diff --git a/.gitattributes b/.gitattributes
index a9f9783a8b7..7736239ca11 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -441,6 +441,7 @@ Developers_manual/doc_tex/Developers_manual/fig/reference_counting.pdf -text svn
 Developers_manual/doc_tex/Developers_manual/fig/use_real.eps -text
 Developers_manual/doc_tex/Developers_manual/fig/use_real.gif -text svneol=unset#unset
 Developers_manual/doc_tex/Developers_manual/fig/use_real.pdf -text svneol=unset#unset
+Envelope_3/examples/Envelope_3/make_xy_mon.C -text
 ExternalMemoryStructures/doc_tex/ExternalMemoryStructures/ExternalMemoryStructures_ref/rtree-classes4.eps -text
 ExternalMemoryStructures/doc_tex/ExternalMemoryStructures/ExternalMemoryStructures_ref/rtree-classes4.fig -text
 ExternalMemoryStructures/doc_tex/ExternalMemoryStructures/ExternalMemoryStructures_ref/rtree-classes4.gif -text svneol=unset#unset
diff --git a/Envelope_3/examples/Envelope_3/make_xy_mon.C b/Envelope_3/examples/Envelope_3/make_xy_mon.C
new file mode 100644
index 00000000000..8edcfca454b
--- /dev/null
+++ b/Envelope_3/examples/Envelope_3/make_xy_mon.C
@@ -0,0 +1,446 @@
+
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <stdlib.h>
+#include <stdio.h>
+
+
+
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Quotient.h>
+#include <CGAL/MP_Float.h>
+#include <CGAL/Polyhedron_3.h>
+#include <CGAL/IO/Polyhedron_iostream.h> 
+
+#include <queue>
+#include <list>
+#include <vector>
+#include <CGAL/Unique_hash_map.h> 
+#include <CGAL/Arr_segment_traits_2.h>
+#include <CGAL/Sweep_line_2_algorithms.h>
+#include <CGAL/Timer.h>
+
+#include <CGAL/Arrangement_2.h>
+#include <CGAL/Arr_segment_traits_2.h>
+#include <CGAL/IO/Arr_iostream.h>
+
+//typedef double                                    NT;
+typedef CGAL::Quotient<CGAL::MP_Float>            NT;
+typedef CGAL::Simple_cartesian<NT>                Kernel;
+typedef Kernel::RT                                RT;
+typedef Kernel::Point_3                           Point_3; 
+typedef Kernel::Point_2                           Point_2;
+typedef Kernel::Plane_3                           Plane_3;
+typedef Kernel::Line_2                            Line_2;
+typedef CGAL::Polyhedron_3<Kernel>                Polyhedron;
+typedef Polyhedron::Halfedge_const_handle         Halfedge_const_handle;
+typedef Polyhedron::Facet_const_iterator          Facet_const_iterator;
+typedef Polyhedron::Halfedge_around_facet_const_circulator 
+  Halfedge_around_facet_const_circulator;
+
+typedef Kernel::Oriented_side_2                   Oriented_side_2;
+typedef Kernel::Construct_line_2                  Construct_line_2;
+typedef Kernel::Construct_projected_xy_point_2    
+  Construct_projected_xy_point_2;
+typedef Kernel::Construct_plane_3                 Construct_plane_3;
+typedef CGAL::Arr_segment_traits_2<Kernel>        Traits_2;
+typedef Traits_2::X_monotone_curve_2              X_monotone_curve_2;
+typedef CGAL::Arrangement_2<Traits_2>             Arrangement_2;
+typedef Arrangement_2::Halfedge_handle            Arr_halfedge;
+
+
+class Make_xy_monotone
+{
+protected:
+  typedef std::list<Arrangement_2*>      XY_surfaces_list;
+
+  std::queue<Facet_const_iterator>                             m_queue;
+  CGAL::Unique_hash_map<Facet_const_iterator, bool>            m_status_map;
+  CGAL::Unique_hash_map<Halfedge_const_handle, Arr_halfedge>   m_edges_map;
+
+public:
+ 
+  void operator()(const Polyhedron& p, XY_surfaces_list& xy_surfaces)
+  {
+    m_status_map = 
+      CGAL::Unique_hash_map<Facet_const_iterator, bool>(false, p.size_of_facets());
+
+    m_edges_map = CGAL::Unique_hash_map<Halfedge_const_handle,
+                                        Arr_halfedge>(Arr_halfedge());
+
+    for (Facet_const_iterator f = p.facets_begin(); f != p.facets_end(); ++f)
+    {
+      if (! m_status_map[f])
+        bfs(f, xy_surfaces);
+    }
+  }
+
