diff --git a/Point_set_processing_3/examples/Point_set_processing_3/include/compute_normal.h b/Point_set_processing_3/examples/Point_set_processing_3/include/compute_normal.h
new file mode 100644
index 00000000000..3437332ab75
--- /dev/null
+++ b/Point_set_processing_3/examples/Point_set_processing_3/include/compute_normal.h
@@ -0,0 +1,45 @@
+#ifndef _COMPUTE_NORMAL_
+#define _COMPUTE_NORMAL_
+
+template <class Facet, class Kernel>
+typename Kernel::Vector_3 compute_facet_normal(const Facet& f)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Facet::Halfedge_around_facet_const_circulator HF_circulator;
+  Vector normal = CGAL::NULL_VECTOR;
+  HF_circulator he = f.facet_begin();
+  HF_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    const Point& prev = he->prev()->vertex()->point();
+    const Point& curr = he->vertex()->point();
+    const Point& next = he->next()->vertex()->point();
+    Vector n = CGAL::cross_product(next-curr,prev-curr);
+    normal = normal + (n / std::sqrt(n*n));
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+template <class Vertex, class Kernel>
+typename Kernel::Vector_3 compute_vertex_normal(const Vertex& v)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Vertex::Halfedge_around_vertex_const_circulator HV_circulator;
+  typedef typename Vertex::Facet Facet;
+  Vector normal = CGAL::NULL_VECTOR;
+  HV_circulator he = v.vertex_begin();
+  HV_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    if(!he->is_border())
+    {
+      Vector n = compute_facet_normal<Facet,Kernel>(*he->facet());
+      normal = normal + (n / std::sqrt(n*n));
+    }
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+#endif // _COMPUTE_NORMAL_
diff --git a/Point_set_processing_3/examples/Point_set_processing_3/include/enriched_polyhedron.h b/Point_set_processing_3/examples/Point_set_processing_3/include/enriched_polyhedron.h
deleted file mode 100644
index feab694e237..00000000000
--- a/Point_set_processing_3/examples/Point_set_processing_3/include/enriched_polyhedron.h
+++ /dev/null
@@ -1,247 +0,0 @@
-///////////////////////////////////////////////////////////////////////////
-//                                                                       //
-//  Class: Enriched_polyhedron                                           //
-//                                                                       //
-///////////////////////////////////////////////////////////////////////////
-
-#ifndef _POLYGON_MESH_
-#define _POLYGON_MESH_
-
-// CGAL
-#include <CGAL/Cartesian.h>
-#include <CGAL/Polyhedron_3.h>
-
-#include <list>
-
-// Forward declarations
-struct Vertex_normal;
-struct Facet_normal;
-
-
-// a refined facet with a normal
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_facet : public CGAL::HalfedgeDS_face_base<Refs, Tag>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_facet()
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-
-// a refined halfedge with a general tag
-template <class Refs, class Tprev, class Tvertex, class Tface, class Norm>
-class Enriched_halfedge : public CGAL::HalfedgeDS_halfedge_base<Refs,Tprev,Tvertex,Tface>
-{
-private:
-
-public:
-
-  // life cycle
-  Enriched_halfedge()
-  {
-  }
-};
-
-
-// a refined vertex with a normal, tag and camera
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_vertex : public CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_vertex()  {}
-  // repeat mandatory constructors
-  Enriched_vertex(const Point_3_& pt)
-    : CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>(pt)
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-// A redefined items class for the Polyhedron_3
-// with a refined vertex class that contains a
-// member for the normal vector and a refined
-// facet with a normal vector instead of the
-// plane equation (this is an alternative
-// solution instead of using
-// Polyhedron_traits_with_normals_3).
-
-struct Enriched_items : public CGAL::Polyhedron_items_3
-{
-  // wrap vertex
-  template <class Refs, class Traits>
-  struct Vertex_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_vertex<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Vertex;
-  };
-
-  // wrap face
-  template <class Refs, class Traits>
-  struct Face_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_facet<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Face;
-  };
-
-  // wrap halfedge
-  template <class Refs, class Traits>
-  struct Halfedge_wrapper
-  {
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_halfedge<Refs,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      Normal> Halfedge;
-  };
-};
-
-
-// Enriched polyhedron
-template <class PolyhedronTraits_3,
-          class PolyhedronItems_3 = Enriched_items>
-class Enriched_polyhedron
-  : public CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3>
-{
-  // Private types
-private:
-
-  typedef CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3> Base;
-
-  // Public types
-public:
-
-  typedef typename PolyhedronTraits_3::FT FT;
-  typedef typename PolyhedronTraits_3::Point_3 Point;
-
-  // Repeat Polyhedron_3 public types
-  typedef typename Base::HalfedgeDS               HalfedgeDS;
-  typedef typename Base::Vertex                   Vertex;
-  typedef typename Base::Halfedge                 Halfedge;
-  typedef typename Base::Facet                    Facet;
-  typedef typename Base::Vertex_handle            Vertex_handle;
-  typedef typename Base::Vertex_const_handle      Vertex_const_handle;
-  typedef typename Base::Halfedge_handle          Halfedge_handle;
-  typedef typename Base::Halfedge_const_handle    Halfedge_const_handle;
-  typedef typename Base::Facet_handle             Facet_handle;
-  typedef typename Base::Facet_const_handle       Facet_const_handle;
-  typedef typename Base::Vertex_iterator          Vertex_iterator;
-  typedef typename Base::Vertex_const_iterator    Vertex_const_iterator;
-  typedef typename Base::Halfedge_iterator        Halfedge_iterator;
-  typedef typename Base::Halfedge_const_iterator  Halfedge_const_iterator;
-  typedef typename Base::Facet_iterator           Facet_iterator;
-  typedef typename Base::Facet_const_iterator     Facet_const_iterator;
-  typedef typename Base::Point_iterator           Point_iterator;
-  typedef typename Base::Point_const_iterator     Point_const_iterator;
-  typedef typename Base::Halfedge_around_facet_circulator         Halfedge_around_facet_circulator;
-  typedef typename Base::Halfedge_around_facet_const_circulator   Halfedge_around_facet_const_circulator;
-  typedef typename Base::Halfedge_around_vertex_circulator        Halfedge_around_vertex_circulator;
-  typedef typename Base::Halfedge_around_vertex_const_circulator  Halfedge_around_vertex_const_circulator;
-
-public :
-
-  // Default constructor, copy constructor and operator =() are fine.
-
-  // Repeat Delaunay_triangulation_3 public methods
-  Base::halfedges_begin;
-  Base::halfedges_end;
-  Base::facets_begin;
-  Base::facets_end;
-  Base::vertices_begin;
-  Base::vertices_end;
-
-  // Compute normals using mesh connectivity (per facet, then per vertex)
-  void compute_normals_per_facet()
-  {
-    std::for_each(facets_begin(),facets_end(),Facet_normal());
-  }
-  void compute_normals_per_vertex()
-  {
-    std::for_each(vertices_begin(),vertices_end(),Vertex_normal());
-  }
-  void compute_normals()
-  {
-    compute_normals_per_facet();
-    compute_normals_per_vertex();
-  }
-};
-
-// compute facet normal (functor)
-struct Facet_normal
-{
-  template <class Facet>
-  void operator()(Facet& f)
-  {
-    typename Facet::Normal_3 sum = CGAL::NULL_VECTOR;
-    typename Facet::Halfedge_around_facet_circulator h = f.facet_begin();
-    do
-    {
-      typename Facet::Normal_3 normal = CGAL::cross_product(
-        h->next()->vertex()->point() - h->vertex()->point(),
-        h->next()->next()->vertex()->point() - h->next()->vertex()->point());
-      double sqnorm = normal * normal;
-      if(sqnorm != 0)
-        normal = normal / (double)std::sqrt(sqnorm);
-      sum = sum + normal;
-    }
-    while(++h != f.facet_begin());
-    double sqnorm = sum * sum;
-    if(sqnorm != 0.0)
-      f.normal() = sum / std::sqrt(sqnorm);
-    else
-    {
-      f.normal() = CGAL::NULL_VECTOR;
-      std::cerr << "degenerate face\n";
-    }
-  }
-};
-
-
-// compute vertex normal (functor)
-struct Vertex_normal
-{
-  template <class Vertex>
-  void operator()(Vertex& v)
-  {
-    typename Vertex::Normal_3 normal = CGAL::NULL_VECTOR;
-    typename Vertex::Halfedge_around_vertex_const_circulator pHalfedge = v.vertex_begin();
-    typename Vertex::Halfedge_around_vertex_const_circulator begin = pHalfedge;
-    CGAL_For_all(pHalfedge,begin)
-      if(!pHalfedge->is_border())
-        normal = normal + pHalfedge->facet()->normal();
-    double sqnorm = normal * normal;
-    if(sqnorm != 0.0f)
-      v.normal() = normal / (float)std::sqrt(sqnorm);
-    else
-      v.normal() = CGAL::NULL_VECTOR;
-  }
-};
-
-
-#endif // _POLYGON_MESH_
diff --git a/Point_set_processing_3/examples/Point_set_processing_3/normal_estimation.cpp b/Point_set_processing_3/examples/Point_set_processing_3/normal_estimation.cpp
index 8ee914a725d..5a047c0e1ff 100644
--- a/Point_set_processing_3/examples/Point_set_processing_3/normal_estimation.cpp
+++ b/Point_set_processing_3/examples/Point_set_processing_3/normal_estimation.cpp
@@ -12,8 +12,8 @@
 // CGAL
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Timer.h>
-#include <CGAL/Memory_sizer.h>
 #include <CGAL/boost/graph/properties.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 
 // This package
@@ -25,12 +25,11 @@
 #include <CGAL/IO/read_xyz_point_set.h>
 #include <CGAL/IO/write_xyz_point_set.h>
 
