diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
index ab8db68c2bd..a58531e02c3 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Vector_2.h
@@ -48,7 +48,9 @@ class VectorC2
 
 public:
 
-  typedef R_                                     R;
+  typedef typename Rep::const_iterator      Cartesian_const_iterator;
+
+  typedef R_                                R;
 
   VectorC2() {}
  
@@ -84,6 +86,16 @@ public:
     return constant<FT, 1>();
   }
 
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return get(base).begin();
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return get(base).end();
+  }
+
 };
 
 template < class R >
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
index 1b5cc2ba48e..59aabbb11bf 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
@@ -47,7 +47,9 @@ class VectorC3
 
 public:
 
-  typedef R_                                     R;
+  typedef typename Rep::const_iterator      Cartesian_const_iterator;
+
+  typedef R_                                R;
 
   VectorC3() {}
 
@@ -103,6 +105,16 @@ public:
       return constant<FT, 1>();
   }
 
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return get(base).begin();
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return get(base).end();
+  }
+
   const FT & cartesian(int i) const;
   const FT & operator[](int i) const;
   const FT & homogeneous(int i) const;
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH2.h
index f27dab275bc..c2856d125eb 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH2.h
@@ -27,6 +27,7 @@
 
 #include <CGAL/Origin.h>
 #include <CGAL/array.h>
+#include <CGAL/Kernel_d/Cartesian_const_iterator_d.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -54,6 +55,8 @@ public:
 
   typedef const FT Cartesian_coordinate_type;
   typedef const RT& Homogeneous_coordinate_type;
+  typedef Cartesian_const_iterator_d<const RT*> Cartesian_const_iterator;
+
   typedef R_                                    R;
 
    VectorH2() {}
@@ -99,6 +102,17 @@ public:
    const RT & homogeneous(int i) const;
    FT      operator[](int i)  const;
 
+   Cartesian_const_iterator cartesian_begin() const
+   {
+     return make_cartesian_const_iterator_begin(get(base).begin(),
+                                                boost::prior(get(base).end()));
+   }
+
+   Cartesian_const_iterator cartesian_end() const
+   {
+     return make_cartesian_const_iterator_end(boost::prior(get(base).end()));
+   }
+
    int     dimension() const;
    Direction_2 direction() const;
    Vector_2 perpendicular(const Orientation& o ) const;
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH3.h
index c04c09479cd..0a44ce5e0e9 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH3.h
@@ -26,6 +26,7 @@
 
 #include <CGAL/Origin.h>
 #include <CGAL/array.h>
+#include <CGAL/Kernel_d/Cartesian_const_iterator_d.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -50,6 +51,8 @@ class VectorH3
 
 public:
 
+  typedef Cartesian_const_iterator_d<const RT*> Cartesian_const_iterator;
+
   typedef R_                 R;
 
   VectorH3() {}
@@ -104,6 +107,17 @@ public:
   FT    cartesian(int i) const;
   FT    operator[](int i) const;
 
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return make_cartesian_const_iterator_begin(get(base).begin(),
+                                               boost::prior(get(base).end()));
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return make_cartesian_const_iterator_end(boost::prior(get(base).end()));
+  }
+
   int   dimension() const { return 3; };
 
   Direction_3 direction() const;
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_2.tex
index 8b742f2292d..96a340aad17 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_2.tex
@@ -11,6 +11,12 @@ A model for this must provide:
   &p, int);} {returns the past the end iterator of the  \ccHtmlNoLinksFrom{Cartesian} coordinates of \ccc{p}.}
 
 
+\ccMemberFunction{Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
+  &v);} {returns an iterator on the 0'th  \ccHtmlNoLinksFrom{Cartesian} coordinate of \ccc{v}.}
+
+\ccMemberFunction{Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
+  &v, int);} {returns the past the end iterator of the  \ccHtmlNoLinksFrom{Cartesian} coordinates of \ccc{v}.}
+
 
 
 \ccRefines
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_3.tex
index adf5e4f68aa..02aa76042d6 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_ConstructCartesianConstIterator_3.tex
@@ -11,6 +11,12 @@ A model for this must provide:
   &p, int);} {returns the past the end iterator of the \ccHtmlNoLinksFrom{Cartesian} coordinates of \ccc{p}.}
 
 
+\ccMemberFunction{Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
+  &v);} {returns an iterator on the 0'th \ccHtmlNoLinksFrom{Cartesian} coordinate of \ccc{v}.}
+
+\ccMemberFunction{Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
+  &v, int);} {returns the past the end iterator of the \ccHtmlNoLinksFrom{Cartesian} coordinates of \ccc{v}.}
+
 
 
 \ccRefines
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Vector_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Vector_2.tex
index c3b551ed33f..4ef98ae61ed 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Vector_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Vector_2.tex
@@ -11,6 +11,12 @@ from   $p_1$ to $p_2$.
 will explicitly state where you can pass this constant as an argument
 instead of a vector initialized with zeros.
 
