diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
index 99ed9550b18..3d47d12099c 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
@@ -287,6 +287,16 @@ compare_distance_to_point(const Point_2<K>& p,
   return internal::compare_distance_to_point(p, q, r, K());
 }
 
+template <class K >
+inline
+typename K::Comparison_result
+compare_power_distance(const Point_2<K> &r,
+                       const Weighted_point_2<K> &p,
+                       const Weighted_point_2<K> &q)
+{
+  return internal::compare_power_distance(r, p, q, K());
+}
+
 template <class K >
 inline
 typename K::Comparison_result
@@ -939,11 +949,50 @@ orientation(const Vector_2<K> &u, const Vector_2<K> &v)
 
 // parallel() functions are in global_functions.h
 
+template <typename K>
+inline
+typename K::Orientation
+power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
+                                    const Weighted_point_2<K> &q)
+{
+  return internal::power_side_of_oriented_power_circle(p, q, K());
+}
+
+template <typename K>
+inline
+typename K::Orientation
+power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
+                                    const Weighted_point_2<K> &q,
+                                    const Weighted_point_2<K> &r)
+{
+  return internal::power_side_of_oriented_power_circle(p, q, r, K());
+}
+
+template <typename K>
+inline
+typename K::Orientation
+power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
+                                    const Weighted_point_2<K> &q,
+                                    const Weighted_point_2<K> &r,
+                                    const Weighted_point_2<K> &s)
+{
+  return internal::power_side_of_oriented_power_circle(p, q, r, s, K());
+}
+
+template <class K>
+inline
+typename K::Line_2
+radical_axis(const Weighted_point_2<K> &p,
+             const Weighted_point_2<K> &q)
+{
+  return internal::radical_axis(p, q, K());
+}
+
 template <class K>
 inline
 typename K::Line_2
 radical_line(const Circle_2<K> &s1,
-              const Circle_2<K> &s2)
+             const Circle_2<K> &s2)
 {
   return K().construct_radical_line_2_object()(s1,s2);
 }
@@ -1020,6 +1069,16 @@ squared_radius(const Point_2<K>& p, const Point_2<K>& q, const Point_2<K>& r)
   return internal::squared_radius(p, q, r, K());
 }
 
+template < class K >
+inline
+typename K::Point_2
+weighted_circumcenter(const Weighted_point_2<K> &p,
+                      const Weighted_point_2<K> &q,
+                      const Weighted_point_2<K> &r)
+{
+  return internal::weighted_circumcenter(p, q, r, K());
+}
+
 template < class K >
 inline
 typename K::Boolean
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_3.h b/Kernel_23/include/CGAL/Kernel/global_functions_3.h
index 43b6eb34f43..30605491fb6 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_3.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_3.h
@@ -344,6 +344,16 @@ compare_distance_to_point(const Point_3<K> &p,
   return internal::compare_distance_to_point(p, q, r, K());
 }
 
+template < class K >
+inline
+typename K::Comparison_result
+compare_power_distance(const Point_3<K> &r,
+                       const Weighted_point_3<K> &p,
+                       const Weighted_point_3<K> &q)
+{
+  return internal::compare_power_distance(r, p, q, K());
+}
+
 template < class K >
 inline
 typename K::Comparison_result
@@ -436,6 +446,48 @@ compare_signed_distance_to_plane(const Point_3<K> &hp,
   return internal::compare_signed_distance_to_plane(hp, hq, hr, p, q, K());
 }
 
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const Weighted_point_3<K> &p,
+                                const typename K::FT &w)
+{
+  return internal::compare_weighted_squared_radius(p, w, K());
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const Weighted_point_3<K> &p,
+                                const Weighted_point_3<K> &q,
+                                const typename K::FT &w)
+{
+  return internal::compare_weighted_squared_radius(p, q, w, K());
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const Weighted_point_3<K> &p,
+                                const Weighted_point_3<K> &q,
+                                const Weighted_point_3<K> &r,
+                                const typename K::FT &w)
+{
+  return internal::compare_weighted_squared_radius(p, q, r, w, K());
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const Weighted_point_3<K> &p,
+                                const Weighted_point_3<K> &q,
+                                const Weighted_point_3<K> &r,
+                                const Weighted_point_3<K> &s,
+                                const typename K::FT &w)
+{
+  return internal::compare_weighted_squared_radius(p, q, r, s, w, K());
+}
+
 template < class K >
 inline
 typename K::Comparison_result
@@ -1003,6 +1055,111 @@ orthogonal_vector(const Plane_3<K>& p)
 
