diff --git a/Filtered_kernel/include/CGAL/internal/Static_filters/Do_intersect_3.h b/Filtered_kernel/include/CGAL/internal/Static_filters/Do_intersect_3.h
index 38f40dc4627..43eaca91403 100644
--- a/Filtered_kernel/include/CGAL/internal/Static_filters/Do_intersect_3.h
+++ b/Filtered_kernel/include/CGAL/internal/Static_filters/Do_intersect_3.h
@@ -30,7 +30,7 @@
 #include <CGAL/internal/Static_filters/Static_filter_error.h>
 #include <CGAL/internal/Static_filters/tools.h>
 
-#include <CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h>
+#include <CGAL/Intersections_3/Bbox_3_Segment_3.h>
 // for CGAL::internal::do_intersect_bbox_segment_aux
 
 #include <iostream>
diff --git a/Intersections_2/include/CGAL/Intersection_traits.h b/Intersections_2/include/CGAL/Intersection_traits.h
index 023be6ea504..83f42231aa9 100644
--- a/Intersections_2/include/CGAL/Intersection_traits.h
+++ b/Intersections_2/include/CGAL/Intersection_traits.h
@@ -68,6 +68,16 @@
 
 #endif
 
+#define CGAL_NO_INTERSECTION_FUNCTION_SELF(A, DIM)                        \
+template <typename K>                                                   \
+inline void intersection(const A<K>&, const A<K>&) {}
+
+#define CGAL_NO_INTERSECTION_FUNCTION(A, B, DIM)                        \
+template <typename K>                                                   \
+inline void intersection(const A<K>&, const B<K>&) {}               \
+template <typename K>                                                   \
+inline void intersection(const B<K>&, const A<K>&) {}
+
 #define CGAL_INTERSECTION_FUNCTION(A, B, DIM)                           \
   template<typename K>                                                  \
   inline                                                                \
diff --git a/Intersections_3/include/CGAL/Intersection_traits_3.h b/Intersections_3/include/CGAL/Intersection_traits_3.h
index c17449a54e0..c74186bc6cc 100644
--- a/Intersections_3/include/CGAL/Intersection_traits_3.h
+++ b/Intersections_3/include/CGAL/Intersection_traits_3.h
@@ -142,7 +142,30 @@ struct Intersection_traits<K, typename K::Point_3, typename K::Iso_cuboid_3>  {
   boost::variant< typename K::Point_3 > variant_type;
   typedef typename boost::optional< variant_type > result_type;
 };
+  
+// Bbox_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, Bbox_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
 
+  template<typename K>
+struct Intersection_traits<K, typename K::Point_3, Bbox_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+  
+// Iso_cuboid_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+  
 // Point_3 Line_3, variant of one
 template<typename K>
 struct Intersection_traits<K, typename K::Point_3, typename K::Line_3>  {
@@ -151,6 +174,14 @@ struct Intersection_traits<K, typename K::Point_3, typename K::Line_3>  {
   typedef typename boost::optional< variant_type > result_type;
 };
 
+// Line_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Line_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+
 // Point_3 Ray_3, variant of one
 template<typename K>
 struct Intersection_traits<K, typename K::Point_3, typename K::Ray_3>  {
@@ -159,6 +190,14 @@ struct Intersection_traits<K, typename K::Point_3, typename K::Ray_3>  {
   typedef typename boost::optional< variant_type > result_type;
 };
 
+// Ray_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Ray_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+
 // Point_3 Segment_3, variant of one
 template<typename K>
 struct Intersection_traits<K, typename K::Point_3, typename K::Segment_3>  {
@@ -167,6 +206,14 @@ struct Intersection_traits<K, typename K::Point_3, typename K::Segment_3>  {
   typedef typename boost::optional< variant_type > result_type;
 };
 
+// Segment_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Segment_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+
 // Point_3 Point_3, variant of one
 template<typename K>
 struct Intersection_traits<K, typename K::Point_3, typename K::Point_3>  {
@@ -182,6 +229,59 @@ struct Intersection_traits<K, typename K::Point_3, typename K::Plane_3>  {
   boost::variant< typename K::Point_3 > variant_type;
   typedef typename boost::optional< variant_type > result_type;
 };
+ 
+// Plane_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Plane_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+   
+// Point_3 Triangle_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Point_3, typename K::Triangle_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+// Triangle_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Triangle_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+  
+// Point_3 Tetrahedron_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Point_3, typename K::Tetrahedron_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+// Tetrahedron_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Tetrahedron_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+  
+// Point_3 Sphere_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Point_3, typename K::Sphere_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
+// Sphere_3 Point_3, variant of one
+template<typename K>
+struct Intersection_traits<K, typename K::Sphere_3, typename K::Point_3>  {
+  typedef typename
+  boost::variant< typename K::Point_3 > variant_type;
+  typedef typename boost::optional< variant_type > result_type;
+};
 } // namespace
 
 #endif // !(CGAL_INTERSECTION_VERSION < 2)
diff --git a/Intersections_3/include/CGAL/Point_3_Iso_cuboid_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Iso_cuboid_3_Point_3.h
similarity index 93%
rename from Intersections_3/include/CGAL/Point_3_Iso_cuboid_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Iso_cuboid_3_Point_3.h
index 2255d0551a8..2d1ace333dd 100644
--- a/Intersections_3/include/CGAL/Point_3_Iso_cuboid_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Iso_cuboid_3_Point_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_ISO_CUBOID_3_INTERSECTION_H
-#define CGAL_POINT_3_ISO_CUBOID_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_ISO_CUBOID_3_POINT_3_H
+#define CGAL_INTERSECTIONS_3_ISO_CUBOID_3_POINT_3_H
 