+\ccTypes
+\ccThree{Cartesian_const_iterator}{Facet }{}
+\ccThreeToTwo
+
+\ccNestedType{Cartesian_const_iterator}{An iterator for enumerating the
+      \ccHtmlNoLinksFrom{Cartesian} coordinates of a vector.}
 
 \ccCreation
 \ccCreationVariable{v}
@@ -103,6 +109,14 @@ with higher dimensional vectors.  Again they come in a
        {returns  \ccStyle{cartesian(i)}.
         \ccPrecond $0\leq i \leq 1$.}
 
+\ccMethod{Cartesian_const_iterator cartesian_begin() const;}
+       {returns an iterator to the \ccHtmlNoLinksFrom{Cartesian} coordinates 
+        of \ccVar, starting with the 0th coordinate.}
+
+\ccMethod{Cartesian_const_iterator cartesian_end() const;}
+       {returns an off the end iterator to the \ccHtmlNoLinksFrom{Cartesian} 
+        coordinates of \ccVar.}
+
 \ccMethod{int dimension() const;}
        {returns the dimension (the constant 2).}
 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
index c0847e97678..6a81392cc9c 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Vector_3.tex
@@ -11,6 +11,12 @@ from   $p_1$ to $p_2$.
 will explicitly state where you can pass this constant as an argument
 instead of a vector initialized with zeros.
 
+\ccTypes
+\ccThree{Cartesian_const_iterator}{Facet }{}
+\ccThreeToTwo
+
+\ccNestedType{Cartesian_const_iterator}{An iterator for enumerating the
+      \ccHtmlNoLinksFrom{Cartesian} coordinates of a vector.}
 
 \ccCreation
 \ccCreationVariable{v}
@@ -108,6 +114,14 @@ with higher dimensional vectors.  Again they come in a
        {returns  \ccStyle{cartesian(i)}.
         \ccPrecond $0\leq i \leq 2$.}
 
+\ccMethod{Cartesian_const_iterator cartesian_begin() const;}
+       {returns an iterator to the \ccHtmlNoLinksFrom{Cartesian} coordinates 
+        of \ccVar, starting with the 0th coordinate.}
+
+\ccMethod{Cartesian_const_iterator cartesian_end() const;}
+       {returns an off the end iterator to the \ccHtmlNoLinksFrom{Cartesian} 
+        coordinates of \ccVar.}
+
 \ccMethod{int dimension() const;}
        {returns the dimension (the constant 3).}
 
diff --git a/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_2.h b/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_2.h
index 55eb3f61511..9e2bc1b53c5 100644
--- a/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_2.h
+++ b/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_2.h
@@ -17,7 +17,7 @@
 //
 // $URL$
 // $Id$
-// 
+//
 //
 // Author(s)     : Andreas Fabri
 
@@ -26,24 +26,29 @@
 
 #include <cstddef>
 #include <iterator>
+#include <boost/variant.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
+// This class should go away.
+// It is now only used by the Filtered_kernel.
+// It allows to iterate over the coordinates of both a Point_2 and a Vector_2,
+// using a boost::variant, as the iterator types are the same at the kernel level.
 
 template <class K>
-class Cartesian_coordinate_iterator_2 
+class Cartesian_coordinate_iterator_2
 {
 
 protected:
   typedef typename K::Point_2 P;
-  const P* point;
+  typedef typename K::Vector_2 V;
+  boost::variant<const P*, const V*> var;
   int index;
   typedef Cartesian_coordinate_iterator_2<K> Self;
 
-public: 
+public:
 
   typedef typename K::FT FT;
-  typedef P Point;
 
   typedef std::random_access_iterator_tag iterator_category;
   typedef FT                              value_type;
@@ -51,33 +56,43 @@ public:
   typedef const value_type&               reference;
   typedef const value_type*               pointer;
 