+  void bfs(Facet_const_iterator f, XY_surfaces_list& xy_surfaces)
+  {
+    m_edges_map.clear(); // clear the previous data of the edges map
+    
+    m_status_map[f] = true;
+    if(is_vertical(f))
+      return;
+
+    Arrangement_2* arr = new Arrangement_2;
+    xy_surfaces.push_back(arr);
+    m_queue.push(f);
+    while(!m_queue.empty())
+    {
+      f = m_queue.front();
+      m_queue.pop();
+
+      // add f to current xy_surface
+      add_facet_to_arr(*arr, f);
+      Halfedge_around_facet_const_circulator haf = f->facet_begin();
+      Halfedge_around_facet_const_circulator curr = haf;
+      do
+      {
+        if(curr->opposite()->is_border())
+        {
+          ++curr;
+          continue;
+        }
+        Facet_const_iterator neighbour_f = curr->opposite()->face();
+
+        bool& is_done = m_status_map[neighbour_f];
+        if (!is_done)
+        {
+          if(is_vertical(neighbour_f))
+          {
+            is_done = true;
+          }
+          else
+            if(are_xy_mon(curr, f, neighbour_f))
+            {
+              is_done = true;
+              m_queue.push(neighbour_f);
+            }
+        }
+            
+        ++curr;
+      } while(curr != haf);
+    }
+  }
+
+  bool is_vertical(Facet_const_iterator f)
+  {
+    CGAL_assertion(f->facet_degree() > 2);
+    Halfedge_const_handle he = f->halfedge();
+    const Point_3& p1 = he->vertex()->point();
+    const Point_3& p2 = he->next()->vertex()->point();
+    const Point_3& p3 = he->next()->next()->vertex()->point();
+    Kernel k;
+    return (k.collinear_2_object()(project_xy(p1),
+                                   project_xy(p2),
+                                   project_xy(p3)));
+  }
+  bool are_xy_mon(Halfedge_const_handle he, Facet_const_iterator f1, Facet_const_iterator f2)
+  {
+    /*
+     *                    t
+     *                   *|*
+     *                  * | *
+     *                 * ^|  *
+     *                *  ||   *
+     *            p1 * he||    * p2
+     *               * f1|| f2 *
+     *                *  ||   *
+     *                 *  |  *
+     *                  * | *
+     *                   *|*
+     *                    s
+     */
+
+    CGAL_assertion(!is_vertical(f1) && !is_vertical(f2));
+    
+    const Point_2& s = project_xy(he->opposite()->vertex()->point());
+    const Point_2& t = project_xy(he->vertex()->point());
+
+    const Point_2& p1 = project_xy(he->next()->vertex()->point());
+    const Point_2& p2 = project_xy(he->opposite()->next()->vertex()->point());
+
+    Kernel k;
+    Line_2 l = k.construct_line_2_object()(s, t); 
+    CGAL::Oriented_side os1, os2;
+
+    os1 = k.oriented_side_2_object()(l, p1);
+    os2 = k.oriented_side_2_object()(l, p2);
+
+    CGAL_assertion(os1 != CGAL::ON_ORIENTED_BOUNDARY &&
+                   os2 != CGAL::ON_ORIENTED_BOUNDARY);
+
+    return (os1 != os2);
+  }
+
+
+  /*Point_2  project_xy (const Point_3& p)
+  {
+    Kernel k;
+    Plane_3 xy_plane = k.construct_plane_3_object()(RT(0), RT(0), RT(1), RT(0));
+    return (k.construct_projected_xy_point_2_object()(xy_plane, p));
+  }*/
+
+  Point_2  project_xy (const Point_3& p)
+  {
+    return (Point_2(p.x(), p.y()));
+  }
+
+  bool is_back_facet(Facet_const_iterator f)
+  {
+    Kernel k;
+    Plane_3 supp_plane =
+      k.construct_plane_3_object()(f->halfedge()->vertex()->point(),
+                                   f->halfedge()->next()->vertex()->point(),
+                                   f->halfedge()->next()->next()->vertex()->point());
+
+    return (supp_plane.c() > 0);
+  }
+
+  void add_facet_to_arr(Arrangement_2& arr, Facet_const_iterator f)
+  {
+    //static int i=1;
+    bool is_back = is_back_facet(f);
+    Halfedge_around_facet_const_circulator haf = f->facet_begin();
+    Halfedge_around_facet_const_circulator curr = haf;
+
+    Kernel k;
+    do
