diff --git a/.gitattributes b/.gitattributes
index cf388fd4e15..7f5671cf71e 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -1798,7 +1798,6 @@ Intersections_2/include/CGAL/Intersection_traits_2.h -text
 Intersections_3/include/CGAL/Intersection_traits_3.h -text
 Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h -text
 Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h -text
-Intersections_3/include/CGAL/intersection_3_0.h -text
 Intersections_3/test/Intersections_3/call_test.cpp -text
 Intersections_3/test/Intersections_3/segment_segment.cpp -text
 Intersections_3/test/Intersections_3/triangle_3_triangle_3_intersection.cpp -text
diff --git a/Intersections_2/include/CGAL/Intersection_traits.h b/Intersections_2/include/CGAL/Intersection_traits.h
index 698cbe28dcd..c9e0e7c4702 100644
--- a/Intersections_2/include/CGAL/Intersection_traits.h
+++ b/Intersections_2/include/CGAL/Intersection_traits.h
@@ -62,10 +62,51 @@
     typedef typename boost::variant<typename K::R1, typename K::R2,     \
                                     typename K::R3> variant_type;       \
     typedef typename boost::optional< variant_type > result_type;       \
-  };
+  };                                                                    
 
 #endif
 
+#define CGAL_INTERSECTION_FUNCTION(A, B, DIM)                           \
+  template<typename K>                                                  \
+  inline                                                                \
+  typename BOOST_PP_CAT(K::Intersect_, DIM)::template Result<typename K::A, typename K::B>::Type \
+  intersection(const A<K>& a, const B<K>& b) {        \
+    return BOOST_PP_CAT(K().intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }                                                                     \
+  template<typename K>                                                  \
+  inline                                                                \
+  typename BOOST_PP_CAT(K::Intersect_, DIM)::template Result<typename K::A, typename K::B>::Type     \
+  intersection(const B<K>& a, const A<K>& b) {        \
+    return BOOST_PP_CAT(K().intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }
+
+#define CGAL_INTERSECTION_FUNCTION_SELF(A, DIM)                         \
+  template<typename K>                                                  \
+  inline                                                                \
+  typename BOOST_PP_CAT(K::Intersect_, DIM)::template Result<typename K::A, typename K::A>::Type \
+  intersection(const A<K> & a, const A<K> & b) {                          \
+    return BOOST_PP_CAT(K().intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }
+
+#define CGAL_DO_INTERSECT_FUNCTION(A, B, DIM)              \
+  template<typename K>                                     \
+  inline bool                                              \
+  do_intersect(const A<K>& a, const B<K>& b) {             \
+    return BOOST_PP_CAT(K().do_intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }                                                        \
+  template<typename K>                                     \
+  inline bool                                              \
+  do_intersect(const B<K>& a, const A<K>& b) {             \
+    return BOOST_PP_CAT(K().do_intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }
+
+#define CGAL_DO_INTERSECT_FUNCTION_SELF(A, DIM)                         \
+  template<typename K>                                                  \
+  inline bool                                                           \
+  do_intersect(const A<K> & a, const A<K> & b) {                          \
+    return BOOST_PP_CAT(K().do_intersect_, BOOST_PP_CAT(DIM, _object()(a, b))); \
+  }
+
 namespace CGAL {
 
 // only declarationn
@@ -224,23 +265,25 @@ do_intersect_impl(const A& a, const B& b, Dynamic_dimension_tag) {
 
 } // internal
 
-template<typename A, typename B>
-inline
-typename Intersection_traits< typename Kernel_traits<A>::Kernel, A, B>::result_type
-intersection(const A& a, const B& b) {
-  CGAL_static_assertion_msg( (boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value),
-                              "intersection with objects of different dimensions not supported");
-  return internal::intersection_impl(a, b, typename A::Ambient_dimension());
-}
+// See overloads in the respective header files
 
-template<typename A, typename B>
-inline
-bool
-do_intersect(const A& a, const B& b) {
-  CGAL_static_assertion_msg((boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value), 
-                        "do_intersect with objects of different dimensions not supported");
-  return internal::do_intersect_impl(a, b, typename A::Ambient_dimension());
-}
+// template<typename A, typename B>
+// inline
+// typename Intersection_traits< typename Kernel_traits<A>::Kernel, A, B>::result_type >::type
+// intersection(const A& a, const B& b) {
+//   CGAL_static_assertion_msg( (boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value),
+//                               "intersection with objects of different dimensions not supported");
+//   return internal::intersection_impl(a, b, typename A::Ambient_dimension());
+// }
+
+// template<typename A, typename B>
+// inline
+// bool
+// do_intersect(const A& a, const B& b) {
+//   CGAL_static_assertion_msg((boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value), 
+//                         "do_intersect with objects of different dimensions not supported");
+//   return internal::do_intersect_impl(a, b, typename A::Ambient_dimension());
+// }
 
