/avizo3d">Avizo</a> software to read 3D geometry.
 
 A single \cgal data structure, `CGAL::Mesh_complex_3_in_triangulation_3`, can be exported into `.am` files.
-This can be done using the function `CGAL::IO::output_to_avizo()`.
+This can be done using the function \link CGAL::IO::output_to_avizo() `CGAL::IO::output_to_avizo()`\endlink.
 
 A precise specification of the format is available
 <a href="https://assets.thermofisher.com/TFS-Assets/MSD/Product-Guides/users-guide-avizo-software-2019.pdf">in this guide</a>.
@@ -497,7 +499,7 @@ A precise specification of the format is available <a href="https://hal.inria.fr
 in the appendices (section 7.2.1, page 36).
 
 Only the `CGAL::Mesh_complex_3_in_triangulation_3` \cgal data structure can be exported into `.mesh`
-This can be done using the function `CGAL::IO::output_to_medit()`.
+This can be done using the function \link CGAL::IO::write_MEDIT `CGAL::IO::write_MEDIT()`\endlink.
 
 
 \section IOStreamTetgen Tetgen File Format
@@ -507,7 +509,7 @@ A precise specification of the format is available at <a href="https://wias-berl
 
 Only the `CGAL::Mesh_complex_3_in_triangulation_3` \cgal data structure can be exported into
 some of the Tetgen file formats, namely `.node`, `.ele` and `.face`.
-This can be done using the function `CGAL::IO::output_to_tetgen()`.
+This can be done using the function \link CGAL::IO::output_to_tetgen `CGAL::IO::output_to_tetgen()`\endlink.
 
 
 \section IOStreamWKT Well-Known Text (WKT) File Format
diff --git a/Stream_support/doc/Stream_support/dependencies b/Stream_support/doc/Stream_support/dependencies
index 50dc362f947..db5367a453b 100644
--- a/Stream_support/doc/Stream_support/dependencies
+++ b/Stream_support/doc/Stream_support/dependencies
@@ -14,5 +14,6 @@ Point_set_processing_3
 STL_Extension
 Surface_mesh
 Surface_mesher
+SMDS_3
 Triangulation
 Triangulation_2
diff --git a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingCellBase_3.h b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingCellBase_3.h
index 6a55d55b842..81ee216aa7f 100644
--- a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingCellBase_3.h
+++ b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingCellBase_3.h
@@ -2,12 +2,35 @@
 \ingroup PkgTetrahedralRemeshingConcepts
 \cgalConcept
 
-\cgalRefines MeshCellBase_3
+\cgalRefines SimplicialMeshCellBase_3
 
 Cell base concept to be used in the triangulation type given to the function `CGAL::tetrahedral_isotropic_remeshing()`.
 
-\cgalHasModel `CGAL::Tetrahedral_remeshing::Remeshing_cell_base_3`.
+\cgalHasModel `CGAL::Tetrahedral_remeshing::Remeshing_cell_base_3`
 
 */
 class RemeshingCellBase_3
-{};
+{
+  /*!
+  These functions are used internally by tetrahedral remeshing.
+  The class should provide storage, accessors and modificators for a cache value for sliverity.*/
+  /// @{
+
+  /*!
+  */
+  void set_sliver_value(double value);
+
+  /*!
+  */
+  double sliver_value() const;
+
+  /*!
+  */
+  bool is_cache_valid() const;
+
+  /*!
+  */
+  void reset_cache_validity() const;
+
+  /// @}
+};
diff --git a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingVertexBase_3.h b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingVertexBase_3.h
index fa524edef74..21fa97e1ed6 100644
--- a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingVertexBase_3.h
+++ b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Concepts/RemeshingVertexBase_3.h
@@ -2,11 +2,11 @@
 \ingroup PkgTetrahedralRemeshingConcepts
 \cgalConcept
 
-\cgalRefines MeshVertexBase_3
+\cgalRefines SimplicialMeshVertexBase_3
 
 Vertex base concept to be used in the triangulation type given to the function `CGAL::tetrahedral_isotropic_remeshing()`.
 