+    {
+      Halfedge_const_handle he = curr;
+      
+      // look for that polyhedron's halfedge at the edges map
+      Arr_halfedge arr_he = m_edges_map[he->opposite()];
+      Arr_halfedge prev_he; 
+
+      if(arr_he == Arr_halfedge())
+      {
+        // this edge was not inserted to the arrangement yet
+
+        const Point_2& s = project_xy(curr->opposite()->vertex()->point());
+        const Point_2& t = project_xy(curr->vertex()->point());
+
+        X_monotone_curve_2 cv(s, t);
+
+        Arr_halfedge next_he = find_halfedge_before_cw(he, is_back);
+        if(prev_he == Arr_halfedge())
+          prev_he = find_halfedge_before_cw(he->opposite(), is_back);
+
+        bool next_exist = (next_he!=Arr_halfedge());
+        bool prev_exist = (prev_he!=Arr_halfedge());
+
+        CGAL::Comparison_result res = k.compare_xy_2_object()(s, t);
+
+        if(!next_exist && !prev_exist)
+        {
+          //std::cout<<"("<<i++<<")"<<"insert_in_face_interior: " << cv<<"\n";
+          prev_he = arr.insert_in_face_interior(cv, arr.unbounded_face());
+          if(prev_he->direction() != res)
+            prev_he = prev_he->twin();
+        }
+        else
+          if(!next_exist && prev_exist)
+          {
+            if(res == CGAL::SMALLER)
+            {
+              //std::cout<<"("<<i++<<")"<<"insert_from_left_vertex: " << cv<<"\n";
+              prev_he = arr.insert_from_left_vertex(cv, prev_he);
+              if(prev_he->direction() != res)
+                prev_he = prev_he->twin();
+            }
+            else
+            {
+              //std::cout<<"("<<i++<<")"<<"insert_from_right_vertex: " << cv<<"\n";
+              prev_he = arr.insert_from_right_vertex(cv, prev_he);
+              if(prev_he->direction() != res)
+                prev_he = prev_he->twin();
+            }
+          }
+          else
+            if(next_exist && !prev_exist)
+            {
+              if(res == CGAL::SMALLER)
+              {
+               // std::cout<<"("<<i++<<")"<<"insert_from_right_vertex: " << cv<<"\n";
+                prev_he = arr.insert_from_right_vertex(cv, next_he);
+                if(prev_he->direction() != res)
+                  prev_he = prev_he->twin();
+              }
+              else
+              {
+                //std::cout<<"("<<i++<<")"<<"insert_from_left_vertex: " << cv<<"\n";
+                prev_he = arr.insert_from_left_vertex(cv, next_he);
+                if(prev_he->direction() != res)
+                  prev_he = prev_he->twin();
+              }
+            }
+            else
+            {
+              //std::cout<<"("<<i++<<")"<<"insert_at_vertices: " << cv<<"\n";
+              //std::cout<<"prev_he: " <<prev_he->source()->point()<<" --> "<< prev_he->target()->point()<<"\n";
+              //std::cout<<"next_he: " <<next_he->source()->point()<<" --> "<< next_he->target()->point()<<"\n";
+              //TODO: can be done much more efficient using the Arr_accessor !!
+              prev_he = arr.insert_at_vertices(cv, prev_he, next_he);
+              if(prev_he->direction() != res)
+                prev_he = prev_he->twin();
+            }
+        //map 'he' of the polyhderon to 'prev_he'
+        m_edges_map[he] = prev_he;
+      }
+      else
+      {
+        prev_he = arr_he->twin();
+      }
+
+      CGAL_assertion(prev_he->source()->point() ==
+                     project_xy(he->opposite()->vertex()->point()));
+      CGAL_assertion(prev_he->target()->point() ==
+                     project_xy(he->vertex()->point()));
+
+     
+      ++curr;
+    } while(curr != haf);
+    
+
+  }
+
+  Arr_halfedge find_halfedge_before_cw(Halfedge_const_handle he, bool is_back_face)
+  {
+    // iterate the halfedges around the target vertex of 'he' counter-clockwise
+    // and find the first halfedge that was inserterd to the arrangement.
