diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
index 6206ae33aec..971b7f58347 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
@@ -84,7 +84,6 @@ public:
   bool      has_on_bounded_side(const Point_3& p) const;
   bool      has_on_unbounded_side(const Point_3& p) const;
   bool      is_degenerate() const;
-  Bbox_3    bbox() const;
   FT        xmin() const;
   FT        ymin() const;
   FT        zmin() const;
@@ -380,12 +379,6 @@ Iso_cuboidH3<R>::is_degenerate() const
          || ( (this->min)().hz() == (this->max)().hz() ) );
 }
 
-template < class R >
-inline
-Bbox_3
-Iso_cuboidH3<R>::bbox() const
-{ return  (this->min)().bbox() + (this->max)().bbox(); }
-
 template < class R >
 CGAL_KERNEL_INLINE
 Iso_cuboidH3<R>
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
index 7c3e5aeea2b..d8666b62954 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
@@ -25,7 +25,6 @@
 #define CGAL_HOMOGENEOUS_POINT_3_H
 
 #include <CGAL/Origin.h>
-#include <CGAL/Bbox_3.h>
 #include <CGAL/Fourtuple.h>
 #include <CGAL/Kernel/Cartesian_coordinate_iterator_3.h>
 
@@ -111,7 +110,6 @@ public:
 
   Direction_3 direction() const;
   Point_3     transform( const Aff_transformation_3 & t) const;
-  Bbox_3      bbox() const;
 
   bool  operator==( const PointH3<R>& p) const;
   bool  operator!=( const PointH3<R>& p) const;
@@ -230,23 +228,6 @@ typename R::Point_3
 PointH3<R>::transform(const typename PointH3<R>::Aff_transformation_3& t) const
 { return t.transform(static_cast<const Point_3&>(*this)); }
 
-template < class R >
-CGAL_KERNEL_LARGE_INLINE
-Bbox_3
-PointH3<R>::bbox() const
-{
-   Interval_nt<> ihx = CGAL_NTS to_interval(hx());
-   Interval_nt<> ihy = CGAL_NTS to_interval(hy());
-   Interval_nt<> ihz = CGAL_NTS to_interval(hz());
-   Interval_nt<> ihw = CGAL_NTS to_interval(hw());
-
-   Interval_nt<> ix = ihx/ihw;
-   Interval_nt<> iy = ihy/ihw;
-   Interval_nt<> iz = ihz/ihw;
-
-   return Bbox_3(ix.inf(), iy.inf(), iz.inf(), ix.sup(), iy.sup(), iz.sup());
-}
-
 CGAL_END_NAMESPACE
 
 #endif // CGAL_HOMOGENEOUS_POINT_3_H
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
index b96fe54f41d..869cce61a13 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
@@ -17,7 +17,7 @@
 //
 // $URL$
 // $Id$
-// 
+//
 //
 // Author(s)     : Stefan Schirra
 
@@ -80,8 +80,6 @@ public:
 
       SphereH3<R> opposite() const;
 
-      Bbox_3 bbox() const;
-
       Oriented_side oriented_side(const Point_3& p) const;
 
       bool
@@ -226,31 +224,6 @@ SphereH3<R>::opposite() const
                          CGAL::opposite(orientation()) );
 }
 
-template <class R>
-CGAL_KERNEL_INLINE
-Bbox_3
-SphereH3<R>::bbox() const
-{
-
-  Bbox_3 b = center().bbox();
-
-  Interval_nt<> x (b.xmin(), b.xmax());
-  Interval_nt<> y (b.ymin(), b.ymax());
-  Interval_nt<> z (b.zmin(), b.zmax());
-
-  Interval_nt<> sqr = CGAL_NTS to_interval(squared_radius());
-  Interval_nt<> r = CGAL::sqrt(sqr);
-  Interval_nt<> minx = x-r;
-  Interval_nt<> maxx = x+r;
-  Interval_nt<> miny = y-r;
-  Interval_nt<> maxy = y+r;
-  Interval_nt<> minz = z-r;
-  Interval_nt<> maxz = z+r;
-
-  return Bbox_3(minx.inf(), miny.inf(), minz.inf(), 
-		maxx.sup(), maxy.sup(), maxz.sup());
-}
-
 CGAL_END_NAMESPACE
 