 // parallel() functions are in Kernel/global_functions.h
 
+template <class K >
+inline
+typename K::FT
+power_distance_to_power_sphere(const Weighted_point_3<K> &p,
+                               const Weighted_point_3<K> &q,
+                               const Weighted_point_3<K> &r,
+                               const Weighted_point_3<K> &s,
+                               const Weighted_point_3<K> &t)
+{
+  return internal::power_distance_to_power_sphere(p, q, r, s, t, K());
+}
+
+template <class K >
+inline
+typename K::FT
+power_product(const Weighted_point_3<K> &p,
+              const Weighted_point_3<K> &q)
+{
+  return internal::power_product(p, q, K());
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
+                                   const Weighted_point_3<K> &q)
+{
+  return internal::power_side_of_bounded_power_sphere(p, q, K());
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
+                                   const Weighted_point_3<K> &q,
+                                   const Weighted_point_3<K> &r)
+{
+  return internal::power_side_of_bounded_power_sphere(p, q, r, K());
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
+                                   const Weighted_point_3<K> &q,
+                                   const Weighted_point_3<K> &r,
+                                   const Weighted_point_3<K> &s)
+{
+  return internal::power_side_of_bounded_power_sphere(p, q, r, s, K());
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
+                                   const Weighted_point_3<K> &q,
+                                   const Weighted_point_3<K> &r,
+                                   const Weighted_point_3<K> &s,
+                                   const Weighted_point_3<K> &t)
+{
+  return internal::power_side_of_bounded_power_sphere(p, q, r, s, t, K());
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
+                                    const Weighted_point_3<K> &q)
+{
+  return internal::power_side_of_oriented_power_sphere(p, q, K());
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
+                                    const Weighted_point_3<K> &q,
+                                    const Weighted_point_3<K> &r)
+{
+  return internal::power_side_of_oriented_power_sphere(p, q, r, K());
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
+                                    const Weighted_point_3<K> &q,
+                                    const Weighted_point_3<K> &r,
+                                    const Weighted_point_3<K> &s)
+{
+  return internal::power_side_of_oriented_power_sphere(p, q, r, s, K());
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
+                                    const Weighted_point_3<K> &q,
+                                    const Weighted_point_3<K> &r,
+                                    const Weighted_point_3<K> &s,
+                                    const Weighted_point_3<K> &t)
+{
+  return internal::power_side_of_oriented_power_sphere(p, q, r, s, t, K());
+}
+
 template <class K>
 inline
 typename K::Plane_3
@@ -1106,6 +1263,44 @@ squared_radius(const Point_3<K> &p)
   return internal::squared_radius(p, K());
 }
 
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p)
+{
+  return internal::squared_radius_smallest_orthogonal_sphere(p, K());
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
+                                          const Weighted_point_3<K> &q)
+{
+  return internal::squared_radius_smallest_orthogonal_sphere(p, q, K());
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
+                                          const Weighted_point_3<K> &q,
+                                          const Weighted_point_3<K> &r)
+{
+  return internal::squared_radius_smallest_orthogonal_sphere(p, q, r, K());
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
+                                          const Weighted_point_3<K> &q,
+                                          const Weighted_point_3<K> &r,
+                                          const Weighted_point_3<K> &s)
+{
+  return internal::squared_radius_smallest_orthogonal_sphere(p, q, r, s, K());
+}
+
 template < class K >
 inline
 typename K::Vector_3
@@ -1123,6 +1318,36 @@ volume(const Point_3<K> &p, const Point_3<K> &q,
   return internal::volume(p, q, r, s, K());
 }
 
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const Weighted_point_3<K> &p,
+                      const Weighted_point_3<K> &q)
+{
+  return internal::weighted_circumcenter(p, q, K());
+}
+
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const Weighted_point_3<K> &p,
+                      const Weighted_point_3<K> &q,
+                      const Weighted_point_3<K> &r)
+{
+  return internal::weighted_circumcenter(p, q, r, K());
+}
+
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const Weighted_point_3<K> &p,
+                      const Weighted_point_3<K> &q,
+                      const Weighted_point_3<K> &r,
+                      const Weighted_point_3<K> &s)
+{
+  return internal::weighted_circumcenter(p, q, r, s, K());
+}
+
 template < class K >
 inline
 typename K::Boolean
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
index 9f144ff7ada..44abff3c9f7 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
@@ -320,6 +320,16 @@ compare_distance_to_point(const typename K::Point_2 &p,
   return k.compare_distance_2_object()(p, q, r);
 }
 