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 
 #include <deque>
 #include <cstdlib>
 #include <fstream>
-#include <cassert>
 
 
 // ----------------------------------------------------------------------------
@@ -222,12 +221,13 @@ int main(int argc, char * argv[])
     PointList points;
 
     // If OFF file format
+    std::cerr << "Open " << input_filename << " for reading..." << std::endl;
     std::string extension = input_filename.substr(input_filename.find_last_of('.'));
     if (extension == ".off" || extension == ".OFF")
     {
       // Read the mesh file in a polyhedron
       std::ifstream stream(input_filename.c_str());
-      typedef Enriched_polyhedron<Kernel,Enriched_items> Polyhedron;
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
       CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
       if(!stream || !input_mesh.is_valid() || input_mesh.empty())
@@ -236,15 +236,13 @@ int main(int argc, char * argv[])
         return EXIT_FAILURE;
       }
 
-      // Compute vertices' normals from connectivity
-      input_mesh.compute_normals();
-
-      // Convert vertices and normals to PointList
-      Polyhedron::Vertex_iterator v;
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
       for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         points.push_back(Point_with_normal(p,n));
       }
     }
@@ -269,11 +267,9 @@ int main(int argc, char * argv[])
     }
 
     // Print status
-    long memory = CGAL::Memory_sizer().virtual_size();
     int nb_vertices = points.size();
     std::cerr << "Read file " << input_filename << ": " << nb_vertices << " vertices, "
                                                         << task_timer.time() << " seconds, "
-                                                        << (memory>>20) << " Mb allocated"
                                                         << std::endl;
     task_timer.reset();
 
diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_scene_item.cpp b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_scene_item.cpp
index 095e9dd127a..e9d4b95fc2b 100644
--- a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_scene_item.cpp
+++ b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_scene_item.cpp
@@ -40,7 +40,7 @@ Point_set_scene_item::Point_set_scene_item(const Polyhedron& input_mesh)
   Polyhedron::Vertex_const_iterator v;
   for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
   {
-    Point p = v->point();
+    const Point& p = v->point();
     Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
     m_points->push_back(UI_point(p,n));
   }
diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/PoissonDoc.cpp b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/PoissonDoc.cpp
index 187cb35dc4b..0406415b980 100644
--- a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/PoissonDoc.cpp
+++ b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/PoissonDoc.cpp
@@ -6,7 +6,7 @@
 #include "Poisson.h"
 #include "DialogOptions.h"
 #include "PoissonDoc.h"
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 #include "read_pwc_point_set.h"
 #include "read_g23_point_set.h"
 #include "outlier_removal_wrt_camera_cone_angle_3.h"
@@ -15,6 +15,7 @@
 // CGAL
 #include <CGAL/make_surface_mesh.h>
 #include <CGAL/Implicit_surface_3.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/IO/File_scanner_OFF.h>
 #include <CGAL/Timer.h>
@@ -242,28 +243,24 @@ BOOL CPoissonDoc::OnOpenDocument(LPCTSTR lpszPathName)
     // Read OFF file as a mesh and compute normals from connectivity
     if (is_mesh)
     {
-      // read file in polyhedron
-      typedef Enriched_polyhedron<Kernel> Polyhedron;
+      // Read the mesh file in a polyhedron
+      std::ifstream stream(lpszPathName);
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
-      std::ifstream file_stream(lpszPathName);
-      CGAL::scan_OFF(file_stream, input_mesh, true /* verbose */);
-      if(!file_stream || !input_mesh.is_valid() || input_mesh.empty())
+      CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
+      if(!stream || !input_mesh.is_valid() || input_mesh.empty())
       {
         prompt_message("Unable to read file");
         return FALSE;
       }
 