-\cgalHasModel `CGAL::Tetrahedral_remeshing::Remeshing_vertex_base_3`.
+\cgalHasModel `Tetrahedral_remeshing::Remeshing_vertex_base_3`
 
 */
 class RemeshingVertexBase_3
diff --git a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/dependencies b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/dependencies
index 30913764fab..7da5a91e523 100644
--- a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/dependencies
+++ b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/dependencies
@@ -8,3 +8,4 @@ Triangulation_3
 BGL
 Mesh_3
 TDS_3
+SMDS_3
diff --git a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
index a2dd90b0efc..f0a9180b655 100644
--- a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
+++ b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
@@ -32,14 +32,17 @@ namespace Tetrahedral_remeshing
     while (tr.number_of_vertices() < nbv)
       tr.insert(Point(rng.get_double(-1., 1.), rng.get_double(-1., 1.), rng.get_double(-1., 1.)));
 
+    using P = typename Tr::Geom_traits::Point_3;
     const typename Tr::Geom_traits::Plane_3
-      plane(Point(0, 0, 0), Point(0, 1, 0), Point(0, 0, 1));
+      plane(P(0, 0, 0), P(0, 1, 0), P(0, 0, 1));
 
     for (Cell_handle c : tr.finite_cell_handles())
     {
       if (plane.has_on_positive_side(
-        CGAL::centroid(c->vertex(0)->point(), c->vertex(1)->point(),
-                       c->vertex(2)->point(), c->vertex(3)->point())))
+        CGAL::centroid(P(c->vertex(0)->point()),
+                       P(c->vertex(1)->point()),
+                       P(c->vertex(2)->point()),
+                       P(c->vertex(3)->point()))))
         c->set_subdomain_index(1);
       else
         c->set_subdomain_index(2);
diff --git a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
index 9b39e266518..032cca7e1d3 100644
--- a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
+++ b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
@@ -62,11 +62,8 @@ public:
 
 void set_subdomain(Remeshing_triangulation& tr, const int index)
 {
-  for (Remeshing_triangulation::Finite_cells_iterator cit = tr.finite_cells_begin();
-       cit != tr.finite_cells_end(); ++cit)
-  {
+  for (auto cit : tr.finite_cell_handles())
     cit->set_subdomain_index(index);
-  }
 }
 
 int main(int argc, char* argv[])
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h
index ca287666196..d8237882726 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h
@@ -15,49 +15,88 @@
 
 #include <CGAL/license/Tetrahedral_remeshing.h>
 
-#include <CGAL/Mesh_cell_base_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
 
 namespace CGAL
 {
 namespace Tetrahedral_remeshing
 {
-namespace internal
+
+template<typename Subdomain_index,
+         typename Surface_patch_index,
+         typename TDS>
+class Remeshing_cell_3
+  : public CGAL::Simplicial_mesh_cell_3<Subdomain_index,
+                                        Surface_patch_index,
+                                        TDS>
 {
-struct Fake_MD_C
-{
-  typedef int Subdomain_index;
-  typedef int Surface_patch_index;
-  typedef int Index;
+private:
+  using Base = CGAL::Simplicial_mesh_cell_3<Subdomain_index,
+                                            Surface_patch_index,
+                                            TDS>;
+
+public:
+  using Base::Base;
+
+  void set_sliver_value(double value)
+  {
+    sliver_cache_validity_ = true;
+    sliver_value_ = value;
+  }
+
+  double sliver_value() const
+  {
+    CGAL_assertion(is_cache_valid());
+    return sliver_value_;
+  }
+
+  bool is_cache_valid() const { return sliver_cache_validity_; }
+  void reset_cache_validity() const { sliver_cache_validity_ = false; }
+
+private:
+  double sliver_value_ = 0.;
+  mutable bool sliver_cache_validity_ = false;
 };
-}
 
 /*!
 \ingroup PkgTetrahedralRemeshingClasses
 
-The class `Remeshing_cell_base_3` is a model of the concept `MeshCellBase_3`.
+The class `Remeshing_cell_base_3` is a model of the concept `SimplicialMeshCellBase_3`.
 It is designed to serve as cell base class for the 3D triangulation
 used in the tetrahedral remeshing process.
 