 #include <CGAL/Iso_cuboid_3.h>
 #include <CGAL/Point_3.h>
@@ -81,4 +81,4 @@ CGAL_DO_INTERSECT_FUNCTION(Point_3, Iso_cuboid_3, 3)
 
 } //namespace CGAL
 
-#endif // CGAL_POINT_3_ISO_CUBOID_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_ISO_CUBOID_3_POINT_3_H
diff --git a/Intersections_3/include/CGAL/Point_3_Line_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Line_3_Point_3.h
similarity index 94%
rename from Intersections_3/include/CGAL/Point_3_Line_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Line_3_Point_3.h
index eb82c52c7a1..6f033fb37de 100644
--- a/Intersections_3/include/CGAL/Point_3_Line_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Line_3_Point_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_LINE_3_INTERSECTION_H
-#define CGAL_POINT_3_LINE_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_LINE_3_POINT_3_H
+#define CGAL_INTERSECTIONS_3_LINE_3_POINT_3_H
 
 #include <CGAL/Line_3.h>
 #include <CGAL/Point_3.h>
@@ -81,4 +81,4 @@ CGAL_DO_INTERSECT_FUNCTION(Point_3, Line_3, 3)
 
 } //namespace CGAL
 
-#endif // CGAL_POINT_3_LINE_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_LINE_3_POINT_3_H
diff --git a/Intersections_3/include/CGAL/Point_3_Plane_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Plane_3_Point_3.h
similarity index 92%
rename from Intersections_3/include/CGAL/Point_3_Plane_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Plane_3_Point_3.h
index 6080ae98a8c..96421de67fe 100644
--- a/Intersections_3/include/CGAL/Point_3_Plane_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Plane_3_Point_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_PLANE_3_INTERSECTION_H
-#define CGAL_POINT_3_PLANE_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_PLANE_3_POINT_3_PLANE_3_H
+#define CGAL_INTERSECTIONS_3_PLANE_3_POINT_3_PLANE_3_H
 
 #include <CGAL/Plane_3.h>
 #include <CGAL/Point_3.h>
@@ -80,4 +80,4 @@ CGAL_INTERSECTION_FUNCTION(Point_3, Plane_3, 3)
 CGAL_DO_INTERSECT_FUNCTION(Point_3, Plane_3, 3)
 
 } //namespace CGAL
-#endif // CGAL_POINT_3_PLANE_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_PLANE_3_POINT_3_PLANE_3_H
diff --git a/Intersections_3/include/CGAL/Point_3_Point_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Point_3_Point_3.h
similarity index 92%
rename from Intersections_3/include/CGAL/Point_3_Point_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Point_3_Point_3.h
index 8ccfb5a29ee..68eac1cdcc5 100644
--- a/Intersections_3/include/CGAL/Point_3_Point_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Point_3_Point_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_POINT_3_INTERSECTION_H
-#define CGAL_POINT_3_POINT_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_POINT_3_POINT_3_H
+#define CGAL_INTERSECTIONS_3_POINT_3_POINT_3_H
 
 #include <CGAL/Point_3.h>
 #include <CGAL/Intersection_traits_3.h>
@@ -60,4 +60,4 @@ CGAL_INTERSECTION_FUNCTION_SELF(Point_3, 3)
 CGAL_DO_INTERSECT_FUNCTION_SELF(Point_3, 3)
 }//nmaespace cgal
 
-#endif // CGAL_POINT_3_POINT_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_POINT_3_POINT_3_H
diff --git a/Intersections_3/include/CGAL/Point_3_Ray_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Point_3_Ray_3.h
similarity index 94%
rename from Intersections_3/include/CGAL/Point_3_Ray_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Point_3_Ray_3.h
index 0ec8b0f2bd7..dbf1e0dfda6 100644
--- a/Intersections_3/include/CGAL/Point_3_Ray_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Point_3_Ray_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_RAY_3_INTERSECTION_H
-#define CGAL_POINT_3_RAY_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_POINT_3_RAY_3_H
+#define CGAL_INTERSECTIONS_3_POINT_3_RAY_3_H
 
 #include <CGAL/Ray_3.h>
 #include <CGAL/Point_3.h>
@@ -85,4 +85,4 @@ CGAL_DO_INTERSECT_FUNCTION(Point_3, Ray_3, 3)
 
 
 } //namespace CGAL
-#endif // CGAL_POINT_3_RAY_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_POINT_3_RAY_3_H
diff --git a/Intersections_3/include/CGAL/Point_3_Segment_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/Point_3_Segment_3.h
similarity index 93%
rename from Intersections_3/include/CGAL/Point_3_Segment_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/Point_3_Segment_3.h
index 89f8de6ff4a..4d0425db3c3 100644
--- a/Intersections_3/include/CGAL/Point_3_Segment_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Point_3_Segment_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_POINT_3_SEGMENT_3_INTERSECTION_H
-#define CGAL_POINT_3_SEGMENT_3_INTERSECTION_H
+#ifndef CGAL_INTERSECTIONS_3_POINT_3_SEGMENT_3_H
+#define CGAL_INTERSECTIONS_3_POINT_3_SEGMENT_3_H
 