 #endif // CGAL_SPHEREH3_H
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index f731081d56e..59c4a3e71fe 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -1952,6 +1952,88 @@ namespace HomogeneousKernelFunctors {
       return Bbox_2(minx.inf(), miny.inf(), maxx.sup(), maxy.sup()); }
   };
 
+
+  template <typename K>
+  class Construct_bbox_3
+  {
+    typedef typename K::Point_3          Point_3;
+    typedef typename K::Segment_3        Segment_3;
+    typedef typename K::Triangle_3       Triangle_3;
+    typedef typename K::Tetrahedron_3    Tetrahedron_3;
+    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
+    typedef typename K::Sphere_3         Sphere_3;
+  public:
+    typedef Bbox_3           result_type;
+    typedef Arity_tag< 1 >   Arity;
+
+    Bbox_3
+    operator()(const Point_3& p) const
+    {
+       Interval_nt<> ihx = CGAL_NTS to_interval(p.hx());
+       Interval_nt<> ihy = CGAL_NTS to_interval(p.hy());
+       Interval_nt<> ihz = CGAL_NTS to_interval(p.hz());
+       Interval_nt<> ihw = CGAL_NTS to_interval(p.hw());
+
+       Interval_nt<> ix = ihx/ihw;
+       Interval_nt<> iy = ihy/ihw;
+       Interval_nt<> iz = ihz/ihw;
+
+       return Bbox_3(ix.inf(), iy.inf(), iz.inf(),
+                     ix.sup(), iy.sup(), iz.sup());
+    }
+
+    Bbox_3
+    operator()(const Segment_3& s) const
+    { return s.source().bbox() + s.target().bbox(); }
+
+    Bbox_3
+    operator()(const Triangle_3& t) const
+    {
+      typename K::Construct_bbox_3 construct_bbox;
+      return construct_bbox(t.vertex(0))
+	   + construct_bbox(t.vertex(1))
+	   + construct_bbox(t.vertex(2));
+    }
+
+    Bbox_3
+    operator()(const Iso_cuboid_3& r) const
+    {
+      typename K::Construct_bbox_3 construct_bbox;
+      return construct_bbox((r.min)()) + construct_bbox((r.max)());
+    }
+
+    Bbox_3
+    operator()(const Tetrahedron_3& t) const
+    {
+      typename K::Construct_bbox_3 construct_bbox_3;
+      return construct_bbox_3(t.vertex(0)) + construct_bbox_3(t.vertex(1))
+           + construct_bbox_3(t.vertex(2)) + construct_bbox_3(t.vertex(3));
+    }
+
+    Bbox_3
+    operator()(const Sphere_3& s) const
+    {
+      Bbox_3 b = s.center().bbox();
+
+      Interval_nt<> x (b.xmin(), b.xmax());
+      Interval_nt<> y (b.ymin(), b.ymax());
+      Interval_nt<> z (b.zmin(), b.zmax());
+
+      Interval_nt<> sqr = CGAL_NTS to_interval(s.squared_radius());
+      Interval_nt<> r = CGAL::sqrt(sqr);
+      Interval_nt<> minx = x-r;
+      Interval_nt<> maxx = x+r;
+      Interval_nt<> miny = y-r;
+      Interval_nt<> maxy = y+r;
+      Interval_nt<> minz = z-r;
+      Interval_nt<> maxz = z+r;
+
+      return Bbox_3(minx.inf(), miny.inf(), minz.inf(),
+		    maxx.sup(), maxy.sup(), maxz.sup());
+    }
+  };
+
+
   template <typename K>
   class Construct_bisector_2
   {