diff --git a/Packages/H3/changes.txt b/Packages/H3/changes.txt
index 1d99092c5aa..e5f2620a682 100644
--- a/Packages/H3/changes.txt
+++ b/Packages/H3/changes.txt
@@ -1,3 +1,16 @@
+2.59 (11 May 2003)
+- Add missing functor for Plane_3(Point_3, Vector_3).
+- In order to get rid of Direction_3 at some point, I have added :
+    - Line_3(Point_3, Vector_3)        ConstructLine_3
+    - Ray_3(Point_3, Vector_3)         ConstructRay_3
+    - Ray_3(Point_3, Line_3)           ConstructRay_3
+    - Vector_3(Line_3)                 ConstructVector_3
+    - Vector_3(Ray_3)                  ConstructVector_3
+    - Vector_3(Segment_3)              ConstructVector_3
+    - Vector_3 Line_3.to_vector()
+    - Vector_3 Ray_3.to_vector()
+    - Vector_3 Segment_3.to_vector()
+
 2.58 (11 April 2003) [af]
 - bug fix in Iso_cuboid_3
 
diff --git a/Packages/H3/include/CGAL/Homogeneous/LineH3.h b/Packages/H3/include/CGAL/Homogeneous/LineH3.h
index 11f7190a90d..a010f83c088 100644
--- a/Packages/H3/include/CGAL/Homogeneous/LineH3.h
+++ b/Packages/H3/include/CGAL/Homogeneous/LineH3.h
@@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
 template < class R_ >
 class LineH3
   : public R_::template Handle<std::pair<typename R_::Point_3,
-                                         typename R_::Direction_3> >::type
+                                         typename R_::Vector_3> >::type
 {
 CGAL_VC7_BUG_PROTECTED
   typedef typename R_::RT                   RT;
@@ -43,7 +43,7 @@ CGAL_VC7_BUG_PROTECTED
   typedef typename R_::Vector_3             Vector_3;
   typedef typename R_::Aff_transformation_3 Aff_transformation_3;
 
-  typedef std::pair<Point_3, Direction_3>          rep;
+  typedef std::pair<Point_3, Vector_3>          rep;
   typedef typename R_::template Handle<rep>::type  base;
 
 public:
@@ -53,16 +53,19 @@ public:
     : base(rep()) {}
 
   LineH3(const Point_3& p, const Point_3& q)
-    : base(rep(p, (q - p).direction())) {}
+    : base(rep(p, q - p)) {}
 
   LineH3(const Segment_3& s)
-    : base(rep(s.start(), s.direction())) {}
+    : base(rep(s.start(), s.to_vector())) {}
 
   LineH3(const Ray_3& r)
-    : base(rep(r.start(), r.direction())) {}
+    : base(rep(r.start(), r.to_vector())) {}
 
   LineH3(const Point_3& p, const Direction_3& d)
-    : base(rep(p, d)) {}
+    : base(rep(p, d.to_vector())) {}
+
+  LineH3(const Point_3& p, const Vector_3& v)
+    : base(rep(p, v)) {}
 
   Plane_3  perpendicular_plane(const Point_3& p) const;
   LineH3<R>   opposite() const;
@@ -70,7 +73,8 @@ public:
   Point_3  point(int i) const;
   Point_3  projection(const Point_3& p) const;
 
-  const Direction_3 & direction() const;
+  Direction_3 direction() const;
+  const Vector_3 & to_vector() const;
 
   bool            has_on( const Point_3& p ) const;
   bool            is_degenerate() const;
@@ -97,11 +101,17 @@ template < class R >
 CGAL_KERNEL_INLINE
 typename LineH3<R>::Point_3
 LineH3<R>::point(int i) const
-{ return point() + RT(i)*direction().to_vector() ; }
+{ return point() + RT(i)*to_vector() ; }
 
 template < class R >
 inline
-const typename LineH3<R>::Direction_3 &
+const typename LineH3<R>::Vector_3 &
+LineH3<R>::to_vector() const
+{ return Ptr()->second; }
+
+template < class R >
+inline
+typename LineH3<R>::Direction_3
 LineH3<R>::direction() const
 { return Ptr()->second; }
 