 #include <CGAL/Segment_3.h>
 #include <CGAL/Point_3.h>
@@ -86,4 +86,4 @@ CGAL_DO_INTERSECT_FUNCTION(Point_3, Segment_3, 3)
 
 } //namespace CGAL
 
-#endif // CGAL_POINT_3_SEGMENT_3_INTERSECTION_H
+#endif // CGAL_INTERSECTIONS_3_POINT_3_SEGMENT_3_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/Point_3_Triangle_3.h
similarity index 73%
rename from Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/Point_3_Triangle_3.h
index ae3d38d9da6..e170ef3bf18 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Point_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/Point_3_Triangle_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Philippe Guigue
 
-#ifndef CGAL_TRIANGLE_3_POINT_3_DO_INTERSECT_H
-#define CGAL_TRIANGLE_3_POINT_3_DO_INTERSECT_H
+#ifndef CGAL_INTERSECTIONS_3_POINT_3_TRIANGLE_3_H
+#define CGAL_INTERSECTIONS_3_POINT_3_TRIANGLE_3_H
 
 #include <CGAL/enum.h>
 #include <CGAL/kernel_assertions.h>
@@ -103,12 +103,36 @@ bool do_intersect(const typename K::Point_3    &p,
   return do_intersect(t, p, k);
 }
 
+template <class K>
+inline
+typename CGAL::Intersection_traits
+<K, typename K::Point_3, typename K::Triangle_3>::result_type
+intersection(const typename K::Point_3 &pt,
+             const typename K::Triangle_3 &tr,
+             const K& k)
+{
+  if (do_intersect(pt,tr, k)) {
+    return intersection_return<typename K::Intersect_3, typename K::Point_3, typename K::Triangle_3>(pt);
+  }
+  return intersection_return<typename K::Intersect_3, typename K::Point_3, typename K::Triangle_3>();
+}
 
+template <class K>
+inline
+typename CGAL::Intersection_traits
+<K, typename K::Triangle_3, typename K::Point_3>::result_type
+intersection( const typename K::Triangle_3 &tr,
+              const typename K::Point_3 &pt,
+              const K& k)
+{
+  return internal::intersection(pt, tr, k);
+}
 } // namespace internal
 } // namespace Intersections
  
 CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Point_3, 3)
+CGAL_INTERSECTION_FUNCTION(Triangle_3, Point_3, 3)
 
 } //namespace CGAL
 
-#endif // CGAL_TRIANGLE_3_POINT_3_DO_INTERSECT_H
+#endif // CGAL_INTERSECTIONS_3_POINT_3_TRIANGLE_3_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Bbox_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Bbox_3_do_intersect.h
similarity index 94%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Bbox_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Bbox_3_do_intersect.h
index 6d21409ce12..cc435e22b10 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Bbox_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Bbox_3_do_intersect.h
@@ -39,6 +39,9 @@ namespace CGAL {
   {
     return CGAL::do_overlap(c, bbox);
   }
+
+  void intersection(const CGAL::Bbox_3&,
+                    const CGAL::Bbox_3&){}
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_BBOX_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Iso_cuboid_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Iso_cuboid_3_do_intersect.h
similarity index 84%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Iso_cuboid_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Iso_cuboid_3_do_intersect.h
index e9b9a042151..fe0710a84d4 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Iso_cuboid_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Iso_cuboid_3_do_intersect.h
@@ -48,21 +48,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-
-
-template<typename K>
-bool do_intersect(const CGAL::Bbox_3& a,
-                  const Iso_cuboid_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-template<typename K>
-bool do_intersect(const Iso_cuboid_3<K>& a,
-                  const CGAL::Bbox_3& b) {
-  return K().do_intersect_3_object()(b, a);
-}
-
-
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_BBOX_3_ISO_CUBOID_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Line_3_do_intersect.h
similarity index 93%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Line_3_do_intersect.h
index 440a652a567..95448fd3c6f 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Line_3_do_intersect.h
@@ -158,20 +158,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-  
-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/Intersections_3/internal/Bbox_3_Plane_3_do_intersect.h
similarity index 90%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Plane_3_do_intersect.h
index 620962bda90..0dbb95e2e02 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Plane_3_do_intersect.h
@@ -153,31 +153,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-  
-template<typename K>
-bool do_intersect(const CGAL::Bbox_3 a,
-                  const Plane_3<K>& b) {
-  return K().do_intersect_3_object()(b, a);
-}
-
-template<typename K>
-bool do_intersect(const Plane_3<K>& a,
-                  const CGAL::Bbox_3& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-template<typename K>
-bool do_intersect(const Iso_cuboid_3<K>& a,
-                  const Plane_3<K>& b) {
-  return K().do_intersect_3_object()(b, a);
-}
-
-template<typename K>
-bool do_intersect(const Plane_3<K>& a,
-                  const Iso_cuboid_3<K>& 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/Intersections_3/internal/Bbox_3_Ray_3_do_intersect.h
similarity index 85%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Ray_3_do_intersect.h
index 009962c1b26..e0fcd062625 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Ray_3_do_intersect.h
@@ -26,7 +26,7 @@
 #include <CGAL/Ray_3.h>
 #include <CGAL/Bbox_3.h>
 
-#include <CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Bbox_3_Segment_3_do_intersect.h>
 // for CGAL::internal::do_intersect_bbox_segment_aux
 