 } // CGAL
 
diff --git a/Intersections_2/include/CGAL/Intersection_traits_2.h b/Intersections_2/include/CGAL/Intersection_traits_2.h
index f40bf50bd37..4d3c1b23637 100644
--- a/Intersections_2/include/CGAL/Intersection_traits_2.h
+++ b/Intersections_2/include/CGAL/Intersection_traits_2.h
@@ -55,7 +55,6 @@ CGAL_INTERSECTION_TRAITS_2(Segment_2, Triangle_2, Point_2, Segment_2)
 CGAL_INTERSECTION_TRAITS_2(Triangle_2, Ray_2, Point_2, Segment_2)
 CGAL_INTERSECTION_TRAITS_2(Ray_2, Triangle_2, Point_2, Segment_2)
 
-
 template<typename K>
 struct Intersection_traits<K, typename K::Triangle_2, typename K::Triangle_2>  {
   typedef typename 
@@ -64,6 +63,7 @@ struct Intersection_traits<K, typename K::Triangle_2, typename K::Triangle_2>  {
   typedef typename boost::optional< variant_type > result_type;
 };
 
+
 CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Line_2, Point_2, Segment_2)
 CGAL_INTERSECTION_TRAITS_2(Line_2, Iso_rectangle_2, Point_2, Segment_2)
 
@@ -82,6 +82,8 @@ struct Intersection_traits<K, typename K::Iso_rectangle_2, typename K::Iso_recta
   typedef boost::optional<variant_type> result_type;
 };
 
+
+// Point_2 is special
 template<typename K, typename B>
 struct Intersection_traits<K, typename K::Point_2, B> {
   typedef typename boost::variant<typename K::Point_2> variant_type;
@@ -94,6 +96,7 @@ struct Intersection_traits<K, A, typename K::Point_2> {
   typedef boost::optional<variant_type> result_type;
 };
 
+
 template<typename K>
 struct Intersection_traits<K, typename K::Iso_rectangle_2, typename K::Triangle_2>
 {
@@ -107,6 +110,7 @@ template<typename K>
 struct Intersection_traits<K, typename K::Triangle_2, typename K::Iso_rectangle_2>
   : public Intersection_traits<K, typename K::Iso_rectangle_2, typename K::Triangle_2> {};
 
+
 // Intersection_traits for the circular kernel
 template<typename K>
 struct Intersection_traits<K, typename K::Circle_2, typename K::Circle_2>
@@ -119,7 +123,6 @@ struct Intersection_traits<K, typename K::Circle_2, typename K::Circle_2>
   result_type;
 };  
 
-
 template<typename K>
 struct Intersection_traits<K, typename K::Circular_arc_2, typename K::Circular_arc_2>
 {
@@ -193,11 +196,10 @@ struct Intersection_traits<K, typename K::Line_2, typename K::Circular_arc_2>
 };  
 
 template<typename K>
-struct Intersection_traits<K, typename K::Circular_arc_2, typename K::Line__2>
+struct Intersection_traits<K, typename K::Circular_arc_2, typename K::Line_2>
   : public Intersection_traits<K, typename K::Line_2, typename K::Circular_arc_2>
 {};
 
-
 // Circular_arc_2 Circle_2 simply aliases
 template<typename K>
 struct Intersection_traits<K, typename K::Circular_arc_2, typename K::Circle_2>
diff --git a/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h b/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
index 1106af18e4c..3d340ab7b99 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
@@ -349,4 +349,6 @@ intersection(const typename K::Triangle_2 &tr1,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Triangle_2, 2)
+
 } //namespace CGAL
diff --git a/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
index 215e71fa0c7..af97b76cffc 100644
--- a/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
@@ -81,17 +81,19 @@ intersection(
     return intersection_return<K, typename K::Iso_rectangle_2, typename K::Iso_rectangle_2>(construct_iso_rectangle_2(newmin, newmax));
 }
 
+template<typename K>
+inline bool
+do_intersect(const typename K::Iso_rectangle_2 &irect1,
+             const typename K::Iso_rectangle_2 &irect2,
+             const K&) {
+  return intersection(irect1, irect2);
+}
 