-  Cartesian_coordinate_iterator_2(const Point *const p = NULL, 
-				  int _index = 0) 
-    : point(p), index(_index) 
-  {}
+  Cartesian_coordinate_iterator_2()
+    : var((const P*) NULL), index(0) {}
+
+  Cartesian_coordinate_iterator_2(const P * const p, int _index = 0)
+    : var(p), index(_index) {}
+
+  Cartesian_coordinate_iterator_2(const V * const v, int _index = 0)
+    : var(v), index(_index) {}
 
 
-  const FT 
+  const FT
   operator*() const {
-    return point->cartesian(index); 
+    if (const P* const* p = boost::get<const P*>(&var))
+      return (*p)->cartesian(index);
+    if (const V* const* v = boost::get<const V*>(&var))
+      return (*v)->cartesian(index);
+    // std::cerr << "type of var = " << var.type().name() << std::endl;
+    CGAL_error();
+    std::abort(); // to kill warning
   }
-  
+
   Self&  operator++() {
-    index++; 
+    index++;
     return *this;
   }
 
-  Self&  
+  Self&
   operator--() {
-    index--; 
+    index--;
     return *this;
   }
 
-  Self 
-  operator++(int) { 
+  Self
+  operator++(int) {
     Self tmp(*this);
-    ++(*this); 
-    return tmp; 
+    ++(*this);
+    return tmp;
   }
 
   Self
@@ -86,55 +101,55 @@ public:
     --(*this);
     return tmp;
   }
-  
-  Self& 
-  operator+=(difference_type i) { 
+
+  Self&
+  operator+=(difference_type i) {
     index+=i;
-    return *this; 
+    return *this;
   }
 
-  Self& 
-  operator-=(difference_type i) { 
-    index -= i; 
-    return *this; 
+  Self&
+  operator-=(difference_type i) {
+    index -= i;
+    return *this;
   }
 
-  Self 
+  Self
   operator+(difference_type i) const {
-    Self tmp=*this; 
-    return tmp += i; 
+    Self tmp=*this;
+    return tmp += i;
   }
 
   Self operator-(difference_type i) const {
-    Self tmp=*this; 
-    return tmp -= i; 
+    Self tmp=*this;
+    return tmp -= i;
   }
 
-  difference_type 
+  difference_type
   operator-(const Self& x) const {
-    CGAL_kernel_assertion(point == x.point);
-    return index - x.index; 
+    CGAL_kernel_assertion(var == x.var);
+    return index - x.index;
   }
 
-  reference operator[](difference_type i) const { 
-    return *(*this + i); 
+  reference operator[](difference_type i) const {
+    return *(*this + i);
   }
 
   bool operator==(const Self& x) const {
-    return (point == x.point)&& (index == x.index) ; 
-  }
-  
-  bool operator!=(const Self& x) const { 
-    return ! (*this==x); 
+    return (var == x.var) && (index == x.index);
   }
 
-  bool operator<(const Self& x) const 
-  { 
-    return (x - *this) > 0; }
+  bool operator!=(const Self& x) const {
+    return ! (*this==x);
+  }
+
+  bool operator<(const Self& x) const
+  {
+    return (x - *this) > 0;
+  }
 
 };
 
-
-
 CGAL_END_NAMESPACE
+
 #endif // CGAL_CARTESIAN_COORDINATE_ITERATOR_2_H
diff --git a/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_3.h b/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_3.h
index 0a9b513d38b..9afa9c5a084 100644
--- a/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_3.h
+++ b/Kernel_23/include/CGAL/Kernel/Cartesian_coordinate_iterator_3.h
@@ -17,7 +17,7 @@
 //
 // $URL$
 // $Id$
-// 
+//
 //
 // Author(s)     : Andreas Fabri
 
@@ -26,23 +26,27 @@
 
 #include <cstddef>
 #include <iterator>
+#include <boost/variant.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
+// This class should go away.
+// It is now only used by the Filtered_kernel.
+// It allows to iterate over the coordinates of both a Point_3 and a Vector_3,
+// using a boost::variant, as the iterator types are the same at the kernel level.
 
 template <class K>
-class Cartesian_coordinate_iterator_3 
+class Cartesian_coordinate_iterator_3
 {
-
   typedef typename K::Point_3 P;
-  const P* point;
+  typedef typename K::Vector_3 V;
+  boost::variant<const P*, const V*> var;
   int index;
   typedef Cartesian_coordinate_iterator_3<K> Self;
 
