diff --git a/.gitattributes b/.gitattributes
index f194392bdda..193c3d58568 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -24,6 +24,8 @@ AABB_tree/include/CGAL/Triangle_3_line_3_intersection.h -text
 AABB_tree/test/AABB_tree/CMakeLists.txt -text
 AABB_tree/test/AABB_tree/aabb_intersection_test.cpp -text
 AABB_tree/test/AABB_tree/aabb_projection_test.cpp -text
+AABB_tree/test/AABB_tree/data/anchor.off -text
+AABB_tree/test/AABB_tree/data/cube.off -text
 Algebraic_foundations/doc_tex/Algebraic_foundations/Algebraic_foundations.png -text
 Algebraic_foundations/doc_tex/Algebraic_foundations/Algebraic_foundations2.png -text
 Algebraic_foundations/doc_tex/Algebraic_foundations/algebraic_structures.tex -text
diff --git a/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_example.cpp b/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_example.cpp
index ecefb88ddb2..17bdb73daab 100644
--- a/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_example.cpp
+++ b/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_example.cpp
@@ -26,7 +26,6 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/AABB_traits.h>
-#include <CGAL/AABB_triangle_primitive.h>
 #include <CGAL/AABB_tree.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
@@ -35,19 +34,21 @@ typedef CGAL::Polyhedron_3<K> Polyhedron;
 typedef K::FT FT;
 typedef K::Ray_3 Ray;
 typedef K::Point_3 Point;
+typedef K::Vector_3 Vector;
 
 class Polyhedron_triangle_primitive
 {
-        // type
+// types
 public:
         typedef K::Triangle_3 Object; // object type
         typedef Polyhedron::Facet_handle Id; // Id type
 
-        // member data
+// member data
 private:
         Id m_handle; // Facet_handle
         Object m_object; // 3D triangle
 
+public:
         Polyhedron_triangle_primitive(Id handle)
                 : m_handle(handle)
         {
@@ -56,13 +57,13 @@ private:
                 const Point& c = handle->halfedge()->prev()->vertex()->point();
                 m_object = Object(a,b,c);
         }
-public:
-        Object object() { return m_object; }
+        const Object& object() const { return m_object; }
+        Object& object() { return m_object; }
         Id id() { return m_handle; }
 };
 
-typedef AABB_traits<K, Polyhedron_triangle_primitive> AABB_Polyhedron_traits;
-typedef AABB_tree<AABB_Polyhedron_traits> Polyhedron_tree;
+typedef CGAL::AABB_traits<K, Polyhedron_triangle_primitive> AABB_Polyhedron_traits;
+typedef CGAL::AABB_tree<AABB_Polyhedron_traits> Polyhedron_tree;
 
 int main(void)
 {
diff --git a/AABB_tree/examples/AABB_tree/AABB_triangle_3_example.cpp b/AABB_tree/examples/AABB_tree/AABB_triangle_3_example.cpp
index 482f194ab20..c8673c5cbf9 100644
--- a/AABB_tree/examples/AABB_tree/AABB_triangle_3_example.cpp
+++ b/AABB_tree/examples/AABB_tree/AABB_triangle_3_example.cpp
@@ -23,9 +23,9 @@
 //******************************************************************************
 
 #include <iostream>
+#include <list>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/AABB_traits.h>
-#include <CGAL/AABB_triangle_primitive.h>
 #include <CGAL/AABB_tree.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
@@ -48,20 +48,22 @@ private:
         Id m_it; // iterator
         Object m_object; // 3D triangle
 
+public:
         Triangle_primitive(Id it)
                 : m_it(it)
         {
                 m_object = *it; // copy triangle
         }
 public:
-        Object object() { return m_object; }
+        const Object& object() const { return m_object; }
+        Object& object() { return m_object; }
         Id id() { return m_it; }
 };
 
-typedef std::list<Triangle>::iterator Iterator;
-typedef typename Triangle_primitive<Iterator> Primitive;
-typedef AABB_traits<K, Primitive> AABB_triangle_traits;
-typedef AABB_tree<AABB_triangle_traits> Polyhedron_tree;
+typedef std::list<typename Triangle>::iterator Iterator;
+typedef Triangle_primitive<Iterator> Primitive;
+typedef CGAL::AABB_traits<typename K, typename Primitive> AABB_triangle_traits;
+typedef CGAL::AABB_tree<typename AABB_triangle_traits> Polyhedron_tree;
 
 int main(void)
 {
diff --git a/AABB_tree/examples/AABB_tree/CMakeLists.txt b/AABB_tree/examples/AABB_tree/CMakeLists.txt
index 9ef3237099e..c133a8ea598 100644
--- a/AABB_tree/examples/AABB_tree/CMakeLists.txt
+++ b/AABB_tree/examples/AABB_tree/CMakeLists.txt
@@ -1,12 +1,11 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-
 project(AABB_example)
 
