diff --git a/Polyhedron/demo/Polyhedron/MainWindow_remeshing.cpp b/Polyhedron/demo/Polyhedron/MainWindow_remeshing.cpp
index 47e00c683cc..636a44d367d 100644
--- a/Polyhedron/demo/Polyhedron/MainWindow_remeshing.cpp
+++ b/Polyhedron/demo/Polyhedron/MainWindow_remeshing.cpp
@@ -82,14 +82,14 @@ void MainWindow::on_actionRemeshing_triggered()
     QTime time;
     time.start();
     std::cout << "Build AABB tree...";
-    typedef CGAL::Simple_cartesian<double> Simple_cartesian_kernel; 
+    typedef CGAL::Cartesian<double> Cartesian_kernel; 
     typedef CGAL::AABB_tree<GT,Polyhedron::Facet_handle,Polyhedron> Tree;
     Tree tree;
     tree.build_faces(*pMesh);
     std::cout << "done (" << time.elapsed() << " ms)" << std::endl;
 
     // input surface
-    typedef CGAL::AABB_polyhedral_oracle<Polyhedron,GT> Input_surface;
+    typedef CGAL::AABB_polyhedral_oracle<Polyhedron,GT,GT> Input_surface;
     Input_surface input(&tree);
 
     // initial point set
@@ -97,11 +97,13 @@ void MainWindow::on_actionRemeshing_triggered()
     std::cout << "Insert initial point set...";
     unsigned int nb_initial_points = 10;
     Polyhedron::Point_iterator it;
+    typedef CGAL::Cartesian_converter<Kernel,GT> Converter;
+    Converter convert;
     unsigned int i = 0;
     for(it = pMesh->points_begin();
         it != pMesh->points_end(), i < nb_initial_points;
 	it++, i++)
-      tr.insert(*it);
+      tr.insert(convert(*it));
     std::cout << "done (" << time.elapsed() << " ms)" << std::endl;
 
     // remesh
diff --git a/Polyhedron/demo/Polyhedron/Polyhedron_type.h b/Polyhedron/demo/Polyhedron/Polyhedron_type.h
index 0bec542bbd9..b018a4033f1 100644
--- a/Polyhedron/demo/Polyhedron/Polyhedron_type.h
+++ b/Polyhedron/demo/Polyhedron/Polyhedron_type.h
@@ -11,7 +11,6 @@
 
 #include "Polyhedron_type_fwd.h"
 
-//typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::FT FT;
 typedef Kernel::Line_3 Line;
 typedef Kernel::Point_3 Point;
@@ -21,7 +20,6 @@ typedef Kernel::Vector_3 Vector;
 typedef Kernel::Triangle_3 Triangle;
 typedef Kernel::Iso_cuboid_3 Iso_cuboid;
 
-// struct Polyhedron : public CGAL::Polyhedron_3<Kernel> {};
 typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 
 #endif // POLYHEDRON_TYPE_H
diff --git a/Polyhedron/demo/Polyhedron/Polyhedron_type_fwd.h b/Polyhedron/demo/Polyhedron/Polyhedron_type_fwd.h
index b0e39a48068..17e47db0717 100644
--- a/Polyhedron/demo/Polyhedron/Polyhedron_type_fwd.h
+++ b/Polyhedron/demo/Polyhedron/Polyhedron_type_fwd.h
@@ -3,10 +3,12 @@
 
 
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Cartesian.h>
 #include <memory>
 
-
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
+// typedef CGAL::Cartesian<double> Kernel;
+
 //struct Kernel;
 namespace CGAL {
   class Polyhedron_items_3;
diff --git a/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_node.h b/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_node.h
index 68a97c3406a..3f4c6ebcd0f 100644
--- a/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_node.h
+++ b/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_node.h
@@ -39,8 +39,10 @@ public:
   typedef std::pair<Point, Input> Point_with_input;
 
   typedef typename PSC::Traits PSC_kernel;
-  typedef typename PSC_kernel::Point_3 PSC_Point;
-  //typedef CGAL::Cartesian_converter<PSC_kernel, Kernel > Converter;
+  typedef typename PSC_kernel::Point_3 PSC_point;
+  typedef typename PSC_kernel::Vector_3 PSC_vector;
+  typedef typename PSC_kernel::Triangle_3 PSC_triangle;
+  typedef CGAL::Cartesian_converter<PSC_kernel, Kernel > Converter;
 
 private:
 
@@ -88,10 +90,9 @@ private:
 
   Bbox compute_bbox(Input f)
   {
-    // Converter convert;
-    const Point a = f->halfedge()->vertex()->point();
-    const Point b = f->halfedge()->next()->vertex()->point();
-    const Point c = f->halfedge()->next()->next()->vertex()->point();
+    const PSC_point a = f->halfedge()->vertex()->point();
+    const PSC_point b = f->halfedge()->next()->vertex()->point();
+    const PSC_point c = f->halfedge()->next()->next()->vertex()->point();
     return a.bbox() + b.bbox() + c.bbox();
   }
 