+template <class K >
+inline
+typename K::Comparison_result
+compare_power_distance(const typename K::Point_2 &r,
+                       const typename K::Weighted_point_2 &p,
+                       const typename K::Weighted_point_2 &q, const K& k)
+{
+  return k.compare_power_distance_2_object()(r, p, q);
+}
+
 template <class K >
 inline
 typename K::Comparison_result
@@ -852,6 +862,45 @@ parallel(const typename K::Segment_2 &s1,
   return k.are_parallel_2_object()(s1, s2);
 }
 
+template <class K>
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
+                                    const typename K::Weighted_point_2 &q, const K &k)
+{
+  return k.power_side_of_oriented_power_circle_2_object()(p, q);
+}
+
+template <class K>
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
+                                    const typename K::Weighted_point_2 &q,
+                                    const typename K::Weighted_point_2 &r, const K &k)
+{
+  return k.power_side_of_oriented_power_circle_2_object()(p, q, r);
+}
+
+template <class K>
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
+                                    const typename K::Weighted_point_2 &q,
+                                    const typename K::Weighted_point_2 &r,
+                                    const typename K::Weighted_point_2 &t, const K &k)
+{
+  return k.power_side_of_oriented_power_circle_2_object()(p, q, r, t);
+}
+
+template <typename K>
+inline
+typename K::Line_2
+radical_axis(const typename K::Weighted_point_2 &p,
+             const typename K::Weighted_point_2 &q, const K &k)
+{
+  return k.construct_radical_axis_2_object()(p, q);
+}
+
 template <typename K>
 inline
 typename K::Boolean
@@ -921,6 +970,16 @@ squared_radius(const typename K::Point_2 &p,
   return k.compute_squared_radius_2_object()(p, q, r);
 }
 
+template < class K >
+inline
+typename K::Point_2
+weighted_circumcenter(const typename K::Weighted_point_2 &p,
+                      const typename K::Weighted_point_2 &q,
+                      const typename K::Weighted_point_2 &r, const K &k)
+{
+  return k.construct_weighted_circumcenter_2_object()(p, q, r);
+}
+
 template < class K >
 inline
 typename K::Boolean
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h b/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
index 9a12175786d..7c603de5ccd 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_internal_3.h
@@ -402,6 +402,17 @@ compare_distance_to_point(const typename K::Point_3 &p,
   return k.compare_distance_3_object()(p, q, r);
 }
 
+template < class K >
+inline
+typename K::Comparison_result
+compare_power_distance(const typename K::Point_3 &r,
+                       const typename K::Weighted_point_3 &p,
+                       const typename K::Weighted_point_3 &q,
+                       const K& k)
+{
+  return k.compare_power_distance_3_object()(r, p, q);
+}
+
 template < class K >
 inline
 typename K::Comparison_result
@@ -499,6 +510,48 @@ compare_signed_distance_to_plane(const typename K::Point_3 &hp,
   return EQUAL;
 }
 
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
+                                const typename K::FT &w, const K &k)
+{
+  return k.compare_weighted_squared_radius_3_object()(p, w);
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
+                                const typename K::Weighted_point_3 &q,
+                                const typename K::FT &w, const K &k)
+{
+  return k.compare_weighted_squared_radius_3_object()(p, q, w);
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
+                                const typename K::Weighted_point_3 &q,
+                                const typename K::Weighted_point_3 &r,
+                                const typename K::FT &w, const K &k)
+{
+  return k.compare_weighted_squared_radius_3_object()(p, q, r, w);
+}
+
+template < class K >
+inline
+typename K::Comparison_result
+compare_weighted_squared_radius(const typename K::Weighted_point_3 &p,
+                                const typename K::Weighted_point_3 &q,
+                                const typename K::Weighted_point_3 &r,
+                                const typename K::Weighted_point_3 &s,
+                                const typename K::FT &w, const K &k)
+{
+  return k.compare_weighted_squared_radius_3_object()(p, q, r, s, w);
+}
+
 template < class K >
 inline
 typename K::Comparison_result
@@ -847,6 +900,111 @@ parallel(const typename K::Segment_3 &s1,
   return k.are_parallel_3_object()(s1, s2);
 }
 