@@ -109,13 +119,13 @@ template < class R >
 CGAL_KERNEL_INLINE
 typename LineH3<R>::Plane_3
 LineH3<R>::perpendicular_plane(const typename LineH3<R>::Point_3& p ) const
-{ return Plane_3( p, direction() ); }
+{ return Plane_3( p, to_vector() ); }
 
 template < class R >
 CGAL_KERNEL_INLINE
 LineH3<R>
 LineH3<R>::opposite() const
-{ return LineH3<R>( point(), -direction() ); }
+{ return LineH3<R>( point(), -to_vector() ); }
 
 template < class R >
 CGAL_KERNEL_LARGE_INLINE
@@ -131,7 +141,7 @@ LineH3<R>::projection(const typename LineH3<R>::Point_3& p) const
   const RT  vy = v.hy();
   const RT  vz = v.hz();
   const RT  vw = v.hw();
-  Vector_3 dir = direction().to_vector();
+  Vector_3 dir = to_vector();
   const RT  dx = dir.hx();
   const RT  dy = dir.hy();
   const RT  dz = dir.hz();
@@ -147,7 +157,7 @@ template < class R >
 CGAL_KERNEL_INLINE
 LineH3<R>
 LineH3<R>::transform(const typename LineH3<R>::Aff_transformation_3& t) const
-{ return LineH3<R>(t.transform(point() ), t.transform(direction() )); }
+{ return LineH3<R>(t.transform(point() ), t.transform(to_vector() )); }
 
 
 #ifndef CGAL_NO_OSTREAM_INSERT_LINEH3
@@ -157,11 +167,11 @@ std::ostream &operator<<(std::ostream &os, const LineH3<R> &l)
   switch(os.iword(IO::mode))
   {
     case IO::ASCII :
-        return os << l.point() << ' ' << l.direction();
+        return os << l.point() << ' ' << l.to_vector();
     case IO::BINARY :
-        return os << l.point() <<  l.direction();
+        return os << l.point() <<  l.to_vector();
     default:
-        return  os << "LineH3(" << l.point() << ", " << l.direction() << ")";
+        return  os << "LineH3(" << l.point() << ", " << l.to_vector() << ")";
   }
 }
 #endif // CGAL_NO_OSTREAM_INSERT_LINEH3
@@ -171,9 +181,9 @@ template < class R >
 std::istream &operator>>(std::istream &is, LineH3<R> &l)
 {
   typename R::Point_3 p;
-  typename R::Direction_3 d;
-  is >> p >> d;
-  l = LineH3<R>(p, d);
+  typename R::Vector_3 v;
+  is >> p >> v;
+  l = LineH3<R>(p, v);
   return is;
 }
 #endif // CGAL_NO_ISTREAM_EXTRACT_LINEH3
@@ -182,20 +192,20 @@ template < class R >
 CGAL_KERNEL_INLINE
 bool
 LineH3<R>::has_on( const typename LineH3<R>::Point_3& p ) const
-{ return collinear(point(), point()+direction().to_vector(), p); }
+{ return collinear(point(), point()+to_vector(), p); }
 
 template < class R >
 CGAL_KERNEL_INLINE
 bool
 LineH3<R>::is_degenerate() const
-{ return direction().is_degenerate(); }
+{ return to_vector() == NULL_VECTOR; }
 
 template < class R >
 CGAL_KERNEL_INLINE
 bool
 LineH3<R>::operator==(const LineH3<R>& l) const
 {
-  return l.direction() == direction() && l.has_on( point() );
+  return l.to_vector() == to_vector() && l.has_on( point() );
 }
 
 CGAL_END_NAMESPACE
diff --git a/Packages/H3/include/CGAL/Homogeneous/RayH3.h b/Packages/H3/include/CGAL/Homogeneous/RayH3.h
index bc83c09764d..8eddda4acf9 100644
--- a/Packages/H3/include/CGAL/Homogeneous/RayH3.h
+++ b/Packages/H3/include/CGAL/Homogeneous/RayH3.h
@@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
 template < class R_ >
 class RayH3
   : public R_::template Handle<std::pair<typename R_::Point_3,
-                                         typename R_::Direction_3> >::type
+                                         typename R_::Vector_3> >::type
 {
 CGAL_VC7_BUG_PROTECTED
    typedef typename R_::RT                   RT;
@@ -38,9 +38,10 @@ CGAL_VC7_BUG_PROTECTED
    typedef typename R_::Point_3              Point_3;
    typedef typename R_::Line_3               Line_3;
    typedef typename R_::Direction_3          Direction_3;
+   typedef typename R_::Vector_3             Vector_3;
    typedef typename R_::Aff_transformation_3 Aff_transformation_3;
 