-\tparam Gt is the geometric traits class.
-It has to be a model of the concept `RemeshingTriangulationTraits_3`.
+\tparam Subdomain_index Type of indices for subdomains of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must match the label
+of the exterior of the domain (which contains at least the unbounded component).
+ It must match the `Subdomain_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
 
-\tparam Cb is a cell base class from which `Remeshing_cell_base_3` derives.
-It must be a model of the `TriangulationCellBase_3` concept.
-It has the default value `Triangulation_cell_base_3<Gt>`.
+\tparam Surface_patch_index Type of indices for surface patches (boundaries and interfaces)
+of the discretized geometric domain.
+Must be a model of `CopyConstructible`, `Assignable`, `DefaultConstructible`
+and `EqualityComparable`. The default constructed value must be the index value
+assigned to a non surface facet.
+ It must match the `Surface_patch_index` of the model
+  of the `MeshDomain_3` concept when used for mesh generation.
 
-\cgalModels `MeshCellBase_3`
+\cgalModels `RemeshingCellBase_3`
+\cgalModels `SimplicialMeshCellBase_3`
 
 */
-#ifndef DOXYGEN_RUNNING
-template<typename Gt,
-         typename Cb = CGAL::Triangulation_cell_base_3<Gt> >
-using Remeshing_cell_base_3
-  = CGAL::Mesh_cell_base_3<Gt, internal::Fake_MD_C, Cb>;
-#else
-template<typename Gt,
-         typename Cb = CGAL::Triangulation_cell_base_3<Gt> >
-class Remeshing_cell_base_3;
-#endif
+template<typename Subdomain_index = int,
+         typename Surface_patch_index = int>
+class Remeshing_cell_base_3
+{
+public:
+  template <typename TDS2>
+  struct Rebind_TDS
+  {
+    typedef Remeshing_cell_3<Subdomain_index,
+                             Surface_patch_index,
+                             TDS2> Other;
+  };
+};
 
 }//end namespace Tetrahedral_remeshing
 }//end namespace CGAL
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h
index 3104978addb..7021252fd26 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_triangulation_3.h
@@ -21,8 +21,6 @@
 #include <CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h>
 #include <CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h>
 
-#include <CGAL/Kernel_traits.h>
-#include <CGAL/Cartesian_converter.h>
 #include <CGAL/tags.h>
 
 #include <boost/static_assert.hpp>
@@ -55,7 +53,7 @@ and `Parallel_if_available_tag`.
 template<typename Gt,
          typename Concurrency_tag = CGAL::Sequential_tag,
          typename Vb = Remeshing_vertex_base_3<Gt>,
-         typename Cb = Remeshing_cell_base_3<Gt>
+         typename Cb = Remeshing_cell_base_3<>
 >
 class Remeshing_triangulation_3
   : public CGAL::Triangulation_3<Gt, CGAL::Triangulation_data_structure_3<Vb,Cb> >
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h
index 3d0f8b20170..b828ffb08d1 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h
@@ -15,23 +15,12 @@
 
 #include <CGAL/license/Tetrahedral_remeshing.h>
 
-#include <CGAL/Mesh_vertex_base_3.h>
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
 
 namespace CGAL
 {
 namespace Tetrahedral_remeshing
 {
-namespace internal
-{
-
-struct Fake_MD_V
-{
-  typedef int Subdomain_index;
-  typedef int Surface_patch_index;
-  typedef int Index;
-};
-
-} // internal
 
 /*!
 \ingroup PkgTetrahedralRemeshingClasses
@@ -47,18 +36,22 @@ It has to be a model of the concept `RemeshingTriangulationTraits_3`.
 It must be a model of the `TriangulationVertexBase_3` concept.
 It has the default value `Triangulation_vertex_base_3<Gt>`.
 
-\cgalModels `MeshVertexBase_3`
+\cgalModels `RemeshingVertexBase_3`
+\cgalModels `SimplicialMeshVertexBase_3`
 */
-#ifndef DOXYGEN_RUNNING
 template<typename GT,
-         typename Vb = CGAL::Triangulation_vertex_base_3<GT> >
+  typename Subdomain_index = int,
+  typename Surface_patch_index = int,
+  typename Curve_index = int,
+  typename Corner_index = int,
+  typename Vb = CGAL::Triangulation_vertex_base_3<GT> >
 using Remeshing_vertex_base_3
-  = CGAL::Mesh_vertex_base_3<GT, internal::Fake_MD_V, Vb>;
-#else
-template<typename GT,
-         typename Vb = CGAL::Triangulation_vertex_base_3<GT> >
-class Remeshing_vertex_base_3;
-#endif
+  = CGAL::Simplicial_mesh_vertex_base_3<GT,
+                                        Subdomain_index,
+                                        Surface_patch_index,
+                                        Curve_index,
+                                        Corner_index,
+                                        Vb>;
 