 } // namespace internal
 
 
-template <class K>
-inline bool
-do_intersect(const Iso_rectangle_2<K> &irect1,
-             const Iso_rectangle_2<K> &irect2)
-{
-    return intersection(irect1, irect2);
-}
+CGAL_INTERSECTION_FUNCTION_SELF(Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Iso_rectangle_2, 2)
 
 } //namespace CGAL
 
diff --git a/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
index d11d63ddeb3..d621a015343 100644
--- a/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
@@ -216,6 +216,9 @@ intersection(const typename K::Iso_rectangle_2 &iso,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Line_2, Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Line_2, Iso_rectangle_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
index 978ffa6633c..9021e4e8bf2 100644
--- a/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
@@ -201,6 +201,10 @@ Line_2_Line_2_pair<K>::intersection_line() const
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Line_2, 2)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Line_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
index fb8b9b4bff5..22d5c7917b6 100644
--- a/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
@@ -193,6 +193,9 @@ intersection(const typename K::Triangle_2 &tr,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Line_2, Triangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Line_2, Triangle_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
index bf74b2205d6..eacdf273d93 100644
--- a/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
@@ -81,6 +81,9 @@ intersection(const typename K::Iso_rectangle_2 &iso,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Point_2, Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Point_2, Iso_rectangle_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
index 20d3391b939..56560121475 100644
--- a/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
@@ -76,6 +76,9 @@ intersection(const typename K::Line_2 &line,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Point_2, Line_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Point_2, Line_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
index 7c6b52b8eff..90b7a320592 100644
--- a/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
@@ -54,6 +54,10 @@ intersection(const typename K::Point_2 &pt1,
 
 }// namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Point_2, 2)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Point_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
index c2387e320e5..f29af85c97f 100644
--- a/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
@@ -80,6 +80,10 @@ intersection(const typename K::Ray_2 &ray,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Point_2, Ray_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Point_2, Ray_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
index 92d760f8e68..3d332cac432 100644
--- a/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
@@ -81,6 +81,9 @@ intersection( const typename K::Segment_2 &seg,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Point_2, Segment_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Point_2, Segment_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
index 551b8d15a04..3b14db3790c 100644
--- a/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
@@ -157,6 +157,9 @@ intersection(const typename K::Triangle_2 &tr,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Point_2, Triangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Point_2, Triangle_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
index 6cc3d4ca59e..9ef0dd3a4c7 100644
--- a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
@@ -203,6 +203,10 @@ Ray_2_Iso_rectangle_2_pair<K>::intersection_point() const
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Ray_2, Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Ray_2, Iso_rectangle_2, 2)
+
+
 } //namespace CGAL
 
 #endif // CGAL_RAY_2_iSO_RECTANGLE_2_INTERSECTION_H
diff --git a/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
index b725c949f76..ab41db9e1e3 100644
--- a/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
@@ -165,6 +165,9 @@ Ray_2_Line_2_pair<K>::intersection_ray() const
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Ray_2, Line_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Ray_2, Line_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
index a1264ca1bec..5292bffbf0a 100644
--- a/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
@@ -256,6 +256,10 @@ intersection(const typename K::Ray_2 &ray1,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Ray_2, 2)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Ray_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
index 72a9ed3994b..ba2e9deef60 100644
--- a/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
@@ -268,6 +268,9 @@ intersection(const typename K::Segment_2 &seg,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Ray_2, Segment_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Ray_2, Segment_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
index ca2f976f06e..4c3a8470680 100644
--- a/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
@@ -199,6 +199,10 @@ inline bool do_intersect(
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Ray_2, Triangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Ray_2, Triangle_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
index 5858983167c..cbba0cd3eb4 100644
--- a/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
@@ -229,6 +229,9 @@ inline bool do_intersect(
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Segment_2, Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Segment_2, Iso_rectangle_2, 2)
+
 } //namespace CGAL
 
 #endif // CGAL_SEGMENT_2_ISO_RECTANGLE_2_INTERSECTION_H
diff --git a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
index ad06e8223f6..b8ed430a6e4 100644
--- a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
@@ -158,6 +158,10 @@ Segment_2_Line_2_pair<K>::intersection_segment() const
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Segment_2, Line_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Segment_2, Line_2, 2)
+
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
index 4d702d217a0..4785a3e1131 100644
--- a/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
@@ -455,6 +455,9 @@ intersection(const typename K::Segment_2 &seg1,
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Segment_2, 2)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Segment_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
index e8fdb8795b2..af20613b492 100644
--- a/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
@@ -197,6 +197,9 @@ inline bool do_intersect(
 
 } // namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Segment_2, Triangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Segment_2, Triangle_2, 2)
+
 } //namespace CGAL
 
 #endif
diff --git a/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
index 779e13c1bb8..bd226f04b63 100644
--- a/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
@@ -281,6 +281,10 @@ namespace internal {
     return intersection_return<R, typename R::Triangle_2, typename R::Iso_rectangle_2>();
   }//end intersection
 }//end namespace internal
+
+CGAL_INTERSECTION_FUNCTION(Triangle_2, Iso_rectangle_2, 2)
+CGAL_DO_INTERSECT_FUNCTION(Triangle_2, Iso_rectangle_2, 2)
+
 }//end namespace
 
 #endif
diff --git a/Intersections_2/include/CGAL/Triangle_2_Triangle_2_do_intersect.h b/Intersections_2/include/CGAL/Triangle_2_Triangle_2_do_intersect.h
index b0ede9e0390..cece6192266 100644
--- a/Intersections_2/include/CGAL/Triangle_2_Triangle_2_do_intersect.h
+++ b/Intersections_2/include/CGAL/Triangle_2_Triangle_2_do_intersect.h
@@ -170,16 +170,7 @@ bool do_intersect(const typename K::Triangle_2 &t1,
 
 } // namespace internal
 
-
-
-
-template <class K>
-inline bool do_intersect(const Triangle_2<K> &t1, 
-			 const Triangle_2<K> &t2)
-{
-  typedef typename K::Do_intersect_2 Do_intersect;
-  return Do_intersect()(t1,t2);
-}
+CGAL_DO_INTERSECT_FUNCTION_SELF(Triangle_2, 2)
 
 } //namespace CGAL
 
diff --git a/Intersections_2/test/Intersections_2/test_intersections_2.cpp b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
index 25618d226c4..8ffbc85735f 100644
--- a/Intersections_2/test/Intersections_2/test_intersections_2.cpp
+++ b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
@@ -1,5 +1,6 @@
 // 2D intersection tests.
 
+#include <CGAL/Intersection_traits_2.h>
 #include <CGAL/Object.h>
 #include <CGAL/Line_2.h>
 #include <CGAL/Point_2.h>
diff --git a/Intersections_3/include/CGAL/Intersection_traits_3.h b/Intersections_3/include/CGAL/Intersection_traits_3.h
index 7c7a7a4b080..a515eb99c2e 100644
--- a/Intersections_3/include/CGAL/Intersection_traits_3.h
+++ b/Intersections_3/include/CGAL/Intersection_traits_3.h
@@ -22,7 +22,26 @@
 #define CGAL_INTERSECTION_TRAITS_3_H
 
 #include <CGAL/Intersection_traits.h>
-#include <CGAL/Bbox_3.h>
+
+namespace CGAL {
+// global intersection declarations
+#define INTERSECT_SELF ((Line_3, 3))((Plane_3, 3))((Ray_3, 3))((Segment_3, 3))((Sphere_3, 3))((Triangle_3, 3))((Iso_cuboid_3, 3))
+#define INTERSECT ((Plane_3, Line_3, 3))((Ray_3, Line_3, 3))((Segment_3, Line_3, 3))((Triangle_3, Line_3, 3))((Ray_3, Plane_3, 3)) \
+  ((Segment_3, Plane_3, 3))((Sphere_3, Plane_3, 3))((Triangle_3, Plane_3, 3))((Segment_3, Ray_3, 3)) \
+  ((Triangle_3, Ray_3, 3))((Triangle_3, Segment_3, 3))((Iso_cuboid_3, Segment_3, 3))((Iso_cuboid_3, Line_3, 3)) \
+  ((Iso_cuboid_3, Ray_3, 3))
+#define EXPAND_SELF(s, state, x) CGAL_INTERSECTION_FUNCTION_SELF( BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(2, 0, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(2, 1, x)) )
+#define EXPAND_BINARY(s, state, x) CGAL_INTERSECTION_FUNCTION( BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 0, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 1, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 2, x)) )
+
+// BOOST_PP_SEQ_FOR_EACH(EXPAND_SELF, _, INTERSECT_SELF)
+// BOOST_PP_SEQ_FOR_EACH(EXPAND_BINARY, _, INTERSECT)
+
+#undef EXPAND_SELF
+#undef EXPAND_BINARY
+#undef INTERSECT_SELF
+#undef INTERSECT
+}
+
 
 #if !(CGAL_INTERSECTION_VERSION < 2)
 
@@ -79,6 +98,7 @@ struct Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>  {
   typedef typename boost::optional< variant_type > result_type;
 };
 
+
 // !!! undocumented !!!
 