 // inspired from http://cag.csail.mit.edu/~amy/papers/box-jgt.pdf
@@ -69,19 +69,6 @@ namespace internal {
   
 } // namespace internal
 } // namespace Intersections
-  
-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/Intersections_3/internal/Bbox_3_Segment_3_do_intersect.h
similarity index 97%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Segment_3_do_intersect.h
index 0b52c5d5ab2..8015f82c464 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Segment_3_do_intersect.h
@@ -461,20 +461,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-  
-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
 
 #include <CGAL/enable_warnings.h>
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Sphere_3_do_intersect.h
similarity index 86%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Sphere_3_do_intersect.h
index efbfcf830d7..29953fe3009 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Sphere_3_do_intersect.h
@@ -115,23 +115,26 @@ namespace internal {
     {
           return do_intersect_sphere_box_3(sphere, bbox, K());  
     }
+  
+    template <class K>
+    bool do_intersect(const typename K::Iso_cuboid_3& bbox,
+                      const typename K::Sphere_3& sphere,
+                      const K&)
+    {
+      return do_intersect_sphere_box_3(sphere, bbox, K());
+    }
+
+  
+    template <class K>
+    bool do_intersect(const typename K::Sphere_3& sphere,
+                      const typename K::Iso_cuboid_3& bbox,
+                      const K&)
+    {
+          return do_intersect_sphere_box_3(sphere, bbox, K());  
+    }
 
 } // namespace internal
 } // namespace Intersections
-  
-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/Intersections_3/internal/Bbox_3_Triangle_3_do_intersect.h
similarity index 97%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Triangle_3_do_intersect.h
index e8ea3ccb01a..58f030a5d5c 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Bbox_3_Triangle_3_do_intersect.h
@@ -33,7 +33,7 @@
 // a minimal cost (and we use C++ ;).
 
 #include <CGAL/Uncertain.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Bbox_3_Plane_3_do_intersect.h>
 
 namespace CGAL {
   
@@ -399,20 +399,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-  
-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
 
 #include <CGAL/enable_warnings.h>
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Ray_3_do_intersect.h
similarity index 86%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Ray_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Ray_3_do_intersect.h
index 470f6673801..4c4e81707a6 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Ray_3_do_intersect.h
@@ -26,7 +26,7 @@
 #include <CGAL/Ray_3.h>
 #include <CGAL/Iso_cuboid_3.h>
 
-#include <CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Bbox_3_Ray_3_do_intersect.h>
 // for CGAL::internal::do_intersect_bbox_segment_aux
 
 // inspired from http://cag.csail.mit.edu/~amy/papers/box-jgt.pdf
@@ -70,19 +70,6 @@ namespace internal {
 
 } // namespace internal
 } // namespace Intersections
-
-template<typename K>
-bool do_intersect(const Iso_cuboid_3<K> 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 Iso_cuboid_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_ISO_CUBOID_3_RAY_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Segment_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Segment_3_do_intersect.h
similarity index 86%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Segment_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Segment_3_do_intersect.h
index 23f42e89277..0581686a99e 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Segment_3_do_intersect.h
@@ -26,7 +26,7 @@
 #include <CGAL/Segment_3.h>
 #include <CGAL/Iso_cuboid_3.h>
 
-#include <CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Bbox_3_Segment_3_do_intersect.h>
 // for CGAL::internal::do_intersect_bbox_segment_aux
 
 // inspired from http://cag.csail.mit.edu/~amy/papers/box-jgt.pdf
@@ -70,19 +70,6 @@ namespace internal {
   
 } // namespace internal
 } // namespace Intersections
-  
-template<typename K>
-bool do_intersect(const Iso_cuboid_3<K> 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 Iso_cuboid_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
 } //namespace CGAL
 
 #endif  // CGAL_INTERNAL_INTERSECTIONS_3_ISO_CUBOID_3_SEGMENT_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Sphere_3_do_intersect.h
similarity index 96%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Sphere_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Sphere_3_do_intersect.h
index a4907ec3ec6..15f500a9cef 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Sphere_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Sphere_3_do_intersect.h
@@ -25,7 +25,7 @@
 
 #include <CGAL/Sphere_3.h>
 #include <CGAL/Iso_cuboid_3.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h>
+#include <CGALL/Intersections_3/internal/Bbox_3_Sphere_3_do_intersect.h>
 
 namespace CGAL {
   
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Triangle_3_do_intersect.h
similarity index 84%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Triangle_3_do_intersect.h
index 430447124f0..2f3e216d802 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Triangle_3_do_intersect.h
@@ -31,7 +31,7 @@
 // a minimal cost (and we use C++ ;).
 