 }//end namespace Tetrahedral_remeshing
 
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/collapse_short_edges.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/collapse_short_edges.h
index 4923e35923d..c107aec320a 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/collapse_short_edges.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/collapse_short_edges.h
@@ -29,7 +29,7 @@
 #include <utility>
 #include <unordered_set>
 
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 #include <CGAL/utility.h>
 #include <CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h>
 
@@ -67,8 +67,8 @@ public:
     , v0_init(e.first->vertex(e.second))
     , v1_init(e.first->vertex(e.third))
   {
-    typedef std::array<int, 3> Facet; // 3 = id
-    typedef std::array<int, 5> Tet_with_ref; // first 4 = id, fifth = reference
+    typedef std::array<int, 3> Facet;
+    typedef std::array<int, 4> Tet;
 
     std::unordered_set<Vertex_handle> vertices_to_insert;
     for (Cell_handle ch : cells_to_insert)
@@ -96,23 +96,25 @@ public:
       }
     }
 
-    std::vector<Tet_with_ref> finite_cells;
+    std::vector<Tet> finite_cells;
+    std::vector<int> subdomains;
     for (Cell_handle ch : cells_to_insert)
     {
-      Tet_with_ref t = { { v2i.at(ch->vertex(0)),
-                           v2i.at(ch->vertex(1)),
-                           v2i.at(ch->vertex(2)),
-                           v2i.at(ch->vertex(3)),
-                           ch->subdomain_index() } };
-      finite_cells.push_back(t);
+      finite_cells.push_back( { v2i.at(ch->vertex(0)),
+                                v2i.at(ch->vertex(1)),
+                                v2i.at(ch->vertex(2)),
+                                v2i.at(ch->vertex(3)) } );
+      subdomains.push_back(ch->subdomain_index());
     }
 
     // finished
     std::vector<Vertex_handle> new_vertices;
     std::map<Facet, typename C3t3::Surface_patch_index> border_facets;
-     if (CGAL::build_triangulation<Tr, false>(triangulation,
-                                              points, finite_cells, border_facets,
-                                              new_vertices, false/*verbose*/))
+    if (CGAL::SMDS_3::build_triangulation_impl(
+            triangulation, points, finite_cells, subdomains, border_facets,
+            new_vertices, /*verbose*/ false,
+            /*replace_domain_0*/ false,
+            /*allow_non_manifold*/false))
     {
       CGAL_assertion(triangulation.tds().is_valid());
       CGAL_assertion(triangulation.infinite_vertex() == new_vertices[0]);
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
index 1a6ecb15002..a2c8191fa8f 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
@@ -39,7 +39,7 @@ void compute_statistics(const Triangulation& tr,
   typedef typename Tr::Cell_handle   Cell_handle;
   typedef typename Tr::Vertex_handle Vertex_handle;
   typedef typename Gt::Point_3       Point;
-  typedef typename Tr::Finite_facets_iterator Finite_facets_iterator;
+  typedef typename Tr::Facet         Facet;
   typedef typename Tr::Finite_cells_iterator  Finite_cells_iterator;
   typedef typename Tr::Cell::Subdomain_index  Subdomain_index;
 
@@ -55,11 +55,10 @@ void compute_statistics(const Triangulation& tr,
   double max_dihedral_angle = 0.;
   double min_dihedral_angle = 180.;
 
-  for (Finite_facets_iterator fit = tr.finite_facets_begin();
-       fit != tr.finite_facets_end(); ++fit)
+  for (Facet fit : tr.finite_facets())
   {
-    const Cell_handle cell = fit->first;
-    const int& index = fit->second;
+    const Cell_handle cell = fit.first;
+    const int& index = fit.second;
     if (!cell_selector(cell) || !cell_selector(cell->neighbor(index)))
       continue;
 