 // Segment_3 Iso_cuboid_3
@@ -101,6 +121,7 @@ struct Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Iso_cuboid_3
   typedef typename boost::optional< variant_type > result_type;
 };
 
+
 // Intersections with BBox returns the same for Ray_3, Line_3 and Segment_3
 // Bbox_3 Line_3
 template<typename K>
@@ -114,6 +135,20 @@ template<typename K>
 struct Intersection_traits<K, typename K::Line_3, CGAL::Bbox_3> : 
     public Intersection_traits<K, CGAL::Bbox_3, typename K::Line_3> {};
 
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Line_3>
+intersection(const CGAL::Bbox_3& a, typename K::Line_3 const& b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Line_3>
+intersection(typename K::Line_3 const& b, const CGAL::Bbox_3& a) {
+  return K().intersect_3_object()(b, a);
+}
+
 // Bbox_3 Segment_3
 template<typename K>
 struct Intersection_traits<K, typename K::Segment_3, CGAL::Bbox_3> : 
@@ -123,6 +158,20 @@ template<typename K>
 struct Intersection_traits<K, CGAL::Bbox_3, typename K::Segment_3> : 
     public Intersection_traits<K, CGAL::Bbox_3, typename K::Line_3> {};
 
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Segment_3>
+intersection(typename K::Segment_3 const& b, const CGAL::Bbox_3& a) {
+  return K().intersect_3_object()(b, a);
+}
+
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Segment_3>
+intersection(typename CGAL::Bbox_3 const& b, typename K::Segment_3 const& a) {
+  return K().intersect_3_object()(b, a);
+}
+
 // Bbox_3 Ray_3
 template<typename K>
 struct Intersection_traits<K, typename K::Ray_3, CGAL::Bbox_3> : 
@@ -132,6 +181,20 @@ template<typename K>
 struct Intersection_traits<K, CGAL::Bbox_3, typename K::Ray_3> : 
     public Intersection_traits<K, CGAL::Bbox_3, typename K::Line_3> {};
 
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Ray_3>
+intersection(typename K::Ray_3 const& b, const CGAL::Bbox_3& a) {
+  return K().intersect_3_object()(b, a);
+}
+
+template<typename K>
+inline
+typename K::Intersect_3::template Result<CGAL::Bbox_3, typename K::Ray_3>
+intersection(const CGAL::Bbox_3& a, typename K::Ray_3 const& b) {
+  return K().intersect_3_object()(b, a);
+}
+
 // Intersection_traits for the circular kernel
 
 // Sphere_3 Line_3
diff --git a/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h b/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
index 8d0f5026eda..d89c8b35c7c 100644
--- a/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
+++ b/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
@@ -30,6 +30,128 @@
 
 namespace CGAL {
 
+
+// the special plane_3 function
+template <class K>
+inline 
+#if CGAL_INTERSECTION_VERSION < 2
+CGAL::Object
+#else
+typename boost::optional< boost::variant< Point_3<K>, Line_3<K>, Plane_3<K> > >
+#endif
+intersection(const Plane_3<K> &plane1, const Plane_3<K> &plane2,
+             const Plane_3<K> &plane3)
+{
+  return K().intersect_3_object()(plane1, plane2, plane3);
+}
+
+CGAL_INTERSECTION_FUNCTION(Plane_3, Line_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Plane_3, Line_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Plane_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Line_3, 3)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Line_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Segment_3, 3)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Segment_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Line_3, Segment_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Line_3, Segment_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Line_3, Ray_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Line_3, Ray_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Segment_3, Ray_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Segment_3, Ray_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Ray_3, 3)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Ray_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Plane_3, Sphere_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Plane_3, Sphere_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Sphere_3, 3)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Sphere_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Plane_3, Ray_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Plane_3, Ray_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Plane_3, Segment_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Plane_3, Segment_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Plane_3, Triangle_3, 3)
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Line_3, Bbox_3>::result_type
+intersection(const Line_3<K> &a,
+	     const Bbox_3 &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Line_3, Bbox_3>::result_type
+intersection(const Bbox_3 &a,
+             const Line_3<K> &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Ray_3, Bbox_3>::result_type
+intersection(const Ray_3<K> &a,
+	     const Bbox_3 &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Ray_3, Bbox_3>::result_type
+intersection(const Bbox_3 &a,
+             const Ray_3<K> &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Segment_3, Bbox_3>::result_type
+intersection(const Segment_3<K> &a,
+	     const Bbox_3 &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+template <class K>
+inline
+typename Intersection_traits<K, typename K::Segment_3, Bbox_3>::result_type
+intersection(const Bbox_3 &a,
+             const Segment_3<K> &b) {
+  return K().intersect_3_object()(a, b);
+}
+
+CGAL_INTERSECTION_FUNCTION(Line_3, Iso_cuboid_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Ray_3, Iso_cuboid_3, 3)
+
+CGAL_INTERSECTION_FUNCTION(Segment_3, Iso_cuboid_3, 3)
+
+CGAL_INTERSECTION_FUNCTION_SELF(Iso_cuboid_3, 3)
+
+CGAL_DO_INTERSECT_FUNCTION_SELF(Plane_3, 3)
+
+template <class R>
+inline bool
+do_intersect(const Plane_3<R> &plane1, const Plane_3<R> &plane2,
+             const Plane_3<R> &plane3) {
+  return R().do_intersect_3_object()(plane1, plane2, plane3);
+}
+
+CGAL_DO_INTERSECT_FUNCTION_SELF(Iso_cuboid_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Iso_cuboid_3, Line_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Iso_cuboid_3, Ray_3, 3)
+CGAL_DO_INTERSECT_FUNCTION(Iso_cuboid_3, Segment_3, 3)
+
 namespace internal {
 