-public: 
+public:
 
   typedef typename K::FT FT;
-  typedef P Point;
 
   typedef std::random_access_iterator_tag iterator_category;
   typedef FT                              value_type;
@@ -50,33 +54,42 @@ public:
   typedef const value_type&               reference;
   typedef const value_type*               pointer;
 
-  Cartesian_coordinate_iterator_3(const Point *const p = NULL,
-				  int _index = 0) 
-    : point(p), index(_index) 
-  {}
+  Cartesian_coordinate_iterator_3()
+    : var((const P*) NULL), index(0) {}
 
+  Cartesian_coordinate_iterator_3(const P *const p, int _index = 0)
+    : var(p), index(_index) {}
 
-  const FT 
+  Cartesian_coordinate_iterator_3(const V *const v, int _index = 0)
+    : var(v), index(_index) {}
+
+  const FT
   operator*() const {
-    return point->cartesian(index); 
+    if (const P* const* p = boost::get<const P*>(&var))
+      return (*p)->cartesian(index);
+    if (const V* const* v = boost::get<const V*>(&var))
+      return (*v)->cartesian(index);
+    // std::cerr << "type of var = " << var.type().name() << std::endl;
+    CGAL_error();
+    std::abort(); // to kill warning
   }
-  
+
   Self&  operator++() {
-    index++; 
+    index++;
     return *this;
   }
 
-  Self&  
+  Self&
   operator--() {
-    index--; 
+    index--;
     return *this;
   }
 
-  Self 
-  operator++(int) { 
+  Self
+  operator++(int) {
     Self tmp(*this);
-    ++(*this); 
-    return tmp; 
+    ++(*this);
+    return tmp;
   }
 
   Self
@@ -85,55 +98,55 @@ public:
     --(*this);
     return tmp;
   }
-  
-  Self& 
-  operator+=(difference_type i) { 
+
+  Self&
+  operator+=(difference_type i) {
     index+=i;
-    return *this; 
+    return *this;
   }
 
-  Self& 
-  operator-=(difference_type i) { 
-    index -= i; 
-    return *this; 
+  Self&
+  operator-=(difference_type i) {
+    index -= i;
+    return *this;
   }
 
-  Self 
+  Self
   operator+(difference_type i) const {
-    Self tmp=*this; 
-    return tmp += i; 
+    Self tmp=*this;
+    return tmp += i;
   }
 
   Self operator-(difference_type i) const {
-    Self tmp=*this; 
-    return tmp -= i; 
+    Self tmp=*this;
+    return tmp -= i;
   }
 
-  difference_type 
+  difference_type
   operator-(const Self& x) const {
-    CGAL_kernel_assertion(point == x.point);
-    return index - x.index; 
+    CGAL_kernel_assertion(var == x.var);
+    return index - x.index;
   }
 
-  reference operator[](difference_type i) const { 
-    return *(*this + i); 
+  reference operator[](difference_type i) const {
+    return *(*this + i);
   }
 
   bool operator==(const Self& x) const {
-    return (point == x.point)&& (index == x.index) ; 
-  }
-  
-  bool operator!=(const Self& x) const { 
-    return ! (*this==x); 
+    return (var == x.var) && (index == x.index) ;
   }
 
-  bool operator<(const Self& x) const 
-  { 
-    return (x - *this) > 0; }
+  bool operator!=(const Self& x) const {
+    return ! (*this==x);
+  }
+
+  bool operator<(const Self& x) const
+  {
+    return (x - *this) > 0;
+  }
 
 };
 
-
-
 CGAL_END_NAMESPACE
+
 #endif // CGAL_CARTESIAN_COORDINATE_ITERATOR_3_H
diff --git a/Kernel_23/include/CGAL/Kernel/function_objects.h b/Kernel_23/include/CGAL/Kernel/function_objects.h
index 1df0d412ce5..86bed02b938 100644
--- a/Kernel_23/include/CGAL/Kernel/function_objects.h
+++ b/Kernel_23/include/CGAL/Kernel/function_objects.h
@@ -1741,6 +1741,7 @@ namespace CommonKernelFunctors {
   class Construct_cartesian_const_iterator_2
   {
     typedef typename K::Point_2          Point_2;
+    typedef typename K::Vector_2         Vector_2;
     typedef typename K::Cartesian_const_iterator_2
     Cartesian_const_iterator_2;
 