-      // Compute normals using mesh connectivity
-      input_mesh.compute_normals();
-
-      // Copy points to m_points
-      Polyhedron::Vertex_iterator v;
-      for(v = input_mesh.vertices_begin();
-          v != input_mesh.vertices_end();
-          v++)
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
+      for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         m_points.push_back(Point_with_normal(p,n));
       }
     }
diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/compute_normal.h b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/compute_normal.h
new file mode 100644
index 00000000000..3437332ab75
--- /dev/null
+++ b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/compute_normal.h
@@ -0,0 +1,45 @@
+#ifndef _COMPUTE_NORMAL_
+#define _COMPUTE_NORMAL_
+
+template <class Facet, class Kernel>
+typename Kernel::Vector_3 compute_facet_normal(const Facet& f)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Facet::Halfedge_around_facet_const_circulator HF_circulator;
+  Vector normal = CGAL::NULL_VECTOR;
+  HF_circulator he = f.facet_begin();
+  HF_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    const Point& prev = he->prev()->vertex()->point();
+    const Point& curr = he->vertex()->point();
+    const Point& next = he->next()->vertex()->point();
+    Vector n = CGAL::cross_product(next-curr,prev-curr);
+    normal = normal + (n / std::sqrt(n*n));
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+template <class Vertex, class Kernel>
+typename Kernel::Vector_3 compute_vertex_normal(const Vertex& v)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Vertex::Halfedge_around_vertex_const_circulator HV_circulator;
+  typedef typename Vertex::Facet Facet;
+  Vector normal = CGAL::NULL_VECTOR;
+  HV_circulator he = v.vertex_begin();
+  HV_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    if(!he->is_border())
+    {
+      Vector n = compute_facet_normal<Facet,Kernel>(*he->facet());
+      normal = normal + (n / std::sqrt(n*n));
+    }
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+#endif // _COMPUTE_NORMAL_
diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/enriched_polyhedron.h b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/enriched_polyhedron.h
deleted file mode 100644
index 9a660bb35ee..00000000000
--- a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/poisson/include/enriched_polyhedron.h
+++ /dev/null
@@ -1,272 +0,0 @@
-///////////////////////////////////////////////////////////////////////////
-//                                                                       //
-//  Class: Enriched_polyhedron                                           //
-//                                                                       //
-///////////////////////////////////////////////////////////////////////////
-
-#ifndef _POLYGON_MESH_
-#define _POLYGON_MESH_
-
-// CGAL
-#include <CGAL/Cartesian.h>
-#include <CGAL/Polyhedron_3.h>
-
-#include <list>
-
-// Forward declarations
-struct Vertex_normal;
-struct Facet_normal;
-
-
-// a refined facet with a normal
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_facet : public CGAL::HalfedgeDS_face_base<Refs, Tag>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_facet()
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-
-// a refined halfedge with a general tag
-template <class Refs, class Tprev, class Tvertex, class Tface, class Norm>
-class Enriched_halfedge : public CGAL::HalfedgeDS_halfedge_base<Refs,Tprev,Tvertex,Tface>
-{
-private:
-
-public:
-
-  // life cycle
-  Enriched_halfedge()
-  {
-  }
-};
-
-
-// a refined vertex with a normal, tag and camera
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_vertex : public CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_vertex()  {}
-  // repeat mandatory constructors
-  Enriched_vertex(const Point_3_& pt)
-    : CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>(pt)
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-// A redefined items class for the Polyhedron_3
-// with a refined vertex class that contains a
-// member for the normal vector and a refined
-// facet with a normal vector instead of the
-// plane equation (this is an alternative
-// solution instead of using
-// Polyhedron_traits_with_normals_3).
-
-struct Enriched_items : public CGAL::Polyhedron_items_3
-{
-  // wrap vertex
-  template <class Refs, class Traits>
-  struct Vertex_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_vertex<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Vertex;
-  };
-
-  // wrap face
-  template <class Refs, class Traits>
-  struct Face_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_facet<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Face;
-  };
-
-  // wrap halfedge
-  template <class Refs, class Traits>
-  struct Halfedge_wrapper
-  {
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_halfedge<Refs,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      Normal> Halfedge;
-  };
-};
-
-
-// Enriched polyhedron
-template <class PolyhedronTraits_3,
-          class PolyhedronItems_3 = Enriched_items>
-class Enriched_polyhedron
-  : public CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3>
-{
-  // Private types
-private:
-
-  typedef CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3> Base;
-
-  // Auxiliary class to build a triangles iterator
-  template <class Node> // Node is Facet
-  struct Project_triangle {
-    typedef Node                                  argument_type;
-    typedef typename PolyhedronTraits_3::Triangle_3 Triangle;
-    typedef Triangle                              result_type;
-    typedef typename PolyhedronTraits_3::Point_3  Point;
-
-    Triangle operator()(const Node& f) const {
-        Halfedge_const_handle he = f.halfedge();
-        const Point& a = he->vertex()->point();
-        const Point& b = he->next()->vertex()->point();
-        const Point& c = he->next()->next()->vertex()->point();
-        return Triangle(a,b,c);
-    }
-  };
-
-  // Public types
-public:
-
-  typedef typename PolyhedronTraits_3::FT         FT;
-  typedef typename PolyhedronTraits_3::Point_3    Point;
-
-  // Repeat Polyhedron_3 public types
-  typedef typename Base::HalfedgeDS               HalfedgeDS;
-  typedef typename Base::Vertex                   Vertex;
-  typedef typename Base::Halfedge                 Halfedge;
-  typedef typename Base::Facet                    Facet;
-  typedef typename Base::Vertex_handle            Vertex_handle;
-  typedef typename Base::Vertex_const_handle      Vertex_const_handle;
-  typedef typename Base::Halfedge_handle          Halfedge_handle;
-  typedef typename Base::Halfedge_const_handle    Halfedge_const_handle;
-  typedef typename Base::Facet_handle             Facet_handle;
-  typedef typename Base::Facet_const_handle       Facet_const_handle;
-  typedef typename Base::Vertex_iterator          Vertex_iterator;
-  typedef typename Base::Vertex_const_iterator    Vertex_const_iterator;
-  typedef typename Base::Halfedge_iterator        Halfedge_iterator;
-  typedef typename Base::Halfedge_const_iterator  Halfedge_const_iterator;
-  typedef typename Base::Facet_iterator           Facet_iterator;
-  typedef typename Base::Facet_const_iterator     Facet_const_iterator;
-  typedef typename Base::Point_iterator           Point_iterator;
-  typedef typename Base::Point_const_iterator     Point_const_iterator;
-  typedef typename Base::Halfedge_around_facet_circulator         Halfedge_around_facet_circulator;
-  typedef typename Base::Halfedge_around_facet_const_circulator   Halfedge_around_facet_const_circulator;
-  typedef typename Base::Halfedge_around_vertex_circulator        Halfedge_around_vertex_circulator;
-  typedef typename Base::Halfedge_around_vertex_const_circulator  Halfedge_around_vertex_const_circulator;
-
-  // Iterator over triangles
-  typedef CGAL::Iterator_project<Facet_const_iterator, Project_triangle<Facet> >
-                                                                  Triangle_const_iterator;
-
-public :
-
-  // Default constructor, copy constructor and operator =() are fine.
-
-  // Repeat Delaunay_triangulation_3 public methods
-  Base::halfedges_begin;
-  Base::halfedges_end;
-  Base::facets_begin;
-  Base::facets_end;
-  Base::vertices_begin;
-  Base::vertices_end;
-
-  // Get first/last iterators over triangles.
-  Triangle_const_iterator triangles_begin() const { return Triangle_const_iterator(facets_begin()); }
-  Triangle_const_iterator triangles_end() const   { return Triangle_const_iterator(facets_end()); }
-
-  // Compute normals using mesh connectivity (per facet, then per vertex)
-  void compute_normals_per_facet()
-  {
-    std::for_each(facets_begin(),facets_end(),Facet_normal());
-  }
-  void compute_normals_per_vertex()
-  {
-    std::for_each(vertices_begin(),vertices_end(),Vertex_normal());
-  }
-  void compute_normals()
-  {
-    compute_normals_per_facet();
-    compute_normals_per_vertex();
-  }
-};
-
-// compute facet normal (functor)
-struct Facet_normal
-{
-  template <class Facet>
-  void operator()(Facet& f)
-  {
-    typename Facet::Normal_3 sum = CGAL::NULL_VECTOR;
-    typename Facet::Halfedge_around_facet_circulator h = f.facet_begin();
-    do
-    {
-      typename Facet::Normal_3 normal = CGAL::cross_product(
-        h->next()->vertex()->point() - h->vertex()->point(),
-        h->next()->next()->vertex()->point() - h->next()->vertex()->point());
-      double sqnorm = normal * normal;
-      if(sqnorm != 0)
-        normal = normal / (double)std::sqrt(sqnorm);
-      sum = sum + normal;
-    }
-    while(++h != f.facet_begin());
-    double sqnorm = sum * sum;
-    if(sqnorm != 0.0)
-      f.normal() = sum / std::sqrt(sqnorm);
-    else
-    {
-      f.normal() = CGAL::NULL_VECTOR;
-      std::cerr << "degenerate face\n";
-    }
-  }
-};
-
-
-// compute vertex normal (functor)
-struct Vertex_normal
-{
-  template <class Vertex>
-  void operator()(Vertex& v)
-  {
-    typename Vertex::Normal_3 normal = CGAL::NULL_VECTOR;
-    typename Vertex::Halfedge_around_vertex_const_circulator pHalfedge = v.vertex_begin();
-    typename Vertex::Halfedge_around_vertex_const_circulator begin = pHalfedge;
-    CGAL_For_all(pHalfedge,begin)
-      if(!pHalfedge->is_border())
-        normal = normal + pHalfedge->facet()->normal();
-    double sqnorm = normal * normal;
-    if(sqnorm != 0.0f)
-      v.normal() = normal / (float)std::sqrt(sqnorm);
-    else
-      v.normal() = CGAL::NULL_VECTOR;
-  }
-};
-
-
-#endif // _POLYGON_MESH_
diff --git a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/APSS_reconstruction.cpp b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/APSS_reconstruction.cpp
index 2c658fcf015..4a534221f71 100644
--- a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/APSS_reconstruction.cpp
+++ b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/APSS_reconstruction.cpp
@@ -11,6 +11,7 @@
 // CGAL
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Timer.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Surface_mesh_default_triangulation_3.h>
 #include <CGAL/make_surface_mesh.h>
@@ -23,7 +24,7 @@
 #include <CGAL/Point_with_normal_3.h>
 #include <CGAL/IO/read_xyz_point_set.h>
 