@@ -138,15 +139,15 @@ private:
 
   static Point centroid(Input f)
   {
-    //Converter convert;
-    const Point a = f->halfedge()->vertex()->point();
-    const Point b = f->halfedge()->next()->vertex()->point();
-    const Point c = f->halfedge()->next()->next()->vertex()->point();
+    const PSC_point a = f->halfedge()->vertex()->point();
+    const PSC_point b = f->halfedge()->next()->vertex()->point();
+    const PSC_point c = f->halfedge()->next()->next()->vertex()->point();
     // somehow CGAL::centroid does not compile
-    Vector u = a - CGAL::ORIGIN;
-    Vector v = b - CGAL::ORIGIN;
-    Vector w = c - CGAL::ORIGIN;
-    return CGAL::ORIGIN + (u + v + w) / 3.0;
+    PSC_vector u = a - CGAL::ORIGIN;
+    PSC_vector v = b - CGAL::ORIGIN;
+    PSC_vector w = c - CGAL::ORIGIN;
+    Converter convert;
+    return convert(CGAL::ORIGIN + (u + v + w) / 3.0);
   }
 
   template<typename Input_>
@@ -330,11 +331,11 @@ public:
 
   static Triangle triangle(Input f)
   {
-    // Converter convert;
-    const Point a = f->halfedge()->vertex()->point();
-    const Point b = f->halfedge()->next()->vertex()->point();
-    const Point c = f->halfedge()->next()->next()->vertex()->point();
-    return Triangle(a,b,c);
+    Converter convert;
+    const PSC_point a = f->halfedge()->vertex()->point();
+    const PSC_point b = f->halfedge()->next()->vertex()->point();
+    const PSC_point c = f->halfedge()->next()->next()->vertex()->point();
+    return convert(PSC_triangle(a,b,c));
   }
 
   static bool do_intersect(const Segment& segment, Input f)
diff --git a/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_polyhedral_oracle.h b/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_polyhedral_oracle.h
index a4a5ce90291..41196c05dac 100644
--- a/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_polyhedral_oracle.h
+++ b/Polyhedron/demo/Polyhedron/include/CGAL/Collisions/AABB_polyhedral_oracle.h
@@ -9,7 +9,7 @@
 
 namespace CGAL {
 
-template <class Polyhedron, class Kernel>
+template <class Polyhedron, class Kernel, class AABBTree_kernel>
 class AABB_polyhedral_oracle : public Polyhedron
 {
 public:
@@ -19,15 +19,15 @@ public:
   typedef typename Kernel::Point_3 Point_3;
   typedef typename Kernel::Segment_3 Segment_3;
 
-  typedef AABB_polyhedral_oracle<Polyhedron,Kernel> Self;
+  typedef AABB_polyhedral_oracle<Polyhedron,Kernel,AABBTree_kernel> Self;
   typedef Self Surface_mesher_traits_3;
   typedef Point_3 Intersection_point;
   typedef Self Surface_3;
 
   // AABB tree
-  typedef AABB_tree<Kernel,typename Polyhedron::Facet_handle,Polyhedron> Tree;
+  typedef AABB_tree<AABBTree_kernel,typename Polyhedron::Facet_handle,Polyhedron> Tree;
   typedef typename Tree::Point_with_input Point_with_facet_handle;
-  // typedef CGAL::Cartesian_converter<Kernel,Tree_kernel> Converter;
+  typedef CGAL::Cartesian_converter<Kernel,AABBTree_kernel> Converter;
   Tree *m_pTree;
 
 public:
@@ -60,9 +60,9 @@ public:
 
     Object operator()(const Surface_3& surface, const Segment_3& segment) const
     {
-      //Converter convert;
+      Converter convert;
       Point_with_facet_handle pwh;
-      if(surface.tree()->first_intersection(segment,pwh))
+      if(surface.tree()->first_intersection(convert(segment),pwh))
 	return make_object(pwh.first);
       else
 	return Object();
@@ -70,9 +70,9 @@ public:
     
     Object operator()(const Surface_3& surface, const Ray_3& ray) const
     {
-      //Converter convert;
+      Converter convert;
       Point_with_facet_handle pwh;
-      if(surface.tree()->first_intersection(ray,pwh))
+      if(surface.tree()->first_intersection(convert(ray),pwh))
 	return make_object(pwh.first);
       else
 	return Object();
@@ -80,9 +80,9 @@ public:
       
     Object operator()(const Surface_3& surface, const Line_3& line) const
     {
-      //Converter convert;
+      Converter convert;
       Point_with_facet_handle pwh;
-      if(surface.tree()->first_intersection(line,pwh))
+      if(surface.tree()->first_intersection(convert(line),pwh))
 	return make_object(pwh.first);
       else
 	return Object();