diff --git a/Principal_component_analysis/include/CGAL/barycenter.h b/Principal_component_analysis/include/CGAL/barycenter.h
index 90a709820fe..d6fcb5e395a 100644
--- a/Principal_component_analysis/include/CGAL/barycenter.h
+++ b/Principal_component_analysis/include/CGAL/barycenter.h
@@ -46,7 +46,7 @@ barycenter(InputIterator begin, InputIterator end, const K & )
   typedef typename std::iterator_traits<InputIterator>::value_type              pair;
   typedef typename pair::second_type                                            FT;
   typedef typename pair::first_type                                             Point;
-  typedef typename Vector<typename Ambient_dimension<Point, K>::type, K>::type  Vector;
+  typedef typename Access::Vector<K, typename Ambient_dimension<Point, K>::type>::type  Vector;
 
   CGAL_precondition(begin != end);
 
@@ -74,7 +74,7 @@ barycenter(PointInputIterator begin, PointInputIterator end,
 {
   typedef typename std::iterator_traits<PointInputIterator>::value_type         Point;
   typedef typename std::iterator_traits<WeightInputIterator>::value_type        FT;
-  typedef typename Vector<typename Ambient_dimension<Point, K>::type, K>::type  Vector;
+  typedef typename Access::Vector<K, typename Ambient_dimension<Point, K>::type>::type  Vector;
 
   CGAL_precondition(begin != end);
 
diff --git a/Principal_component_analysis/include/CGAL/centroid.h b/Principal_component_analysis/include/CGAL/centroid.h
index e4cbbb4c58b..09d8bd631b6 100644
--- a/Principal_component_analysis/include/CGAL/centroid.h
+++ b/Principal_component_analysis/include/CGAL/centroid.h
@@ -812,9 +812,7 @@ template < typename InputIterator,
            typename K, 
            typename Dim_tag  >
 inline
-typename Point<typename Ambient_dimension<typename std::iterator_traits<InputIterator>::value_type, K>::type,
-               K
-              >::type
+typename Access::Point<K, typename Ambient_dimension<typename std::iterator_traits<InputIterator>::value_type, K>::type>::type
 centroid(InputIterator begin,
          InputIterator end, 
          const K& k,
@@ -832,9 +830,7 @@ template < typename InputIterator, typename Kernel_or_Dim >
 struct Dispatch_centroid
 {
   typedef Kernel_or_Dim K;
-  typedef typename Point<typename Ambient_dimension<typename std::iterator_traits<InputIterator>::value_type, K>::type,
-               K
-              >::type result_type;
+  typedef typename Access::Point<K, typename Ambient_dimension<typename std::iterator_traits<InputIterator>::value_type, K>::type >::type result_type;
 
   result_type operator()(InputIterator begin, InputIterator end, const K& k) const
   {
@@ -848,10 +844,9 @@ struct Dispatch_centroid
 template < typename InputIterator, int dim >
 struct Dispatch_centroid < InputIterator, Dimension_tag<dim> >
 {
-  typedef typename Point<typename Ambient_dimension<
-               typename std::iterator_traits<InputIterator>::value_type,
-               typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type,
-               typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type result_type;
+  typedef typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel K;
+  typedef typename Access::Point<K, typename Ambient_dimension<
+               typename std::iterator_traits<InputIterator>::value_type, K >::type >::type result_type;
 
   result_type operator()(InputIterator begin, InputIterator end, Dimension_tag<dim> tag) const
   {
@@ -865,10 +860,10 @@ struct Dispatch_centroid < InputIterator, Dimension_tag<dim> >
 template < typename InputIterator >
 struct Dispatch_centroid <InputIterator, Dynamic_dimension_tag>
 {
-  typedef typename Point<typename Ambient_dimension<
+  typedef typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel K;
+  typedef typename Access::Point<K, typename Ambient_dimension<
                typename std::iterator_traits<InputIterator>::value_type,
-               typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type,
-               typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type result_type;
+               K >::type >::type result_type;
 
   result_type operator()(InputIterator begin, InputIterator end, Dynamic_dimension_tag tag) const
   {
@@ -896,10 +891,11 @@ centroid(InputIterator begin, InputIterator end, const Kernel_or_dim& k_or_d)
 // and uses Kernel_traits<> to find out its kernel, and Feature_dimension for the dimension tag.
 template < typename InputIterator >
 inline
-typename Point<typename Ambient_dimension<
+typename Access::Point<typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel,
+               typename Ambient_dimension<
                typename std::iterator_traits<InputIterator>::value_type,
-               typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type,
                typename Kernel_traits<typename std::iterator_traits<InputIterator>::value_type>::Kernel >::type
+                >::type
 centroid(InputIterator begin, InputIterator end)
 {
   typedef typename std::iterator_traits<InputIterator>::value_type  Point;