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 
 #include <deque>
 #include <cstdlib>
@@ -114,12 +115,13 @@ int main(int argc, char * argv[])
     PointList points;
 
     // If OFF file format
+    std::cerr << "Open " << input_filename << " for reading..." << std::endl;
     std::string extension = input_filename.substr(input_filename.find_last_of('.'));
     if (extension == ".off" || extension == ".OFF")
     {
       // Read the mesh file in a polyhedron
       std::ifstream stream(input_filename.c_str());
-      typedef Enriched_polyhedron<Kernel,Enriched_items> Polyhedron;
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
       CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
       if(!stream || !input_mesh.is_valid() || input_mesh.empty())
@@ -128,15 +130,13 @@ int main(int argc, char * argv[])
         return EXIT_FAILURE;
       }
 
-      // Compute vertices' normals from connectivity
-      input_mesh.compute_normals();
-
-      // Convert vertices and normals to PointList
-      Polyhedron::Vertex_iterator v;
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
       for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         points.push_back(Point_with_normal(p,n));
       }
     }
diff --git a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/compute_normal.h b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/compute_normal.h
new file mode 100644
index 00000000000..3437332ab75
--- /dev/null
+++ b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/compute_normal.h
@@ -0,0 +1,45 @@
+#ifndef _COMPUTE_NORMAL_
+#define _COMPUTE_NORMAL_
+
+template <class Facet, class Kernel>
+typename Kernel::Vector_3 compute_facet_normal(const Facet& f)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Facet::Halfedge_around_facet_const_circulator HF_circulator;
+  Vector normal = CGAL::NULL_VECTOR;
+  HF_circulator he = f.facet_begin();
+  HF_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    const Point& prev = he->prev()->vertex()->point();
+    const Point& curr = he->vertex()->point();
+    const Point& next = he->next()->vertex()->point();
+    Vector n = CGAL::cross_product(next-curr,prev-curr);
+    normal = normal + (n / std::sqrt(n*n));
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+template <class Vertex, class Kernel>
+typename Kernel::Vector_3 compute_vertex_normal(const Vertex& v)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Vertex::Halfedge_around_vertex_const_circulator HV_circulator;
+  typedef typename Vertex::Facet Facet;
+  Vector normal = CGAL::NULL_VECTOR;
+  HV_circulator he = v.vertex_begin();
+  HV_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    if(!he->is_border())
+    {
+      Vector n = compute_facet_normal<Facet,Kernel>(*he->facet());
+      normal = normal + (n / std::sqrt(n*n));
+    }
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+#endif // _COMPUTE_NORMAL_
diff --git a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/enriched_polyhedron.h b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/enriched_polyhedron.h
deleted file mode 100644
index feab694e237..00000000000
--- a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/include/enriched_polyhedron.h
+++ /dev/null
@@ -1,247 +0,0 @@
-///////////////////////////////////////////////////////////////////////////
-//                                                                       //
-//  Class: Enriched_polyhedron                                           //
-//                                                                       //
-///////////////////////////////////////////////////////////////////////////
-
-#ifndef _POLYGON_MESH_
-#define _POLYGON_MESH_
-
-// CGAL
-#include <CGAL/Cartesian.h>
-#include <CGAL/Polyhedron_3.h>
-
-#include <list>
-
-// Forward declarations
-struct Vertex_normal;
-struct Facet_normal;
-
-
-// a refined facet with a normal
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_facet : public CGAL::HalfedgeDS_face_base<Refs, Tag>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_facet()
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-
-// a refined halfedge with a general tag
-template <class Refs, class Tprev, class Tvertex, class Tface, class Norm>
-class Enriched_halfedge : public CGAL::HalfedgeDS_halfedge_base<Refs,Tprev,Tvertex,Tface>
-{
-private:
-
-public:
-
-  // life cycle
-  Enriched_halfedge()
-  {
-  }
-};
-
-
-// a refined vertex with a normal, tag and camera
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_vertex : public CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_vertex()  {}
-  // repeat mandatory constructors
-  Enriched_vertex(const Point_3_& pt)
-    : CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>(pt)
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-// A redefined items class for the Polyhedron_3
-// with a refined vertex class that contains a
-// member for the normal vector and a refined
-// facet with a normal vector instead of the
-// plane equation (this is an alternative
-// solution instead of using
-// Polyhedron_traits_with_normals_3).
-
-struct Enriched_items : public CGAL::Polyhedron_items_3
-{
-  // wrap vertex
-  template <class Refs, class Traits>
-  struct Vertex_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_vertex<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Vertex;
-  };
-
-  // wrap face
-  template <class Refs, class Traits>
-  struct Face_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_facet<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Face;
-  };
-
-  // wrap halfedge
-  template <class Refs, class Traits>
-  struct Halfedge_wrapper
-  {
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_halfedge<Refs,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      Normal> Halfedge;
-  };
-};
-
-
-// Enriched polyhedron
-template <class PolyhedronTraits_3,
-          class PolyhedronItems_3 = Enriched_items>
-class Enriched_polyhedron
-  : public CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3>
-{
-  // Private types
-private:
-
-  typedef CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3> Base;
-
-  // Public types
-public:
-
-  typedef typename PolyhedronTraits_3::FT FT;
-  typedef typename PolyhedronTraits_3::Point_3 Point;
-
-  // Repeat Polyhedron_3 public types
-  typedef typename Base::HalfedgeDS               HalfedgeDS;
-  typedef typename Base::Vertex                   Vertex;
-  typedef typename Base::Halfedge                 Halfedge;
-  typedef typename Base::Facet                    Facet;
-  typedef typename Base::Vertex_handle            Vertex_handle;
-  typedef typename Base::Vertex_const_handle      Vertex_const_handle;
-  typedef typename Base::Halfedge_handle          Halfedge_handle;
-  typedef typename Base::Halfedge_const_handle    Halfedge_const_handle;
-  typedef typename Base::Facet_handle             Facet_handle;
-  typedef typename Base::Facet_const_handle       Facet_const_handle;
-  typedef typename Base::Vertex_iterator          Vertex_iterator;
-  typedef typename Base::Vertex_const_iterator    Vertex_const_iterator;
-  typedef typename Base::Halfedge_iterator        Halfedge_iterator;
-  typedef typename Base::Halfedge_const_iterator  Halfedge_const_iterator;
-  typedef typename Base::Facet_iterator           Facet_iterator;
-  typedef typename Base::Facet_const_iterator     Facet_const_iterator;
-  typedef typename Base::Point_iterator           Point_iterator;
-  typedef typename Base::Point_const_iterator     Point_const_iterator;
-  typedef typename Base::Halfedge_around_facet_circulator         Halfedge_around_facet_circulator;
-  typedef typename Base::Halfedge_around_facet_const_circulator   Halfedge_around_facet_const_circulator;
-  typedef typename Base::Halfedge_around_vertex_circulator        Halfedge_around_vertex_circulator;
-  typedef typename Base::Halfedge_around_vertex_const_circulator  Halfedge_around_vertex_const_circulator;
-
-public :
-
-  // Default constructor, copy constructor and operator =() are fine.
-
-  // Repeat Delaunay_triangulation_3 public methods
-  Base::halfedges_begin;
-  Base::halfedges_end;
-  Base::facets_begin;
-  Base::facets_end;
-  Base::vertices_begin;
-  Base::vertices_end;
-
-  // Compute normals using mesh connectivity (per facet, then per vertex)
-  void compute_normals_per_facet()
-  {
-    std::for_each(facets_begin(),facets_end(),Facet_normal());
-  }
-  void compute_normals_per_vertex()
-  {
-    std::for_each(vertices_begin(),vertices_end(),Vertex_normal());
-  }
-  void compute_normals()
-  {
-    compute_normals_per_facet();
-    compute_normals_per_vertex();
-  }
-};
-
-// compute facet normal (functor)
-struct Facet_normal
-{
-  template <class Facet>
-  void operator()(Facet& f)
-  {
-    typename Facet::Normal_3 sum = CGAL::NULL_VECTOR;
-    typename Facet::Halfedge_around_facet_circulator h = f.facet_begin();
-    do
-    {
-      typename Facet::Normal_3 normal = CGAL::cross_product(
-        h->next()->vertex()->point() - h->vertex()->point(),
-        h->next()->next()->vertex()->point() - h->next()->vertex()->point());
-      double sqnorm = normal * normal;
-      if(sqnorm != 0)
-        normal = normal / (double)std::sqrt(sqnorm);
-      sum = sum + normal;
-    }
-    while(++h != f.facet_begin());
-    double sqnorm = sum * sum;
-    if(sqnorm != 0.0)
-      f.normal() = sum / std::sqrt(sqnorm);
-    else
-    {
-      f.normal() = CGAL::NULL_VECTOR;
-      std::cerr << "degenerate face\n";
-    }
-  }
-};
-
-
-// compute vertex normal (functor)
-struct Vertex_normal
-{
-  template <class Vertex>
-  void operator()(Vertex& v)
-  {
-    typename Vertex::Normal_3 normal = CGAL::NULL_VECTOR;
-    typename Vertex::Halfedge_around_vertex_const_circulator pHalfedge = v.vertex_begin();
-    typename Vertex::Halfedge_around_vertex_const_circulator begin = pHalfedge;
-    CGAL_For_all(pHalfedge,begin)
-      if(!pHalfedge->is_border())
-        normal = normal + pHalfedge->facet()->normal();
-    double sqnorm = normal * normal;
-    if(sqnorm != 0.0f)
-      v.normal() = normal / (float)std::sqrt(sqnorm);
-    else
-      v.normal() = CGAL::NULL_VECTOR;
-  }
-};
-
-
-#endif // _POLYGON_MESH_
diff --git a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/poisson_reconstruction.cpp b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/poisson_reconstruction.cpp
index fe340ee0ceb..41e577eb38f 100644
--- a/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/poisson_reconstruction.cpp
+++ b/Surface_reconstruction_points_3/examples/Surface_reconstruction_points_3/poisson_reconstruction.cpp
@@ -11,6 +11,7 @@
 // CGAL
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Timer.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Surface_mesh_default_triangulation_3.h>
 #include <CGAL/make_surface_mesh.h>
@@ -23,7 +24,7 @@
 #include <CGAL/Point_with_normal_3.h>
 #include <CGAL/IO/read_xyz_point_set.h>
 
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 
 #include <deque>
 #include <cstdlib>
@@ -109,12 +110,13 @@ int main(int argc, char * argv[])
     PointList points;
 