 template <class K>
diff --git a/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h
index 123ced169d2..f8eb1efa09f 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h
@@ -105,9 +105,10 @@ bool do_intersect(const typename K::Line_3     &l,
   return do_intersect(t, l, k);
 }
 
-
 } // namespace internal
 
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Line_3, 3)
+
 } //namespace CGAL
 
 #endif //CGAL_TRIANGLE_3_LINE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h
index 90cebb0bd6a..e144ee710ee 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h
@@ -70,6 +70,9 @@ bool do_intersect(const typename K::Plane_3   &h,
 
 
 } // namespace internal
+
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Plane_3, 3)
+
 } //namespace CGAL
 
 #endif //CGAL_TRIANGLE_3_PLANE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h
index 9b89ca21269..ed2fea8c16b 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h
@@ -93,29 +93,7 @@ bool do_intersect(const typename K::Point_3    &p,
 } // namespace internal
 
  
-template <class K>
-inline bool do_intersect(const Point_3<K> &p, 
-			 const Triangle_3<K> &t)
-{ 
-  return typename K::Do_intersect_3()(t,p);
-} 
-
-template <class K>
-inline bool do_intersect(const Triangle_3<K> &t, 
-			 const Point_3<K> &p)
-{ 
-  return typename K::Do_intersect_3()(t,p);
-} 
-
-/*
-template <class K>
-inline bool do_intersect(const Point_3<K> &p, 
-			 const Triangle_3<K> &t,
-			 const K & k)
-{ 
-  return do_intersect(t,p,k);
-} 
-*/
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Point_3, 3)
 
 } //namespace CGAL
 
diff --git a/Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h
index d244f159c2b..20347b1e77e 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h
@@ -297,6 +297,9 @@ bool do_intersect_coplanar(const typename K::Triangle_3 &t,
 
 
 } // namespace internal
+
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Ray_3, 3)
+
 } //namespace CGAL
 
 #endif // CGAL_TRIANGLE_3_RAY_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h
index 4f79bb29aa7..df90777abbd 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h
@@ -318,6 +318,9 @@ bool do_intersect(const typename K::Segment_3  &s,
 }
 
 } // namespace internal
+
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Segment_3, 3)
+
 } //namespace CGAL
 
 #endif //CGAL_TRIANGLE_3_SEGMENT_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
index af51b2a4be2..1ffdfeb8ac5 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
@@ -69,21 +69,7 @@ do_intersect(const typename K::Tetrahedron_3 &tet,
 
 } // namespace internal
 
-
-
-template <class K>
-inline bool do_intersect(const Tetrahedron_3<K> &tet,
-			 const Triangle_3<K> &tr)
-{
-  return typename K::Do_intersect_3()(tr,tet);
-}
-
-template <class K>
-inline bool do_intersect(const Triangle_3<K> &tr,
-			 const Tetrahedron_3<K> &tet)
-{
-  return typename K::Do_intersect_3()(tr,tet);
-}
+CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Tetrahedron_3, 3)
 