+template <typename K>
+inline
+typename K::FT
+power_distance_to_power_sphere(const typename K::Weighted_point_3 &p,
+                               const typename K::Weighted_point_3 &q,
+                               const typename K::Weighted_point_3 &r,
+                               const typename K::Weighted_point_3 &s,
+                               const typename K::Weighted_point_3 &t, const K &k)
+{
+  return k.compute_power_distance_to_power_sphere_3_object()(p, q, r, s, t);
+}
+
+template <class K >
+inline
+typename K::FT
+power_product(const typename K::Weighted_point_3 &p,
+              const typename K::Weighted_point_3 &q, const K &k)
+{
+  return k.compute_power_product_3_object()(p, q);
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
+                                   const typename K::Weighted_point_3 &q, const K &k)
+{
+  return k.power_side_of_bounded_power_sphere_3_object()(p, q);
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
+                                   const typename K::Weighted_point_3 &q,
+                                   const typename K::Weighted_point_3 &r, const K &k)
+{
+  return k.power_side_of_bounded_power_sphere_3_object()(p, q, r);
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
+                                   const typename K::Weighted_point_3 &q,
+                                   const typename K::Weighted_point_3 &r,
+                                   const typename K::Weighted_point_3 &s, const K &k)
+{
+  return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s);
+}
+
+template <class K >
+inline
+typename K::Bounded_side
+power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p,
+                                   const typename K::Weighted_point_3 &q,
+                                   const typename K::Weighted_point_3 &r,
+                                   const typename K::Weighted_point_3 &s,
+                                   const typename K::Weighted_point_3 &t, const K &k)
+{
+  return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s, t);
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
+                                    const typename K::Weighted_point_3 &q, const K &k)
+{
+  return k.power_side_of_oriented_power_sphere_3_object()(p, q);
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
+                                    const typename K::Weighted_point_3 &q,
+                                    const typename K::Weighted_point_3 &r, const K &k)
+{
+  return k.power_side_of_oriented_power_sphere_3_object()(p, q, r);
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
+                                    const typename K::Weighted_point_3 &q,
+                                    const typename K::Weighted_point_3 &r,
+                                    const typename K::Weighted_point_3 &s, const K &k)
+{
+  return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s);
+}
+
+template <class K >
+inline
+typename K::Oriented_side
+power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p,
+                                    const typename K::Weighted_point_3 &q,
+                                    const typename K::Weighted_point_3 &r,
+                                    const typename K::Weighted_point_3 &s,
+                                    const typename K::Weighted_point_3 &t, const K &k)
+{
+  return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s, t);
+}
+
 template <class K >
 inline
 typename K::Bounded_side
@@ -940,6 +1098,48 @@ squared_radius(const typename K::Point_3 &p, const K &k)
   return k.compute_squared_radius_3_object()(p);
 }
 
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
+                                          const K &k)
+{
+  return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p);
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
+                                          const typename K::Weighted_point_3 &q,
+                                          const K &k)
+{
+  return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q);
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
+                                          const typename K::Weighted_point_3 &q,
+                                          const typename K::Weighted_point_3 &r,
+                                          const K &k)
+{
+  return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r);
+}
+
+template < class K >
+inline
+typename K::FT
+squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p,
+                                          const typename K::Weighted_point_3 &q,
+                                          const typename K::Weighted_point_3 &r,
+                                          const typename K::Weighted_point_3 &s,
+                                          const K &k)
+{
+  return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r, s);
+}
+
 template < class K >
 inline
 typename K::FT
@@ -951,6 +1151,36 @@ volume(const typename K::Point_3 &p,
   return k.compute_volume_3_object()(p, q, r, s);
 }
 
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const typename K::Weighted_point_3 &p,
+                      const typename K::Weighted_point_3 &q, const K &k)
+{
+  return k.construct_weighted_circumcenter_3_object()(p, q);
+}
+
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const typename K::Weighted_point_3 &p,
+                      const typename K::Weighted_point_3 &q,
+                      const typename K::Weighted_point_3 &r, const K &k)
+{
+  return k.construct_weighted_circumcenter_3_object()(p, q, r);
+}
+
+template < class K >
+inline
+typename K::Point_3
+weighted_circumcenter(const typename K::Weighted_point_3 &p,
+                      const typename K::Weighted_point_3 &q,
+                      const typename K::Weighted_point_3 &r,
+                      const typename K::Weighted_point_3 &s, const K &k)
+{
+  return k.construct_weighted_circumcenter_3_object()(p, q, r, s);
+}
+
 template < class K >
 inline
 typename K::Boolean