     // If OFF file format
+    std::cerr << "Open " << input_filename << " for reading..." << std::endl;
     std::string extension = input_filename.substr(input_filename.find_last_of('.'));
     if (extension == ".off" || extension == ".OFF")
     {
       // Read the mesh file in a polyhedron
       std::ifstream stream(input_filename.c_str());
-      typedef Enriched_polyhedron<Kernel,Enriched_items> Polyhedron;
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
       CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
       if(!stream || !input_mesh.is_valid() || input_mesh.empty())
@@ -123,15 +125,13 @@ int main(int argc, char * argv[])
         return EXIT_FAILURE;
       }
 
-      // Compute vertices' normals from connectivity
-      input_mesh.compute_normals();
-
-      // Convert vertices and normals to PointList
-      Polyhedron::Vertex_iterator v;
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
       for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         points.push_back(Point_with_normal(p,n));
       }
     }
diff --git a/Surface_reconstruction_points_3/include/CGAL/polyhedron_connected_components.h b/Surface_reconstruction_points_3/include/CGAL/polyhedron_connected_components.h
new file mode 100644
index 00000000000..4c013bafde5
--- /dev/null
+++ b/Surface_reconstruction_points_3/include/CGAL/polyhedron_connected_components.h
@@ -0,0 +1,177 @@
+// Copyright (c) 2005-2009  INRIA (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you may redistribute it under
+// the terms of the Q Public License version 1.0.
+// See the file LICENSE.QPL distributed with CGAL.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+//
+//
+// Author(s)     : Laurent Saboret, Pierre Alliez
+
+#ifndef CGAL_POLYHEDRON_CONNECTED_COMPONENTS_H
+#define CGAL_POLYHEDRON_CONNECTED_COMPONENTS_H
+
+#include <CGAL/Polyhedron_3.h>
+
+#include <map>
+#include <list>
+
+CGAL_BEGIN_NAMESPACE
+
+
+// ----------------------------------------------------------------------------
+// Private section
+// ----------------------------------------------------------------------------
+namespace CGALi {
+
+
+/// Get any vertex with tag == tag_value.
+///
+/// @commentheading Template Parameters:
+/// @param Polyhedron an instance of CGAL::Polyhedron_3<>.
+///
+/// @return a list of pairs (component size, a vertex of the component), 
+/// ordered by size.
+
+template<class Polyhedron> 
+typename Polyhedron::Vertex_handle 
+get_any_vertex_tag(Polyhedron& polyhedron, 
+                   std::map<typename Polyhedron::Vertex*, int>& tags, 
+                   const int tag_value)
+{
+    typedef typename Polyhedron::Vertex_handle Vertex_handle;
+    typedef typename Polyhedron::Vertex_iterator Vertex_iterator;
+
+    for (Vertex_iterator it = polyhedron.vertices_begin();
+         it != polyhedron.vertices_end();
+         it++)
+    {
+        if (tags[&*it] == tag_value)
+            return it;
+    }
+
+    return NULL;
+}
+
+/// Tag a "free" connected component as "done". 
+///
+/// @commentheading Template Parameters:
+/// @param Polyhedron an instance of CGAL::Polyhedron_3<>.
+///
+/// @return the size (number of vertices) of the component.
+template<class Polyhedron> 
+unsigned int tag_component(Polyhedron& polyhedron, 
+                           typename Polyhedron::Vertex_handle pSeedVertex,
+                           std::map<typename Polyhedron::Vertex*, int>& tags, 
+                           const int tag_free,
+                           const int tag_done)
+{
+    typedef typename Polyhedron::Vertex_handle Vertex_handle;
+    typedef typename Polyhedron::Vertex_iterator Vertex_iterator;
+    typedef typename Polyhedron::Halfedge_around_vertex_circulator 
+      Halfedge_around_vertex_circulator;
+
+    unsigned int number_of_vertices = 0; // size (number of vertices) of the component
+    
+    std::list<Vertex_handle> vertices;
+    vertices.push_front(pSeedVertex);
+    while (!vertices.empty())
+    {
+        Vertex_handle pVertex = vertices.front();
+        vertices.pop_front();
+
+        // Skip vertex if already done
+        if (tags[&*pVertex] == tag_done)
+            continue;
+
+        // Mark vertex done
+        tags[&*pVertex] = tag_done;
+        number_of_vertices++;
+
+        // Add free neighbors to the list
+        Halfedge_around_vertex_circulator cir, cir_end;
+        cir     = pVertex->vertex_begin();
+        cir_end = cir;
+        CGAL_For_all(cir,cir_end)
+        {
+            Vertex_handle neighbor = cir->opposite()->vertex();
+            if (tags[&*neighbor] == tag_free)
+                vertices.push_front(neighbor);
+        }
+    }
+    
+    return number_of_vertices;
+}
+
+
+} /* namespace CGALi */
+
+
+// ----------------------------------------------------------------------------
+// Public section
+// ----------------------------------------------------------------------------
+
+
+/// Compute the list of all connected components of a polyhedron.
+///
+/// @commentheading Template Parameters:
+/// @param Polyhedron an instance of CGAL::Polyhedron_3<> that supports positions.
+///
+/// @return a list of pairs (component size, a halfedge of the component), 
+/// ordered by size.
+
+template<class Polyhedron> 
+std::multimap<unsigned int, typename Polyhedron::Halfedge_handle>
+get_polyhedron_connected_components(Polyhedron& polyhedron)
+{
+    // Implementation note: 
+    // We tag vertices instead of halfedges to save a factor 6.
+    // The drawback is that we require the Polyhedron_3<> to support positions.
+    // TODO: replace std::map to tag vertices by a property map.
+    Assert_compile_time_tag(Polyhedron::Supports_halfedge_vertex(), Tag_true());
+    std::map<typename Polyhedron::Vertex*, int> tags;
+
+    typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
+    typedef typename Polyhedron::Vertex_handle Vertex_handle;
+    typedef typename Polyhedron::Vertex_iterator Vertex_iterator;
+
+    /// list of all connected components of a polyhedron, ordered by size.
+    std::multimap<unsigned int, Halfedge_handle> components;
+
+    // Tag all mesh vertices as "free".
+    const int tag_free = 0;
+    const int tag_done = 1;
+    for (Vertex_iterator it = polyhedron.vertices_begin();
+         it != polyhedron.vertices_end();
+         it++)
+    {
+         tags[&*it] = tag_free;
+    }
+
+    // For each component
+    Vertex_handle seed_vertex = NULL;
+    while((seed_vertex = CGALi::get_any_vertex_tag(polyhedron, tags, tag_free)) != NULL)
+    {
+        // Tag it as "done" and compute its size
+        unsigned int component_size = CGALi::tag_component(polyhedron, seed_vertex, tags, tag_free, tag_done);
+
+        // Add component to list, ordered by size
+        components.insert(std::make_pair(component_size, seed_vertex->halfedge()));
+    }
+    
+    return components;
+}
+
+
+CGAL_END_NAMESPACE
+
+#endif // CGAL_POLYHEDRON_CONNECTED_COMPONENTS_H
diff --git a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/APSS_reconstruction_test.cpp b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/APSS_reconstruction_test.cpp
index 5f3e16287df..e0f89e6fda5 100644
--- a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/APSS_reconstruction_test.cpp
+++ b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/APSS_reconstruction_test.cpp
@@ -11,6 +11,7 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Timer.h>
 #include <CGAL/Memory_sizer.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Surface_mesh_default_triangulation_3.h>
 #include <CGAL/make_surface_mesh.h>
@@ -21,7 +22,7 @@
 #include <CGAL/Point_with_normal_3.h>
 #include <CGAL/IO/read_xyz_point_set.h>
 