 #include <CGAL/Uncertain.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Bbox_3_Triangle_3_do_intersect.h>
 
 namespace CGAL {
   
@@ -59,18 +59,6 @@ namespace internal {
 } // namespace Intersections
 
 
-template<typename K>
-bool do_intersect(const Iso_cuboid_3<K>& 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 Iso_cuboid_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
 
 } //namespace CGAL
 
diff --git a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Bounded_3_do_intersect.h
similarity index 82%
rename from Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Bounded_3_do_intersect.h
index e7ad745a4a0..5debbb9cef3 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Tetrahedron_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Bounded_3_do_intersect.h
@@ -23,12 +23,13 @@
 //
 // Author(s)     : Nico Kruithof
 
-#ifndef CGAL_TRIANGLE_3_TETRAHEDRON_3_DO_INTERSECT_H
-#define CGAL_TRIANGLE_3_TETRAHEDRON_3_DO_INTERSECT_H
+#ifndef CGAL_TETRAHEDRON_3_BOUNDED_3_DO_INTERSECT_H
+#define CGAL_TETRAHEDRON_3_BOUNDED_3_DO_INTERSECT_H
 
-#include <CGAL/Triangle_3_Triangle_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h>
+#include <CGAL/Intersections_3/Triangle_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Segment_3_Triangle_3.h>
+#include <CGAL/Intersections_3/internal/Iso_cuboid_3_Triangle_3_do_intersect.h>
+#include <CGAL/Intersections_3/internal/Triangle_3_Sphere_3_do_intersect.h>
 
 namespace CGAL {
 
@@ -175,7 +176,7 @@ do_intersect(const typename K::Tetrahedron_3 &tet,
   template <class K>
 inline
 typename K::Boolean
-  do_intersect(const CGAL::Bbox_3 &bb,
+do_intersect(const CGAL::Bbox_3 &bb,
              const typename K::Tetrahedron_3 &tet,
 	     const K & k)
 {
@@ -184,27 +185,6 @@ typename K::Boolean
   
 } // namespace internal
 } // namespace Intersections
-  
-CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Tetrahedron_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Segment_3, Tetrahedron_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Iso_cuboid_3, Tetrahedron_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Sphere_3, Tetrahedron_3, 3)
-CGAL_DO_INTERSECT_FUNCTION_SELF(Tetrahedron_3, 3)
-
-
-template<typename K>
-bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
-                  const CGAL::Bbox_3& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Bbox_3& b,
-                  const CGAL::Tetrahedron_3<K>& a) {
-  return K().do_intersect_3_object()(a, b);
-}
-
 } //namespace CGAL
 
-#endif // CGAL_TRIANGLE_3_TETRAHEDRON_3_DO_INTERSECT_H
+#endif // CGAL_TETRAHEDRON_3_BOUNDED_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Unbounded_3_do_intersect.h
similarity index 71%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Unbounded_3_do_intersect.h
index 5d6513cf8f7..18f9fa15374 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Tetrahedron_3_Unbounded_3_do_intersect.h
@@ -26,7 +26,8 @@
 #include <CGAL/Plane_3.h>
 #include <CGAL/Line_3.h>
 #include <CGAL/Ray_3.h>
-#include <CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h>
+#include <CGAL/Intersections_3/Sphere_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Plane_3_Triangle_3.h>
 
 namespace CGAL {
   
@@ -48,6 +49,13 @@ bool do_intersect_tetrahedron_unbounded(const typename K::Tetrahedron_3& tet,
 
 
 
+template<typename K>
+bool do_intersect(const typename K::Plane_3& unb,
+                  const typename K::Tetrahedron_3& tet,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+  
 template<typename K>
 bool do_intersect(const typename K::Tetrahedron_3& tet,
                   const typename K::Plane_3& unb,
@@ -56,6 +64,13 @@ bool do_intersect(const typename K::Tetrahedron_3& tet,
 }
 
 
+template<typename K>
+bool do_intersect(const typename K::Line_3& unb,
+                  const typename K::Tetrahedron_3& tet,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+  
 template<typename K>
 bool do_intersect(const typename K::Tetrahedron_3& tet,
                   const typename K::Line_3& unb,
@@ -64,6 +79,13 @@ bool do_intersect(const typename K::Tetrahedron_3& tet,
 }
 
 
+template<typename K>
+bool do_intersect(const typename K::Ray_3& unb,
+                  const typename K::Tetrahedron_3& tet,
+                  const K& k) {
+  return do_intersect_tetrahedron_unbounded(tet, unb, k);
+}
+  
 template<typename K>
 bool do_intersect(const typename K::Tetrahedron_3& tet,
                   const typename K::Ray_3& unb,
@@ -73,48 +95,6 @@ bool do_intersect(const typename K::Tetrahedron_3& tet,
   
 } // namespace internal
 } // namespace Intersections
-    
-template<typename K>
-bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
-                  const CGAL::Plane_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Plane_3<K>& b,
-                  const CGAL::Tetrahedron_3<K>& a) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
-                  const CGAL::Line_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Line_3<K>& b,
-                  const CGAL::Tetrahedron_3<K>& a) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Tetrahedron_3<K>& a,
-                  const CGAL::Ray_3<K>& b) {
-  return K().do_intersect_3_object()(a, b);
-}
-
-  
-template<typename K>
-bool do_intersect(const CGAL::Ray_3<K>& b,
-                  const CGAL::Tetrahedron_3<K>& a) {
-  return K().do_intersect_3_object()(a, b);
-}
-
 } // namespace CGAL
 
 #endif // CGAL_INTERNAL_INTERSECTIONS_3_TETRAHEDRON_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_do_intersect.h
similarity index 98%
rename from Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_do_intersect.h
index d5a08becbae..d68297aebea 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Line_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_do_intersect.h
@@ -121,9 +121,6 @@ bool do_intersect(const typename K::Line_3     &l,
 
 } // namespace internal
 } // namespace Intersections
-  
-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/internal/Intersections_3/Triangle_3_Line_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_intersection.h
similarity index 99%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_intersection.h
index 5b64f0cf45d..fa32149ab80 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Line_3_intersection.h
@@ -424,10 +424,6 @@ intersection(const typename K::Line_3 &l,
 
