diff --git a/Packages/Interpolation/include/CGAL/Regular_neighbor_coordinates_traits_2.h b/Packages/Interpolation/include/CGAL/Regular_neighbor_coordinates_traits_2.h
index 5ba3bc7e005..9fb16779393 100644
--- a/Packages/Interpolation/include/CGAL/Regular_neighbor_coordinates_traits_2.h
+++ b/Packages/Interpolation/include/CGAL/Regular_neighbor_coordinates_traits_2.h
@@ -33,16 +33,10 @@ class Regular_neighbor_coordinates_traits_2
 public:
   typedef R                                     Rep;
   typedef typename R::FT                        FT;
-
   typedef typename Rep::Compute_area_2          Compute_area_2;
-  typedef typename Rep::Construct_triangle_2    Construct_triangle_2;
-
+ 
   Compute_area_2 compute_area_2_object() const
     {return Compute_area_2();}
-  
-  Construct_triangle_2 construct_triangle_2_object() const
-    {return Construct_triangle_2();}
-
 };
  
 CGAL_END_NAMESPACE
diff --git a/Packages/Interpolation/include/CGAL/interpolation_functions.h b/Packages/Interpolation/include/CGAL/interpolation_functions.h
index 2884e56a2ad..541fcbb067c 100644
--- a/Packages/Interpolation/include/CGAL/interpolation_functions.h
+++ b/Packages/Interpolation/include/CGAL/interpolation_functions.h
@@ -30,12 +30,12 @@ template< class Map >
 struct Data_access : public std::unary_function< typename Map::key_type,
 		     std::pair< typename Map::mapped_type, bool> > {
   typedef typename Map::mapped_type Data_type;
-  typedef typename Map::key_type  Point;
+  typedef typename Map::key_type  Key_type;
   
   Data_access< Map >(const Map& m): map(m){};
   
   std::pair< Data_type, bool> 
-  operator()(const Point& p) { 
+  operator()(const Key_type& p) { 
     typename Map::const_iterator mit = map.find(p);
     if(mit!= map.end())
       return std::make_pair(mit->second, true);
diff --git a/Packages/Interpolation/include/CGAL/regular_neighbor_coordinates_2.h b/Packages/Interpolation/include/CGAL/regular_neighbor_coordinates_2.h
index 82db1919dff..3e9e33caced 100644
--- a/Packages/Interpolation/include/CGAL/regular_neighbor_coordinates_2.h
+++ b/Packages/Interpolation/include/CGAL/regular_neighbor_coordinates_2.h
@@ -27,7 +27,7 @@ CGAL_BEGIN_NAMESPACE
 //-------------------------------------------------------------------
 
 template <class Rt, class OutputIterator>
-std::pair< OutputIterator, typename Rt::Geom_traits::Rep::FT > 
+std::pair< OutputIterator, typename Rt::Geom_traits::FT > 
 regular_neighbor_coordinates_2(const Rt& rt, 
 			       const typename Rt::Geom_traits::
 			       Weighted_point& p, 
@@ -38,7 +38,7 @@ regular_neighbor_coordinates_2(const Rt& rt,
 };
   
 template <class Rt, class OutputIterator, class Traits>
-std::pair< OutputIterator, typename Rt::Geom_traits::Rep::FT > 
+std::pair< OutputIterator, typename Traits::FT > 
 regular_neighbor_coordinates_2(const Rt& rt, 
 			       const typename Rt::Geom_traits::
 			       Weighted_point& p, 
@@ -51,13 +51,13 @@ regular_neighbor_coordinates_2(const Rt& rt,
 };
 
 template <class Rt, class OutputIterator, class Traits>
-std::pair< OutputIterator, typename Traits::Rep::FT > 
+std::pair< OutputIterator, typename Traits::FT > 
 regular_neighbor_coordinates_2(const Rt& rt,
 			     const typename Traits::Weighted_point& p, 
 			     OutputIterator out, const Traits& traits, 
 		 	     typename Rt::Face_handle start){
   
-  typedef typename Traits::Rep::FT            Coord_type;
+  typedef typename Traits::FT            Coord_type;
   typedef typename Traits::Weighted_point  Weighted_point;
   
   typedef typename Rt::Vertex_handle     Vertex_handle;
@@ -104,7 +104,7 @@ regular_neighbor_coordinates_2(const Rt& rt,
 
 template <class Rt, class OutputIterator, class Traits, class
 EdgeIterator, class VertexIterator  >
-std::pair< OutputIterator, typename Traits::Rep::FT > 
+std::pair< OutputIterator, typename Traits::FT > 
 regular_neighbor_coordinates_2(const Rt& rt, 
 			       const typename Traits::Weighted_point& p, 
 			       OutputIterator out, EdgeIterator
@@ -117,14 +117,13 @@ regular_neighbor_coordinates_2(const Rt& rt,
   //               (=^ inside convex hull of neighbors)
   CGAL_precondition(rt.dimension()==2);
 
-  typedef typename Traits::Rep::FT         Coord_type;
+  typedef typename Traits::FT         Coord_type;
   typedef typename Traits::Bare_point      Bare_point;
   typedef typename Traits::Weighted_point  Weighted_point;
   
   typedef typename Rt::Vertex_handle     Vertex_handle;
   typedef typename Rt::Face_circulator   Face_circulator;
   
-
   //no hole because only (exactly!) one vertex is hidden:
   if(hole_begin==hole_end){
     *out++= std::make_pair((*hidden_vertices_begin)->point(),