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 
 #include <deque>
 #include <cstdlib>
@@ -102,12 +103,13 @@ int main(int argc, char * argv[])
     PointList points;
 
     // If OFF file format
+    std::cerr << "Open " << input_filename << " for reading..." << std::endl;
     std::string extension = input_filename.substr(input_filename.find_last_of('.'));
     if (extension == ".off" || extension == ".OFF")
     {
       // Read the mesh file in a polyhedron
       std::ifstream stream(input_filename.c_str());
-      typedef Enriched_polyhedron<Kernel,Enriched_items> Polyhedron;
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
       CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
       if(!stream || !input_mesh.is_valid() || input_mesh.empty())
@@ -117,15 +119,13 @@ int main(int argc, char * argv[])
         continue;
       }
 
-      // Compute vertices' normals from connectivity
-      input_mesh.compute_normals();
-
-      // Convert vertices and normals to PointList
-      Polyhedron::Vertex_iterator v;
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
       for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         points.push_back(Point_with_normal(p,n));
       }
     }
diff --git a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/compute_normal.h b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/compute_normal.h
new file mode 100644
index 00000000000..3437332ab75
--- /dev/null
+++ b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/compute_normal.h
@@ -0,0 +1,45 @@
+#ifndef _COMPUTE_NORMAL_
+#define _COMPUTE_NORMAL_
+
+template <class Facet, class Kernel>
+typename Kernel::Vector_3 compute_facet_normal(const Facet& f)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Facet::Halfedge_around_facet_const_circulator HF_circulator;
+  Vector normal = CGAL::NULL_VECTOR;
+  HF_circulator he = f.facet_begin();
+  HF_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    const Point& prev = he->prev()->vertex()->point();
+    const Point& curr = he->vertex()->point();
+    const Point& next = he->next()->vertex()->point();
+    Vector n = CGAL::cross_product(next-curr,prev-curr);
+    normal = normal + (n / std::sqrt(n*n));
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+template <class Vertex, class Kernel>
+typename Kernel::Vector_3 compute_vertex_normal(const Vertex& v)
+{
+  typedef typename Kernel::Point_3 Point;
+  typedef typename Kernel::Vector_3 Vector;
+  typedef typename Vertex::Halfedge_around_vertex_const_circulator HV_circulator;
+  typedef typename Vertex::Facet Facet;
+  Vector normal = CGAL::NULL_VECTOR;
+  HV_circulator he = v.vertex_begin();
+  HV_circulator end = he;
+  CGAL_For_all(he,end)
+  {
+    if(!he->is_border())
+    {
+      Vector n = compute_facet_normal<Facet,Kernel>(*he->facet());
+      normal = normal + (n / std::sqrt(n*n));
+    }
+  }
+  return normal / std::sqrt(normal * normal);
+}
+
+#endif // _COMPUTE_NORMAL_
diff --git a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/enriched_polyhedron.h b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/enriched_polyhedron.h
deleted file mode 100644
index feab694e237..00000000000
--- a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/include/enriched_polyhedron.h
+++ /dev/null
@@ -1,247 +0,0 @@
-///////////////////////////////////////////////////////////////////////////
-//                                                                       //
-//  Class: Enriched_polyhedron                                           //
-//                                                                       //
-///////////////////////////////////////////////////////////////////////////
-
-#ifndef _POLYGON_MESH_
-#define _POLYGON_MESH_
-
-// CGAL
-#include <CGAL/Cartesian.h>
-#include <CGAL/Polyhedron_3.h>
-
-#include <list>
-
-// Forward declarations
-struct Vertex_normal;
-struct Facet_normal;
-
-
-// a refined facet with a normal
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_facet : public CGAL::HalfedgeDS_face_base<Refs, Tag>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_facet()
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-
-// a refined halfedge with a general tag
-template <class Refs, class Tprev, class Tvertex, class Tface, class Norm>
-class Enriched_halfedge : public CGAL::HalfedgeDS_halfedge_base<Refs,Tprev,Tvertex,Tface>
-{
-private:
-
-public:
-
-  // life cycle
-  Enriched_halfedge()
-  {
-  }
-};
-
-
-// a refined vertex with a normal, tag and camera
-template <class Refs, class Tag, class Point_3_, class Norm>
-class Enriched_vertex : public CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>
-{
-  // normal
-  Norm m_normal;
-
-public:
-  // life cycle
-  Enriched_vertex()  {}
-  // repeat mandatory constructors
-  Enriched_vertex(const Point_3_& pt)
-    : CGAL::HalfedgeDS_vertex_base<Refs, Tag, Point_3_>(pt)
-  {
-  }
-
-  // normal
-  typedef Norm Normal_3;
-  Normal_3& normal() { return m_normal; }
-  const Normal_3& normal() const { return m_normal; }
-};
-
-// A redefined items class for the Polyhedron_3
-// with a refined vertex class that contains a
-// member for the normal vector and a refined
-// facet with a normal vector instead of the
-// plane equation (this is an alternative
-// solution instead of using
-// Polyhedron_traits_with_normals_3).
-
-struct Enriched_items : public CGAL::Polyhedron_items_3
-{
-  // wrap vertex
-  template <class Refs, class Traits>
-  struct Vertex_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_vertex<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Vertex;
-  };
-
-  // wrap face
-  template <class Refs, class Traits>