 } //namespace CGAL
 
diff --git a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h
index 4f194d5d708..94e307b9202 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h
@@ -443,6 +443,9 @@ do_intersect(const typename K::Triangle_3 &t1,
 }
 
 } // namespace internal
+
+CGAL_DO_INTERSECT_FUNCTION_SELF(Triangle_3, 3)
+
 } //namespace CGAL
 
 #endif // CGAL_TRIANGLE_3_TRIANGLE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
index 3d96fc2eaa4..7e18d7bee1e 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
@@ -218,6 +218,8 @@ intersection(
 
 }//namespace internal
 
+CGAL_INTERSECTION_FUNCTION_SELF(Triangle_3, 3)
+
 } // namespace CGAL
 
 
diff --git a/Intersections_3/include/CGAL/bbox_intersection_3.h b/Intersections_3/include/CGAL/bbox_intersection_3.h
index b168c6174b5..d77aefc6b36 100644
--- a/Intersections_3/include/CGAL/bbox_intersection_3.h
+++ b/Intersections_3/include/CGAL/bbox_intersection_3.h
@@ -34,18 +34,27 @@ namespace CGAL {
 // But it must be a template function since the original kernel must be 
 // taken into account. (Michael.Hemmer@sophia.inria.fr)
 template <class K> 
+#if CGAL_INTERSECTION_VERSION < 2
+CGAL::Object
+#else
 typename boost::optional< boost::variant< 
                             typename K::Segment_3, 
                             typename K::Point_3 > >
+#endif
 intersection_bl(const Bbox_3 &box,
         double lpx, double lpy, double lpz,
         double ldx, double ldy, double ldz,
         bool min_infinite, bool max_infinite)
 {
-  typedef typename 
+  typedef 
+#if CGAL_INTERSECTION_VERSION < 2
+    CGAL::Object
+#else
+    typename 
     boost::optional< 
       boost::variant< typename K::Segment_3, 
                       typename K::Point_3 > >
+#endif
     result_type;
 
   double seg_min = 0.0, seg_max = 1.0;
@@ -159,10 +168,20 @@ intersection_bl(const Bbox_3 &box,
   Point_3 ref_point = Point_3( FT(lpx), FT(lpy), FT(lpz));
   Vector_3 dir = Vector_3( FT(ldx), FT(ldy), FT(ldz));
   
-  if (seg_max == seg_min)
+  if (seg_max == seg_min) {
+#if CGAL_INTERSECTION_VERSION < 2
+    return make_object(ref_point + dir * FT(seg_max));
+#else
     return result_type(ref_point + dir * FT(seg_max));
+#endif
+  } 
+#if CGAL_INTERSECTION_VERSION < 2
+  return make_object(
+      Segment_3(ref_point + dir*FT(seg_min), ref_point + dir*FT(seg_max)));
+#else
   return result_type(
-      Segment_3(ref_point + dir*FT(seg_min), ref_point + dir*FT(seg_max))); 
+      Segment_3(ref_point + dir*FT(seg_min), ref_point + dir*FT(seg_max)));
+#endif
 }
 
 
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h
index fcdd2896e1c..c8908d2567f 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h
@@ -154,6 +154,20 @@ namespace internal {
 
 
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3 a,
+                  const Line_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Line_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_LINE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h
index 826e7ad20ff..b039ad6fcec 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h
@@ -127,6 +127,20 @@ namespace internal {
 
 
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3 a,
+                  const Plane_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Plane_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_PLANE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h
index 9762ce71e81..4f56977ef87 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h
@@ -149,6 +149,19 @@ namespace internal {
     return do_intersect(ray, bbox, K());
   }
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3 a,
+                  const Ray_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Ray_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_RAY_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
index 33c2ff0f6df..48d0cf45f2b 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
@@ -152,6 +152,20 @@ namespace internal {
   }
 
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3 a,
+                  const Segment_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Segment_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_SEGMENT_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h
index c9c1892838a..2301296daa1 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h
@@ -104,6 +104,20 @@ namespace internal {
 
 
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3& a,
+                  const Sphere_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Sphere_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_SPHERE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h
index 8f7a88ca60b..436d4dc48f6 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h
@@ -382,6 +382,20 @@ namespace internal {
   }
 
 } // namespace internal
+
+template<typename K>
+bool do_intersect(const CGAL::Bbox_3 a,
+                  const Triangle_3<K>& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+template<typename K>
+bool do_intersect(const Triangle_3<K>& a,
+                  const CGAL::Bbox_3& b) {
+  return K().do_intersect_3_object()(a, b);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_TRIANGLE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
index e42a18d8159..a6f659373b5 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
@@ -423,6 +423,9 @@ intersection(const typename K::Line_3 &l,
 