-   typedef std::pair<Point_3, Direction_3>          rep;
+   typedef std::pair<Point_3, Vector_3>             rep;
    typedef typename R_::template Handle<rep>::type  base;
 
 public:
@@ -50,16 +51,23 @@ public:
       : base(rep()) {}
 
     RayH3( const Point_3& sp, const Point_3& secondp)
-      : base(rep(sp, (secondp-sp).direction())) {}
+      : base(rep(sp, secondp-sp)) {}
+
+    RayH3( const Point_3& sp, const Vector_3& v)
+      : base(rep(sp, v)) {}
 
     RayH3( const Point_3& sp, const Direction_3& d)
-      : base(rep(sp, d)) {}
+      : base(rep(sp, d.to_vector())) {}
+
+    RayH3( const Point_3& sp, const Line_3& l)
+      : base(rep(sp, l.to_vector())) {}
 
     const Point_3 & start() const;
     const Point_3 & source() const;
     Point_3 second_point() const;
     Point_3 point(int i) const;
-    const Direction_3 & direction() const;
+    Direction_3 direction() const;
+    const Vector_3 & to_vector() const;
     Line_3  supporting_line() const;
     RayH3<R>   opposite() const;
     RayH3<R>   transform( const Aff_transformation_3 & t) const;
@@ -85,18 +93,26 @@ RayH3<R>::start() const
 
 template < class R >
 inline
-const typename RayH3<R>::Direction_3 &
-RayH3<R>::direction() const
+const typename RayH3<R>::Vector_3 &
+RayH3<R>::to_vector() const
 {
   CGAL_kernel_precondition( !is_degenerate() );
   return Ptr()->second;
 }
 
+template < class R >
+inline
+typename RayH3<R>::Direction_3
+RayH3<R>::direction() const
+{
+  return to_vector().direction();
+}
+
 template < class R >
 CGAL_KERNEL_INLINE
 typename RayH3<R>::Point_3
 RayH3<R>::second_point() const
-{ return start() + direction().to_vector(); }
+{ return start() + to_vector(); }
 
 template < class R >
 CGAL_KERNEL_INLINE
@@ -104,7 +120,7 @@ typename RayH3<R>::Point_3
 RayH3<R>::point(int i) const
 {
   CGAL_kernel_precondition( i >= 0 );
-  return start() + RT(i)*(direction().to_vector() ) ;
+  return start() + RT(i)*to_vector();
 }
 
 template < class R >
@@ -176,7 +192,7 @@ template < class R >
 inline
 bool
 RayH3<R>::is_degenerate() const
-{ return (Ptr()->second).is_degenerate() ; }
+{ return to_vector() == NULL_VECTOR; }
 
 template < class R >
 CGAL_KERNEL_INLINE
diff --git a/Packages/H3/include/CGAL/Homogeneous/SegmentH3.h b/Packages/H3/include/CGAL/Homogeneous/SegmentH3.h
index bb2e8edda30..5610cd98c15 100644
--- a/Packages/H3/include/CGAL/Homogeneous/SegmentH3.h
+++ b/Packages/H3/include/CGAL/Homogeneous/SegmentH3.h
@@ -36,6 +36,7 @@ CGAL_VC7_BUG_PROTECTED
   typedef typename R_::FT                   FT;
   typedef typename R_::Point_3              Point_3;
   typedef typename R_::Direction_3          Direction_3;
+  typedef typename R_::Vector_3             Vector_3;
   typedef typename R_::Line_3               Line_3;
   typedef typename R_::Aff_transformation_3 Aff_transformation_3;
 
@@ -63,10 +64,11 @@ public:
   const Point_3 &  operator[](int i) const;
 
   FT                squared_length() const;
-  Direction_3   direction() const;
-  Line_3        supporting_line() const;
-  SegmentH3<R>  opposite() const;
-  SegmentH3<R>  transform( const Aff_transformation_3& t) const;
+  Direction_3       direction() const;
+  Vector_3          to_vector() const;
+  Line_3            supporting_line() const;
+  SegmentH3<R>      opposite() const;
+  SegmentH3<R>      transform( const Aff_transformation_3& t) const;
   Bbox_3            bbox() const;
   bool              has_on(const Point_3& p) const;
   bool              collinear_has_on(const Point_3& p) const;
@@ -147,6 +149,12 @@ SegmentH3<R>::squared_length() const
           (end() - start())   ;
 }
 
+template < class R >
+CGAL_KERNEL_INLINE
+typename SegmentH3<R>::Vector_3
+SegmentH3<R>::to_vector() const
+{ return end() - start(); }
+
 template < class R >
 CGAL_KERNEL_INLINE
 typename SegmentH3<R>::Direction_3