 } // end namespace internal
 } // namespace Intersections
-  
-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/Triangle_3_Plane_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Plane_3_do_intersect.h
similarity index 97%
rename from Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Plane_3_do_intersect.h
index b4386fa6b93..5d6c5a1e5e3 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Plane_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Plane_3_do_intersect.h
@@ -84,9 +84,6 @@ bool do_intersect(const typename K::Plane_3   &h,
 
 } // namespace internal
 } // namespace Intersections
-  
-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_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_do_intersect.h
similarity index 99%
rename from Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_do_intersect.h
index b00d872a9d8..3a181a43466 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_do_intersect.h
@@ -383,9 +383,6 @@ do_intersect_coplanar(const typename K::Triangle_3 &t,
 
 } // namespace internal
 } // namespace Intersections
-  
-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/internal/Intersections_3/Triangle_3_Ray_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_intersection.h
similarity index 99%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_intersection.h
index 716ceb1c090..da50c997f0a 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Ray_3_intersection.h
@@ -585,9 +585,6 @@ intersection(const typename K::Ray_3 &r,
 
 } // end namespace internal
 } // namespace Intersections
-  
-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/Triangle_3_Segment_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_do_intersect.h
similarity index 99%
rename from Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_do_intersect.h
index 1a76711bca4..95431085bff 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_do_intersect.h
@@ -332,9 +332,6 @@ bool do_intersect(const typename K::Segment_3  &s,
 
 } // namespace internal
 } // namespace Intersections
-  
-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/internal/Intersections_3/Triangle_3_Segment_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_intersection.h
similarity index 99%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_intersection.h
index 9a3a4d988df..f0bf64c31f3 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Segment_3_intersection.h
@@ -563,12 +563,8 @@ intersection(const typename K::Segment_3  &s,
   return internal::intersection(t,s,k);
 }
 
-
 } // end namespace internal
 } // namespace Intersections
-
-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/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Sphere_3_do_intersect.h
similarity index 92%
rename from Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Sphere_3_do_intersect.h
index ad0e36ad2b0..84e05f0ef66 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Sphere_3_do_intersect.h
@@ -49,7 +49,16 @@ do_intersect(const typename K::Sphere_3 &sp,
 {
   return squared_distance(sp.center(), tr) <= sp.squared_radius();
 }
-  
+ 
+template <class K>
+inline
+typename K::Boolean
+do_intersect(const typename K::Triangle_3 &tr,
+             const typename K::Sphere_3 &sp,
+	     const K & k)
+{
+  return squared_distance(sp.center(), tr) <= sp.squared_radius();
+} 
 template <class K>
 inline
 typename K::Boolean
@@ -117,12 +126,6 @@ do_intersect(const typename K::Segment_3 &lin,
   
 } // namespace internal
 } // namespace Intersections
-  
-CGAL_DO_INTERSECT_FUNCTION(Triangle_3, Sphere_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Line_3, Sphere_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Ray_3, Sphere_3, 3)
-CGAL_DO_INTERSECT_FUNCTION(Segment_3, Sphere_3, 3)
-
 } // namespace CGAL
 
 #endif // CGAL_TRIANGLE_3_SPHERE_3_DO_INTERSECT_H
diff --git a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
similarity index 99%
rename from Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
index 9a0ee416c1e..72b6893d6ee 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_do_intersect.h
@@ -453,9 +453,6 @@ do_intersect(const typename K::Triangle_3 &t1,
 
 } // namespace internal
 } // namespace Intersections
-  
-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/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h
similarity index 99%
rename from Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
rename to Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h
index 397aa9d57b2..8bcf0c3963d 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h
@@ -24,6 +24,7 @@
 #define CGAL_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H
 
 #include <CGAL/Intersection_traits_3.h>
+#include <CGAL/Intersections_3/Line_3_Triangle_3.h>
 
 #include <boost/next_prior.hpp>
 #include <list>
@@ -230,9 +231,6 @@ intersection(
 
 } //namespace internal
 } // namespace Intersections
-  
-CGAL_INTERSECTION_FUNCTION_SELF(Triangle_3, 3)
-
 } // namespace CGAL
 
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/intersection_3_1_impl.h b/Intersections_3/include/CGAL/Intersections_3/internal/intersection_3_1_impl.h
index 511fd048bfd..12cf65fcc16 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/intersection_3_1_impl.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/intersection_3_1_impl.h
@@ -24,12 +24,17 @@
 // Author(s)     : Geert-Jan Giezeman <geert@cs.uu.nl>
 //                 Sebastien Loriot <Sebastien.Loriot@geometryfactory.com>
 
+#ifndef CGAL_INTERSECTIONS_3_INTERNAL_INTERSECTION_3_1_IMPL_H
+#define CGAL_INTERSECTIONS_3_INTERNAL_INTERSECTION_3_1_IMPL_H
 
 #include <CGAL/wmult.h>
 #include <boost/next_prior.hpp>
 #include <CGAL/Intersection_traits_3.h>
 #include <CGAL/number_utils.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Iso_cuboid_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Line_3.h>
 