-  struct Face_wrapper
-  {
-    typedef typename Traits::Point_3 Point;
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_facet<Refs,
-      CGAL::Tag_true,
-      Point,
-      Normal> Face;
-  };
-
-  // wrap halfedge
-  template <class Refs, class Traits>
-  struct Halfedge_wrapper
-  {
-    typedef typename Traits::Vector_3 Normal;
-    typedef Enriched_halfedge<Refs,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      CGAL::Tag_true,
-      Normal> Halfedge;
-  };
-};
-
-
-// Enriched polyhedron
-template <class PolyhedronTraits_3,
-          class PolyhedronItems_3 = Enriched_items>
-class Enriched_polyhedron
-  : public CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3>
-{
-  // Private types
-private:
-
-  typedef CGAL::Polyhedron_3<PolyhedronTraits_3, PolyhedronItems_3> Base;
-
-  // Public types
-public:
-
-  typedef typename PolyhedronTraits_3::FT FT;
-  typedef typename PolyhedronTraits_3::Point_3 Point;
-
-  // Repeat Polyhedron_3 public types
-  typedef typename Base::HalfedgeDS               HalfedgeDS;
-  typedef typename Base::Vertex                   Vertex;
-  typedef typename Base::Halfedge                 Halfedge;
-  typedef typename Base::Facet                    Facet;
-  typedef typename Base::Vertex_handle            Vertex_handle;
-  typedef typename Base::Vertex_const_handle      Vertex_const_handle;
-  typedef typename Base::Halfedge_handle          Halfedge_handle;
-  typedef typename Base::Halfedge_const_handle    Halfedge_const_handle;
-  typedef typename Base::Facet_handle             Facet_handle;
-  typedef typename Base::Facet_const_handle       Facet_const_handle;
-  typedef typename Base::Vertex_iterator          Vertex_iterator;
-  typedef typename Base::Vertex_const_iterator    Vertex_const_iterator;
-  typedef typename Base::Halfedge_iterator        Halfedge_iterator;
-  typedef typename Base::Halfedge_const_iterator  Halfedge_const_iterator;
-  typedef typename Base::Facet_iterator           Facet_iterator;
-  typedef typename Base::Facet_const_iterator     Facet_const_iterator;
-  typedef typename Base::Point_iterator           Point_iterator;
-  typedef typename Base::Point_const_iterator     Point_const_iterator;
-  typedef typename Base::Halfedge_around_facet_circulator         Halfedge_around_facet_circulator;
-  typedef typename Base::Halfedge_around_facet_const_circulator   Halfedge_around_facet_const_circulator;
-  typedef typename Base::Halfedge_around_vertex_circulator        Halfedge_around_vertex_circulator;
-  typedef typename Base::Halfedge_around_vertex_const_circulator  Halfedge_around_vertex_const_circulator;
-
-public :
-
-  // Default constructor, copy constructor and operator =() are fine.
-
-  // Repeat Delaunay_triangulation_3 public methods
-  Base::halfedges_begin;
-  Base::halfedges_end;
-  Base::facets_begin;
-  Base::facets_end;
-  Base::vertices_begin;
-  Base::vertices_end;
-
-  // Compute normals using mesh connectivity (per facet, then per vertex)
-  void compute_normals_per_facet()
-  {
-    std::for_each(facets_begin(),facets_end(),Facet_normal());
-  }
-  void compute_normals_per_vertex()
-  {
-    std::for_each(vertices_begin(),vertices_end(),Vertex_normal());
-  }
-  void compute_normals()
-  {
-    compute_normals_per_facet();
-    compute_normals_per_vertex();
-  }
-};
-
-// compute facet normal (functor)
-struct Facet_normal
-{
-  template <class Facet>
-  void operator()(Facet& f)
-  {
-    typename Facet::Normal_3 sum = CGAL::NULL_VECTOR;
-    typename Facet::Halfedge_around_facet_circulator h = f.facet_begin();
-    do
-    {
-      typename Facet::Normal_3 normal = CGAL::cross_product(
-        h->next()->vertex()->point() - h->vertex()->point(),
-        h->next()->next()->vertex()->point() - h->next()->vertex()->point());
-      double sqnorm = normal * normal;
-      if(sqnorm != 0)
-        normal = normal / (double)std::sqrt(sqnorm);
-      sum = sum + normal;
-    }
-    while(++h != f.facet_begin());
-    double sqnorm = sum * sum;
-    if(sqnorm != 0.0)
-      f.normal() = sum / std::sqrt(sqnorm);
-    else
-    {
-      f.normal() = CGAL::NULL_VECTOR;
-      std::cerr << "degenerate face\n";
-    }
-  }
-};
-
-
-// compute vertex normal (functor)
-struct Vertex_normal
-{
-  template <class Vertex>
-  void operator()(Vertex& v)
-  {
-    typename Vertex::Normal_3 normal = CGAL::NULL_VECTOR;
-    typename Vertex::Halfedge_around_vertex_const_circulator pHalfedge = v.vertex_begin();
-    typename Vertex::Halfedge_around_vertex_const_circulator begin = pHalfedge;
-    CGAL_For_all(pHalfedge,begin)
-      if(!pHalfedge->is_border())
-        normal = normal + pHalfedge->facet()->normal();
-    double sqnorm = normal * normal;
-    if(sqnorm != 0.0f)
-      v.normal() = normal / (float)std::sqrt(sqnorm);
-    else
-      v.normal() = CGAL::NULL_VECTOR;
-  }
-};
-
-
-#endif // _POLYGON_MESH_
diff --git a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/poisson_reconstruction_test.cpp b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/poisson_reconstruction_test.cpp
index d3c8cf833ad..5adac1f9588 100644
--- a/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/poisson_reconstruction_test.cpp
+++ b/Surface_reconstruction_points_3/test/Surface_reconstruction_points_3/poisson_reconstruction_test.cpp
@@ -11,6 +11,7 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Timer.h>
 #include <CGAL/Memory_sizer.h>
+#include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/Surface_mesh_default_triangulation_3.h>
 #include <CGAL/make_surface_mesh.h>
@@ -21,7 +22,7 @@
 #include <CGAL/Point_with_normal_3.h>
 #include <CGAL/IO/read_xyz_point_set.h>
 