@@ -1750,21 +1751,34 @@ namespace CommonKernelFunctors {
 
     Cartesian_const_iterator_2
     operator()( const Point_2& p) const
-      {
-	return p.rep().cartesian_begin();
-      }
+    {
+      return p.rep().cartesian_begin();
+    }
 
     Cartesian_const_iterator_2
     operator()( const Point_2& p, int) const
     {
       return p.rep().cartesian_end();
     }
+
+    Cartesian_const_iterator_2
+    operator()( const Vector_2& v) const
+    {
+      return v.rep().cartesian_begin();
+    }
+
+    Cartesian_const_iterator_2
+    operator()( const Vector_2& v, int) const
+    {
+      return v.rep().cartesian_end();
+    }
   };
 
   template <typename K>
   class Construct_cartesian_const_iterator_3
   {
     typedef typename K::Point_3          Point_3;
+    typedef typename K::Vector_3         Vector_3;
     typedef typename K::Cartesian_const_iterator_3
     Cartesian_const_iterator_3;
 
@@ -1774,15 +1788,27 @@ namespace CommonKernelFunctors {
 
     Cartesian_const_iterator_3
     operator()( const Point_3& p) const
-      {
-	return p.rep().cartesian_begin();
-      }
+    {
+      return p.rep().cartesian_begin();
+    }
 
     Cartesian_const_iterator_3
     operator()( const Point_3& p, int) const
     {
       return p.rep().cartesian_end();
     }
+
+    Cartesian_const_iterator_3
+    operator()( const Vector_3& v) const
+    {
+      return v.rep().cartesian_begin();
+    }
+
+    Cartesian_const_iterator_3
+    operator()( const Vector_3& v, int) const
+    {
+      return v.rep().cartesian_end();
+    }
   };
 
   template <typename K>
diff --git a/Kernel_23/include/CGAL/Vector_2.h b/Kernel_23/include/CGAL/Vector_2.h
index 23fe321c788..a2b3728b8c7 100644
--- a/Kernel_23/include/CGAL/Vector_2.h
+++ b/Kernel_23/include/CGAL/Vector_2.h
@@ -52,6 +52,7 @@ class Vector_2 : public R_::Kernel_base::Vector_2
 public:
 
   typedef RVector_2 Rep;
+  typedef typename R_::Cartesian_const_iterator_2 Cartesian_const_iterator;
 
   const Rep& rep() const
   {
@@ -123,6 +124,16 @@ public:
       return cartesian(i);
   }
 
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return typename R::Construct_cartesian_const_iterator_2()(*this);
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return typename R::Construct_cartesian_const_iterator_2()(*this,2);
+  }
+
   typename Qualified_result_of<typename R::Compute_hx_2,Vector_2>::type
   hx() const
   {
diff --git a/Kernel_23/include/CGAL/Vector_3.h b/Kernel_23/include/CGAL/Vector_3.h
index fe18077b631..8ce54737b91 100644
--- a/Kernel_23/include/CGAL/Vector_3.h
+++ b/Kernel_23/include/CGAL/Vector_3.h
@@ -50,7 +50,8 @@ class Vector_3 : public R_::Kernel_base::Vector_3
 
 public:
 
-  typedef typename R_::Kernel_base::Vector_3         Rep;
+  typedef typename R_::Cartesian_const_iterator_3 Cartesian_const_iterator;
+  typedef typename R_::Kernel_base::Vector_3      Rep;
 
   const Rep& rep() const
   {
@@ -203,6 +204,16 @@ public:
       return cartesian(i);
   }
 
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this);
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this,3);
+  }
+
   typename Qualified_result_of<typename R::Compute_squared_length_3, Vector_3>::type
   squared_length() const
   {
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_2.h
index dd1c0efe9e8..aad38e399cd 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_2.h
@@ -32,6 +32,8 @@ _test_cls_vector_2(const R& )
  typedef typename  R::FT    FT;
 
  typename R::Vector_2       iv;
+ typedef typename R::Vector_2::Cartesian_const_iterator CCI;
+
  CGAL::Vector_2<R>  v1;
  CGAL::Vector_2<R>  v2(iv);
  CGAL::Vector_2<R>  v0(CGAL::NULL_VECTOR);
@@ -100,6 +102,63 @@ _test_cls_vector_2(const R& )
  assert( v10.direction() == v8.direction() );
  assert( v11.direction() == v8.direction() );
 