 CMAKE_MINIMUM_REQUIRED(VERSION 2.4.5)
 
-include_directories(../../include/CGAL/AABB_tree)
+include_directories(../../include/)
 
 set(CMAKE_ALLOW_LOOSE_LOOP_CONSTRUCTS true)
  
@@ -24,12 +23,11 @@ if ( CGAL_FOUND )
 
   include( CGAL_CreateSingleSourceCGALProgram )
 
-  create_single_source_cgal_program("AABB_polyhedron_facet_example.cpp")
   create_single_source_cgal_program("AABB_triangle_3_example.cpp")
+  create_single_source_cgal_program("AABB_polyhedron_facet_example.cpp")
 
 else()
   
     message(STATUS "This program requires the CGAL library, and will not be compiled.")
   
 endif()
-
diff --git a/AABB_tree/include/CGAL/AABB_intersections.h b/AABB_tree/include/CGAL/AABB_intersections.h
index 74cfc2711cb..3b278c329b6 100644
--- a/AABB_tree/include/CGAL/AABB_intersections.h
+++ b/AABB_tree/include/CGAL/AABB_intersections.h
@@ -1,9 +1,11 @@
-#include <CGAL/AABB_tree/Ray_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Bbox_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Segment_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Plane_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Triangle_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Line_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Sphere_3_Bbox_do_intersect.h>
-#include <CGAL/AABB_tree/Triangle_3_segment_3_intersection.h>
-#include <CGAL/AABB_tree/Triangle_3_ray_3_intersection.h>
+// PA: this file will move later to the kernel folder
+
+#include <CGAL/Ray_3_Bbox_3_do_intersect.h>
+#include <CGAL/Bbox_3_Bbox_3_do_intersect.h>
+#include <CGAL/Segment_3_Bbox_3_do_intersect.h>
+#include <CGAL/Plane_3_Bbox_3_do_intersect.h>
+#include <CGAL/Triangle_3_Bbox_3_do_intersect.h>
+#include <CGAL/Line_3_Bbox_3_do_intersect.h>
+#include <CGAL/Sphere_3_Bbox_do_intersect.h>
+#include <CGAL/Triangle_3_segment_3_intersection.h>
+#include <CGAL/Triangle_3_ray_3_intersection.h>
diff --git a/AABB_tree/include/CGAL/AABB_node.h b/AABB_tree/include/CGAL/AABB_node.h
index 7de2e354c7e..b372dec542e 100644
--- a/AABB_tree/include/CGAL/AABB_node.h
+++ b/AABB_tree/include/CGAL/AABB_node.h
@@ -31,15 +31,7 @@
 #include <boost/utility/enable_if.hpp>
 #include <boost/mpl/contains.hpp>
 
-#include <CGAL/AABB_tree/Ray_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Bbox_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Segment_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Plane_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Triangle_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Line_3_Bbox_3_do_intersect.h>
-#include <CGAL/AABB_tree/Sphere_3_Bbox_do_intersect.h>
-#include <CGAL/AABB_tree/Triangle_3_segment_3_intersection.h>
-#include <CGAL/AABB_tree/Triangle_3_ray_3_intersection.h>
+#include <CGAL/AABB_intersections.h>
 
 namespace CGAL {
 
diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index 1375af00abd..2b6b1bb89a4 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -26,6 +26,7 @@
 #define AABB_TRAITS_H_
 
 #include <CGAL/Bbox_3.h>
+#include <CGAL/AABB_intersections.h>
 
 namespace CGAL {
 
@@ -34,7 +35,7 @@ namespace CGAL {
  *
  *
  */
-template<typename GeomTraits, typename Primitive>
+template<typename GeomTraits, typename AABB_primitive>
 class AABB_traits
 {
 public:
@@ -45,10 +46,14 @@ public:
   /// Segment query type
   typedef typename GeomTraits::Segment_3 Segment_3;
 
+  // TODO: delete once "inside..." disappears
+  typedef typename GeomTraits::Triangle_3 Triangle_3;
+
   /// AABBTraits concept types
   typedef typename CGAL::Bbox_3 Bounding_box;
 