-#include "enriched_polyhedron.h"
+#include "compute_normal.h"
 
 #include <deque>
 #include <cstdlib>
@@ -101,12 +102,13 @@ int main(int argc, char * argv[])
     PointList points;
 
     // If OFF file format
+    std::cerr << "Open " << input_filename << " for reading..." << std::endl;
     std::string extension = input_filename.substr(input_filename.find_last_of('.'));
     if (extension == ".off" || extension == ".OFF")
     {
       // Read the mesh file in a polyhedron
       std::ifstream stream(input_filename.c_str());
-      typedef Enriched_polyhedron<Kernel,Enriched_items> Polyhedron;
+      typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
       Polyhedron input_mesh;
       CGAL::scan_OFF(stream, input_mesh, true /* verbose */);
       if(!stream || !input_mesh.is_valid() || input_mesh.empty())
@@ -116,15 +118,13 @@ int main(int argc, char * argv[])
         continue;
       }
 
-      // Compute vertices' normals from connectivity
-      input_mesh.compute_normals();
-
-      // Convert vertices and normals to PointList
-      Polyhedron::Vertex_iterator v;
+      // Convert Polyhedron vertices to point set.
+      // Compute vertices' normals from connectivity.
+      Polyhedron::Vertex_const_iterator v;
       for (v = input_mesh.vertices_begin(); v != input_mesh.vertices_end(); v++)
       {
         const Point& p = v->point();
-        const Vector& n = v->normal();
+        Vector n = compute_vertex_normal<Polyhedron::Vertex,Kernel>(*v);
         points.push_back(Point_with_normal(p,n));
       }
     }