+    Halfedge_const_handle curr;
+    if(is_back_face)
+      curr = he->prev_on_vertex();
+    else
+      curr = he->next_on_vertex();
+    do
+    {
+      Arr_halfedge res = m_edges_map[curr];
+      if(res != Arr_halfedge())
+        return res;
+
+      res = m_edges_map[curr->opposite()];
+      if(res != Arr_halfedge())
+        return res->twin();
+
+      if(is_back_face)
+        curr = curr->prev_on_vertex();
+      else
+        curr = curr->next_on_vertex();
+    } while(curr != he);
+
+    return Arr_halfedge();
+  }
+
+};
+
+Point_2  project_xy (const Point_3& p)
+{
+  return (Point_2(p.x(), p.y()));
+}
+
+bool test_xy_mon(std::vector<Facet_const_iterator>& surf)
+{
+  CGAL::Unique_hash_map<Halfedge_const_handle, bool> edges_hash(false);
+  typedef CGAL::Arr_segment_traits_2<Kernel>   Traits;
+  typedef  Traits::Curve_2  Curve_2;
+  std::list<Curve_2>  curves;
+  for(unsigned int i=0; i< surf.size(); ++i)
+  {
+    Facet_const_iterator curr_f = surf[i];
+    Halfedge_around_facet_const_circulator haf = curr_f->facet_begin();
+    Halfedge_around_facet_const_circulator curr = haf;
+    do
+    {
+      Halfedge_const_handle he = curr;
+      if(!edges_hash[he] && !edges_hash[he->opposite()])
+      {
+        Curve_2 cv(project_xy(he->vertex()->point()),
+                   project_xy(he->opposite()->vertex()->point()));
+        curves.push_back(cv);
+        edges_hash[he] = edges_hash[he->opposite()] = true;
+      }
+      
+      ++curr;
+    }while(curr != haf);
+  }
+
+  bool do_x = CGAL::do_curves_intersect(curves.begin(), curves.end());
+  return (!do_x);
+}
+int main(int argc, char** argv)
+{
+  if(argc<2)
+  {
+    std::cout<<"Missing off file\n";
+    return (-1);
+  }
+
+  std::ifstream off_file(argv[1]);
+  if(!off_file.is_open())
+  {
+    std::cout<<"Failed to open file\n";
+    return (-1);
+  }
+
+  CGAL::Timer t;
+  Polyhedron p;
+  //off_file >> p;
+  // reads a polyhedron from `in' and appends it to P.
+  t.start();
+  CGAL::scan_OFF(off_file, p, true);
+  t.stop();
+
+  if ( (off_file.rdstate() & std::ios::badbit ) != 0 )
+    std::cerr << "Error opening "<<argv[1] <<"\n";
+
+  std::cout<<"Reading OFF file took: " <<t.time()<<" seconds\n";
+  t.reset();
+  if(p.empty())
+    return 0;
+
+  Facet_const_iterator f = p.facets_begin();
+
+  std::cout << "|V| = " <<p.size_of_vertices()<<std::endl;
+  std::cout << "|E| = " <<p.size_of_halfedges()<<std::endl;
+  std::cout << "|F| = " <<p.size_of_facets()<<std::endl;
+
+  std::list<Arrangement_2*> xy_surfs;
+  typedef std::list<Arrangement_2*>::iterator Xy_surf_itr;
+  Make_xy_monotone make_xy;
+  t.start();
+  make_xy(p, xy_surfs);
+  t.stop();
+  std::cout<<"Making the surface xy-monotone took: " <<t.time()<<" seconds\n";
+
+
+  std::cout<<"There are: " << xy_surfs.size() << " xy-surfaces\n";
+  unsigned int i=1;
+  for(Xy_surf_itr itr = xy_surfs.begin(); itr != xy_surfs.end(); ++itr, ++i)
+  {
+    std::cout<<"#" <<i<<" surface : "<<std::endl;
+    std::cout<<"  |V| = "<<(*itr)->number_of_vertices()<<std::endl;
+    std::cout<<"  |E| = "<<(*itr)->number_of_edges()<<std::endl;
+    std::cout<<"  |F| = "<<(*itr)->number_of_faces()<<std::endl;
+
+    char buffer[33];
+    buffer[0] = '1' + i-1;
+    buffer[1] = '\0';
+    std::string prog_name (argv[1]);
+    std::string filename("surface");
+    std::string prefix (buffer);
+    std::string temp(".arr");
+    prefix += temp;
+    filename += prefix; 
+    std::cout << filename<<"\n";
+    std::ofstream arr_file(filename.c_str());
+    if(!arr_file.is_open())
+      std::cout<<"Failed to open: " << filename<<"\n";
+    arr_file << **itr;
+
+  }
+
+  return (0);
+}