+#include <CGAL/Intersections_3/internal/bbox_intersection_3.h>
 namespace CGAL {
 
   template <class K>
@@ -70,100 +75,7 @@ intersection(const Plane_3<K> &plane1, const Plane_3<K> &plane2,
   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
-cpp11::result_of<typename K::Intersect_3(typename K::Line_3, Bbox_3)>::type
-intersection(const Line_3<K> &a,
-	     const Bbox_3 &b) {
-  return K().intersect_3_object()(a, b);
-}
-
-template <class K>
-inline typename
-cpp11::result_of<typename K::Intersect_3(typename K::Line_3, Bbox_3)>::type
-intersection(const Bbox_3 &a,
-             const Line_3<K> &b) {
-  return K().intersect_3_object()(a, b);
-}
-
-template <class K>
-inline typename
-cpp11::result_of<typename K::Intersect_3(typename K::Ray_3, Bbox_3)>::type
-intersection(const Ray_3<K> &a,
-	     const Bbox_3 &b) {
-  return K().intersect_3_object()(a, b);
-}
-
-template <class K>
-inline typename
-cpp11::result_of<typename K::Intersect_3(typename K::Ray_3, Bbox_3)>::type
-intersection(const Bbox_3 &a,
-             const Ray_3<K> &b) {
-  return K().intersect_3_object()(a, b);
-}
-
-template <class K>
-inline typename
-cpp11::result_of<typename K::Intersect_3(typename K::Segment_3, Bbox_3)>::type
-intersection(const Segment_3<K> &a,
-	     const Bbox_3 &b) {
-  return K().intersect_3_object()(a, b);
-}
-
-template <class K>
-inline typename
-cpp11::result_of<typename K::Intersect_3(typename K::Segment_3, Bbox_3)>::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
@@ -172,8 +84,7 @@ do_intersect(const Plane_3<R> &plane1, const Plane_3<R> &plane2,
   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)
+
 
 
 namespace Intersections {
@@ -1705,3 +1616,5 @@ do_intersect(const Iso_cuboid_3<R> &j, const Line_3<R> &l, const R&)
 } // namespace internal
 } // namespace Intersections
 } // namespace CGAL
+
+#endif CGAL_INTERSECTIONS_3_INTERNAL_INTERSECTION_3_1_IMPL_H
diff --git a/Intersections_3/include/CGAL/intersection_3.h b/Intersections_3/include/CGAL/intersection_3.h
index 3d74dbf38d4..c32e8a12a54 100644
--- a/Intersections_3/include/CGAL/intersection_3.h
+++ b/Intersections_3/include/CGAL/intersection_3.h
@@ -1,9 +1,9 @@
-// Copyright (c) 1997  
+// Copyright (c) 1997
 // Utrecht University (The Netherlands),
 // ETH Zurich (Switzerland),
 // INRIA Sophia-Antipolis (France),
 // Max-Planck-Institute Saarbruecken (Germany),
-// and Tel-Aviv University (Israel).  All rights reserved. 
+// and Tel-Aviv University (Israel).  All rights reserved.
 //
 // 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
@@ -19,7 +19,7 @@
 // $URL$
 // $Id$
 // SPDX-License-Identifier: LGPL-3.0+
-// 
+//
 //
 // Author(s)     : Geert-Jan Giezeman <geert@cs.uu.nl>
 
@@ -29,43 +29,72 @@
 
 #include <CGAL/disable_warnings.h>
 
-#include <CGAL/intersection_3_1.h>
+#include <CGAL/Intersections_3/Bbox_3_Bbox_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Iso_cuboid_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Line_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Plane_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Point_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Ray_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Segment_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Bbox_3_Triangle_3.h>
 
-#include <CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h>
-#include <CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h>
-#include <CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h>
-#include <CGAL/Triangle_3_Triangle_3_intersection.h>
 
-#include <CGAL/Triangle_3_Line_3_do_intersect.h>
-#include <CGAL/Triangle_3_Plane_3_do_intersect.h>
-#include <CGAL/Triangle_3_Point_3_do_intersect.h> 
-#include <CGAL/Triangle_3_Ray_3_do_intersect.h>
-#include <CGAL/Triangle_3_Segment_3_do_intersect.h> 
-#include <CGAL/Triangle_3_Tetrahedron_3_do_intersect.h> 
-#include <CGAL/Triangle_3_Triangle_3_do_intersect.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Iso_cuboid_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Line_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Plane_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Point_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Ray_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Segment_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Iso_cuboid_3_Triangle_3.h>
 
-#include <CGAL/Point_3_Iso_cuboid_3_intersection.h>
-#include <CGAL/Point_3_Line_3_intersection.h>
-#include <CGAL/Point_3_Ray_3_intersection.h>
-#include <CGAL/Point_3_Segment_3_intersection.h>
-#include <CGAL/Point_3_Point_3_intersection.h>
-#include <CGAL/Point_3_Plane_3_intersection.h>
+#include <CGAL/Intersections_3/Line_3_Line_3.h>
+#include <CGAL/Intersections_3/Line_3_Plane_3.h>
+#include <CGAL/Intersections_3/Line_3_Point_3.h>
+#include <CGAL/Intersections_3/Line_3_Ray_3.h>
+#include <CGAL/Intersections_3/Line_3_Segment_3.h>
+#include <CGAL/Intersections_3/Line_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Line_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Line_3_Triangle_3.h>
 