 } // end namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Triangle_3, Line_3, 3)
+
+
 } // end namespace CGAL
 
 #endif // CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_LINE_3_INTERSECTION_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
index a3280332910..e8645f0686e 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
@@ -593,6 +593,8 @@ intersection(const typename K::Ray_3  &r,
 
 } // end namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Triangle_3, Ray_3, 3)
+
 } // end namespace CGAL
 
 #endif // CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_RAY_3_INTERSECTION_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
index e0e480f4341..1006eac8ad0 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
@@ -559,6 +559,8 @@ intersection(const typename K::Segment_3  &s,
 
 } // end namespace internal
 
+CGAL_INTERSECTION_FUNCTION(Triangle_3, Segment_3, 3)
+
 } // end namespace CGAL
 
 #endif // CGAL_INTERNAL_INTERSECTIONS_3_TRIANGLE_3_SEGMENT_3_INTERSECTION_H
diff --git a/Intersections_3/include/CGAL/intersection_3.h b/Intersections_3/include/CGAL/intersection_3.h
index 352e6315841..2a398d5db49 100644
--- a/Intersections_3/include/CGAL/intersection_3.h
+++ b/Intersections_3/include/CGAL/intersection_3.h
@@ -25,7 +25,6 @@
 #ifndef CGAL_INTERSECTION_3_H
 #define CGAL_INTERSECTION_3_H
 
-#include <CGAL/intersection_3_0.h>
 #include <CGAL/intersection_3_1.h>
 
 #include <CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h>
diff --git a/Intersections_3/include/CGAL/intersection_3_0.h b/Intersections_3/include/CGAL/intersection_3_0.h
deleted file mode 100644
index a2ef096e15e..00000000000
--- a/Intersections_3/include/CGAL/intersection_3_0.h
+++ /dev/null
@@ -1,77 +0,0 @@
-// Copyright (c) 2011 GeometryFactory (France). All rights reserved.
-// All rights reserved.
-//
-// Licensees holding a valid commercial license may use this file in
-// accordance with the commercial license agreement provided with the software.
-//
-// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
-// modify it under the terms of the GNU Lesser General Public License as
-// published by the Free Software Foundation; version 2.1 of the License.
-// See the file LICENSE.LGPL distributed with CGAL.
-//
-// 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)     : Philipp Möller
-
-#ifndef CGAL_INTERSECTION_3_0_H
-#define CGAL_INTERSECTION_3_0_H
-
-#include <CGAL/Intersection_traits_3.h>
-#include <CGAL/Kernel_traits.h>
-
-namespace CGAL {
-  // Intersection_traits.h provides the defaults, we add overloads for all special cases
-
-  // the special plane_3 function
-  template <class K>
-  inline 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
-  typename boost::optional< boost::variant< Point_3<K>, Line_3<K>, Plane_3<K> > >
-  #endif
-  intersection(const Plane_3<K> &plane1, const Plane_3<K> &plane2,
-               const Plane_3<K> &plane3)
-  {
-    return K().intersect_3_object()(plane1, plane2, plane3);
-  }
-
-  // intersections with Bbox_3 for which no kernel traits exist
-  template<class A>
-  inline 
-  typename Intersection_traits< typename CGAL::Kernel_traits<A>::Kernel, A, CGAL::Bbox_3 >::result_type
-  intersection(const A& a, const CGAL::Bbox_3& b) {
-    typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
-    return Kernel().intersect_3_object()(a, b);
-  }
-
-  template<class A>
-  inline 
-  typename Intersection_traits< typename CGAL::Kernel_traits<A>::Kernel, A, CGAL::Bbox_3 >::result_type
-  intersection(const CGAL::Bbox_3& b, const A& a) {
-    typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
-    return Kernel().intersect_3_object()(a, b);
-  }
-
-  template<class A>
-  inline bool
-  do_intersect(const A& a, const CGAL::Bbox_3& b) {
-    typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
-    return Kernel().do_intersect_3_object()(a, b);
-  }
-
-  template<class A>
-  inline bool
-  do_intersect(const CGAL::Bbox_3& b, const A& a) {
-    typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
-    return Kernel().do_intersect_3_object()(a, b);
-  }
-} // CGAL
-
-
-#endif /* _INTERSECTION_3_0_H_ */