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
index 0b371947a6e..745f89bb1d2 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
@@ -381,15 +381,13 @@ private:
     std::unordered_map<Vertex_handle,
     std::vector<Surface_patch_index> >& vertices_surface_indices)
   {
-    for (typename C3t3::Facets_in_complex_iterator
-         fit = c3t3.facets_in_complex_begin();
-         fit != c3t3.facets_in_complex_end(); ++fit)
+    for (Facet fit : c3t3.facets_in_complex())
     {
-      const Surface_patch_index& surface_index = c3t3.surface_patch_index(*fit);
+      const Surface_patch_index& surface_index = c3t3.surface_patch_index(fit);
 
       for (int i = 0; i < 3; i++)
       {
-        const Vertex_handle vi = fit->first->vertex(indices(fit->second, i));
+        const Vertex_handle vi = fit.first->vertex(indices(fit.second, i));
 
         std::vector<Surface_patch_index>& v_surface_indices = vertices_surface_indices[vi];
         if (std::find(v_surface_indices.begin(), v_surface_indices.end(), surface_index) == v_surface_indices.end())
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
index 76851bc76e9..86e7aa27856 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
@@ -239,7 +239,6 @@ void split_long_edges(C3T3& c3t3,
   typedef typename C3T3::Triangulation       T3;
   typedef typename T3::Cell_handle           Cell_handle;
   typedef typename T3::Edge                  Edge;
-  typedef typename T3::Finite_edges_iterator Finite_edges_iterator;
   typedef typename T3::Vertex_handle         Vertex_handle;
   typedef typename std::pair<Vertex_handle, Vertex_handle> Edge_vv;
 
@@ -260,10 +259,8 @@ void split_long_edges(C3T3& c3t3,
   //collect long edges
   T3& tr = c3t3.triangulation();
   Boost_bimap long_edges;
-  for (Finite_edges_iterator eit = tr.finite_edges_begin();
-       eit != tr.finite_edges_end(); ++eit)
+  for (Edge e : tr.finite_edges())
   {
-    Edge e = *eit;
     if (!can_be_split(e, c3t3, protect_boundaries, cell_selector))
       continue;
 
diff --git a/Tetrahedral_remeshing/package_info/Tetrahedral_remeshing/dependencies b/Tetrahedral_remeshing/package_info/Tetrahedral_remeshing/dependencies
index 57bd26ce97b..d9c5098d64f 100644
--- a/Tetrahedral_remeshing/package_info/Tetrahedral_remeshing/dependencies
+++ b/Tetrahedral_remeshing/package_info/Tetrahedral_remeshing/dependencies
@@ -14,13 +14,13 @@ Intersections_3
 Interval_support
 Kernel_23
 Kernel_d
-Mesh_3
 Modular_arithmetic
 Number_types
 Polygon_mesh_processing
 Profiling_tools
 Property_map
 Random_numbers
+SMDS_3
 STL_Extension
 Spatial_sorting
 Stream_support
diff --git a/Tetrahedral_remeshing/test/Tetrahedral_remeshing/test_tetrahedral_remeshing_from_mesh_file.cpp b/Tetrahedral_remeshing/test/Tetrahedral_remeshing/test_tetrahedral_remeshing_from_mesh_file.cpp
index cb748e0e92b..30c83e1c533 100644
--- a/Tetrahedral_remeshing/test/Tetrahedral_remeshing/test_tetrahedral_remeshing_from_mesh_file.cpp
+++ b/Tetrahedral_remeshing/test/Tetrahedral_remeshing/test_tetrahedral_remeshing_from_mesh_file.cpp
@@ -10,7 +10,7 @@
 #include <iostream>
 #include <fstream>
 
-#include <CGAL/Mesh_3/tet_soup_to_c3t3.h>
+#include <CGAL/SMDS_3/tet_soup_to_c3t3.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 
@@ -23,7 +23,7 @@ int main(int argc, char* argv[])
   Remeshing_triangulation tr;
 
   std::ifstream in("data/sphere.mesh");
-  if (CGAL::build_triangulation_from_file<Remeshing_triangulation, true>(in, tr))
+  if (CGAL::SMDS_3::build_triangulation_from_file(in, tr))
     std::cout << "build triangulation ok" << std::endl;
 
   CGAL::tetrahedral_isotropic_remeshing(tr, target_edge_length);