+
+  // now we test the Coordinate iterator
+  const CGAL::Vector_2<R> v(1, 2);
+
+  CCI it = v.cartesian_begin();
+
+  // Default constructor
+  CCI itt;
+
+  // Copy constructor
+  CCI itc(it);
+
+  assert(itc == it);
+
+  // Assignment
+  itt = it;
+
+  // Equality
+  assert(itt == it);
+
+  assert(itt - it == 0);
+
+  // Increment
+  itt++;
+
+  // Inequality
+  assert(itt != it);
+
+  assert(it < itt);
+  assert(itt - it == 1);
+
+  // dereference
+  assert(*it == FT(1));
+
+  it++;
+  assert(*it == FT(2));
+  it++;
+
+  CCI it2 = v.cartesian_end();
+
+  assert(it == it2);
+  it--;
+  it--;
+  assert(*it == FT(1));
+  it += 1;
+  assert(*it == FT(2));
+  it -= 1;
+  assert(*it == FT(1));
+
+  it2 = it + 1;
+  it2--;
+  assert(it == it2);
+  it++;
+  it2 = it - 1;
+  it2++;
+  assert(it == it2);
+
  std::cout << "done" << std::endl;
  return true;
 }
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_3.h
index c416da77cbc..855d0c8a5be 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_vector_3.h
@@ -32,6 +32,7 @@ _test_cls_vector_3(const R& )
  typedef typename  R::FT    FT;
 
  typename R::Vector_3       iv;
+ typedef typename R::Vector_3::Cartesian_const_iterator CCI;
 
  CGAL::Vector_3<R>  v1;
  CGAL::Vector_3<R>  v2(iv);
@@ -91,6 +92,69 @@ _test_cls_vector_3(const R& )
 
  assert( v0.dimension() == 3 );
 
+
+ // now we test the Coordinate iterator
+  const CGAL::Vector_3<R> v(1, 2, 3);
+
+  CCI it = v.cartesian_begin();
+
+  // Default constructor
+  CCI itt;
+
+  // Copy constructor
+  CCI itc(it);
+
+  assert(itc == it);
+
+  // Assignment
+  itt = it;
+
+  // Equality
+  assert(itt == it);
+
+  assert(itt - it == 0);
+
+  // Increment
+  itt++;
+
+  // Inequality
+  assert(itt != it);
+
+  assert(it < itt);
+  assert(itt - it == 1);
+
+  itt++;
+  assert(itt - it == 2);
+
+  // dereference
+  assert(*it == FT(1));
+
+  it++;
+  assert(*it == FT(2));
+  it++;
+  assert(*it == FT(3));
+
+  it++;
+  CCI it2 = v.cartesian_end();
+
+  assert(it == it2);
+  it--;
+  it--;
+  it--;
+  assert(*it == FT(1));
+  it += 1;
+  assert(*it == FT(2));
+  it -= 1;
+  assert(*it == FT(1));
+
+  it2 = it + 1;
+  it2--;
+  assert(it == it2);
+  it++;
+  it2 = it - 1;
+  it2++;
+  assert(it == it2);
+
  std::cout << "done" << std::endl;
  return true;
 }
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
index d7e214950d2..b55cd8fde5c 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
@@ -248,6 +248,8 @@ test_new_2(const R& rep)
 
   cccit = construct_cartesian_const_iterator_2(p1);
   cccit = construct_cartesian_const_iterator_2(p1,0);
+  cccit = construct_cartesian_const_iterator_2(v6);
+  cccit = construct_cartesian_const_iterator_2(v6,0);
   
 #ifndef CGAL_NO_DEPRECATED_CODE
   typename R::Construct_supporting_line_2 construct_supporting_line
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
index d3773119ac9..c1023c6d63f 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
@@ -299,6 +299,8 @@ test_new_3(const R& rep)
 
   cccit = construct_cartesian_const_iterator_3(p1);
   cccit = construct_cartesian_const_iterator_3(p1,0);
+  cccit = construct_cartesian_const_iterator_3(v5);
+  cccit = construct_cartesian_const_iterator_3(v5,0);
 
 #ifndef CGAL_NO_DEPRECATED_CODE
   typename R::Construct_supporting_line_3 construct_supporting_line