-#include <CGAL/internal/Intersections_3/Bbox_3_Bbox_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Line_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Ray_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Plane_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Sphere_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Triangle_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Bbox_3_Iso_cuboid_3_do_intersect.h>
+#include <CGAL/Intersections_3/Plane_3_Plane_3.h>
+#include <CGAL/Intersections_3/Plane_3_Point_3.h>
+#include <CGAL/Intersections_3/Plane_3_Ray_3.h>
+#include <CGAL/Intersections_3/Plane_3_Segment_3.h>
+#include <CGAL/Intersections_3/Plane_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Plane_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Plane_3_Triangle_3.h>
 
-#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Segment_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Ray_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Sphere_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Iso_cuboid_3_Triangle_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Tetrahedron_3_do_intersect.h>
-#include <CGAL/internal/Intersections_3/Triangle_3_Sphere_3_do_intersect.h>
+#include <CGAL/Intersections_3/Point_3_Line_3.h>
+#include <CGAL/Intersections_3/Point_3_Point_3.h>
+#include <CGAL/Intersections_3/Point_3_Ray_3.h>
+#include <CGAL/Intersections_3/Point_3_Segment_3.h>
+#include <CGAL/Intersections_3/Point_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Point_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Point_3_Triangle_3.h>
+
+#include <CGAL/Intersections_3/Ray_3_Ray_3.h>
+#include <CGAL/Intersections_3/Ray_3_Segment_3.h>
+#include <CGAL/Intersections_3/Ray_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Ray_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Ray_3_Triangle_3.h>
+
+#include <CGAL/Intersections_3/Segment_3_Segment_3.h>
+#include <CGAL/Intersections_3/Segment_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Segment_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Segment_3_Triangle_3.h>
+
+#include <CGAL/Intersections_3/Sphere_3_Sphere_3.h>
+#include <CGAL/Intersections_3/Sphere_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Sphere_3_Triangle_3.h>
+
+#include <CGAL/Intersections_3/Tetrahedron_3_Tetrahedron_3.h>
+#include <CGAL/Intersections_3/Tetrahedron_3_Triangle_3.h>
+
+#include <CGAL/Intersections_3/Triangle_3_Triangle_3.h>
 
 #include <CGAL/enable_warnings.h>
 
diff --git a/Intersections_3/test/Intersections_3/CMakeLists.txt b/Intersections_3/test/Intersections_3/CMakeLists.txt
index a13cf22451a..36d2d70e1d3 100644
--- a/Intersections_3/test/Intersections_3/CMakeLists.txt
+++ b/Intersections_3/test/Intersections_3/CMakeLists.txt
@@ -22,6 +22,17 @@ if ( CGAL_FOUND )
     create_single_source_cgal_program( "${cppfile}" )
   endforeach()
 
+foreach(VAL RANGE 1 55)
+     message(STATUS "NOTICE: Compiling one_${VAL}")
+    add_executable(one_${VAL} one.cpp)
+    target_compile_definitions(one_${VAL} PRIVATE -DSEL=${VAL})
+
+    target_link_libraries(one_${VAL} PRIVATE CGAL::CGAL)
+    if(CGAL_3RD_PARTY_LIBRARIES)
+      target_link_libraries(one_${VAL} PRIVATE ${CGAL_3RD_PARTY_LIBRARIES})
+    endif()    
+  endforeach()
+  
 else()
   
     message(STATUS "This program requires the CGAL library, and will not be compiled.")
diff --git a/Intersections_3/test/Intersections_3/test_intersections_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
index 1390d6a407b..b3c63e243b1 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
@@ -1,3 +1,18 @@
+#if 0
+
+#include <CGAL/Cartesian.h>
+#include <CGAL/Intersections_3/Segment_3_Segment_3.h>
+
+typedef CGAL::Cartesian<double> K;
+
+int main()
+{
+  K::Segment_3 s1, s2;
+  std::cout << do_intersect(s1,s2) << std::endl;
+  return 0;
+}
+
+#else
 // 3D intersection tests.
 
 #include <CGAL/Object.h>
@@ -583,3 +598,4 @@ int main()
 	Test< CGAL::Homogeneous<CGAL::MP_Float> >().run();
 	// TODO : test more kernels.
 }
+#endif
diff --git a/Intersections_3/test/Intersections_3/triangle_other.cpp b/Intersections_3/test/Intersections_3/triangle_other.cpp
index d96a444b24b..e9ffa8b5861 100644
--- a/Intersections_3/test/Intersections_3/triangle_other.cpp
+++ b/Intersections_3/test/Intersections_3/triangle_other.cpp
@@ -1,13 +1,14 @@
 #include <cassert>
 
 #include <CGAL/Cartesian.h>
-#include <CGAL/Triangle_2_Triangle_2_do_intersect.h>
-#include <CGAL/Triangle_3_Line_3_do_intersect.h>
-#include <CGAL/Triangle_3_Plane_3_do_intersect.h>
-#include <CGAL/Triangle_3_Segment_3_do_intersect.h>
-#include <CGAL/Triangle_3_Ray_3_do_intersect.h>
-#include <CGAL/Triangle_3_Triangle_3_do_intersect.h>
-#include <CGAL/Triangle_3_Tetrahedron_3_do_intersect.h>
+#include <CGAL/Intersections_3/Triangle_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Line_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Plane_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Segment_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Ray_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Triangle_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Tetrahedron_3_Triangle_3.h>
+#include <CGAL/Intersections_3/Plane_3_Tetrahedron_3.h>
 
 #include <CGAL/Lazy_exact_nt.h>
 #include <CGAL/Quotient.h>