-  typedef typename Primitive::Data Data;
+  typedef typename AABB_primitive Primitive;
+  typedef typename AABB_primitive::Object Object;
 
   typedef typename GeomTraits::Sphere_3 Sphere;
   typedef typename GeomTraits::Point_3 Projection;
@@ -121,7 +126,6 @@ private:
   /// Private types
   typedef typename GeomTraits::FT FT;
   typedef typename GeomTraits::Point_3 Point_3;
-  typedef typename TrianglePrimitive::Triangle_3 Triangle_3;
 
 private:
   /**
@@ -131,7 +135,7 @@ private:
    */
   Bounding_box compute_bbox(const Primitive& pr) const
   {
-    return pr.data().bbox();
+    return pr.object().bbox();
   }
 
   typedef enum { CGAL_AXIS_X = 0,
@@ -144,7 +148,7 @@ private:
 
 private:
   // Disabled copy constructor & assignment operator
-  typedef AABB_traits<GeomTraits, TrianglePrimitive> Self;
+  typedef AABB_traits<GeomTraits, Primitive> Self;
   AABB_traits(const Self& src);
   Self& operator=(const Self& src);
 
@@ -152,59 +156,59 @@ private:
 
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::x_less_than(const Primitive& pr1,
-                                const Primitive& pr2)
+AABB_traits<GT,P>::x_less_than(const P& pr1,
+                                const P& pr2)
 {
-  const FT& ax1 = pr1.data().vertex(0).x();
-  const FT& bx1 = pr1.data().vertex(1).x();
-  const FT& cx1 = pr1.data().vertex(2).x();
+  const FT& ax1 = pr1.object().vertex(0).x();
+  const FT& bx1 = pr1.object().vertex(1).x();
+  const FT& cx1 = pr1.object().vertex(2).x();
 
-  const FT& ax2 = pr2.data().vertex(0).x();
-  const FT& bx2 = pr2.data().vertex(1).x();
-  const FT& cx2 = pr2.data().vertex(2).x();
+  const FT& ax2 = pr2.object().vertex(0).x();
+  const FT& bx2 = pr2.object().vertex(1).x();
+  const FT& cx2 = pr2.object().vertex(2).x();
 
   return (ax1+bx1+cx1) < (ax2+bx2+cx2);
 }
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::y_less_than(const Primitive& pr1,
-                                const Primitive& pr2)
+AABB_traits<GT,P>::y_less_than(const P& pr1,
+                                const P& pr2)
 {
-  const FT& ay1 = pr1.data().vertex(0).y();
-  const FT& by1 = pr1.data().vertex(1).y();
-  const FT& cy1 = pr1.data().vertex(2).y();
+  const FT& ay1 = pr1.object().vertex(0).y();
+  const FT& by1 = pr1.object().vertex(1).y();
+  const FT& cy1 = pr1.object().vertex(2).y();
 
-  const FT& ay2 = pr2.data().vertex(0).y();
-  const FT& by2 = pr2.data().vertex(1).y();
-  const FT& cy2 = pr2.data().vertex(2).y();
+  const FT& ay2 = pr2.object().vertex(0).y();
+  const FT& by2 = pr2.object().vertex(1).y();
+  const FT& cy2 = pr2.object().vertex(2).y();
 
   return (ay1+by1+cy1) < (ay2+by2+cy2);
 }
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::z_less_than(const Primitive& pr1,
-                                const Primitive& pr2)
+AABB_traits<GT,P>::z_less_than(const P& pr1,
+                                const P& pr2)
 {
-  const FT& az1 = pr1.data().vertex(0).z();
-  const FT& bz1 = pr1.data().vertex(1).z();
-  const FT& cz1 = pr1.data().vertex(2).z();
+  const FT& az1 = pr1.object().vertex(0).z();
+  const FT& bz1 = pr1.object().vertex(1).z();
+  const FT& cz1 = pr1.object().vertex(2).z();
 
-  const FT& az2 = pr2.data().vertex(0).z();
-  const FT& bz2 = pr2.data().vertex(1).z();
-  const FT& cz2 = pr2.data().vertex(2).z();
+  const FT& az2 = pr2.object().vertex(0).z();
+  const FT& bz2 = pr2.object().vertex(1).z();
+  const FT& cz2 = pr2.object().vertex(2).z();
 
   return (az1+bz1+cz1) < (az2+bz2+cz2);
 }
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 template<typename PrimitiveIterator>
 void
-AABB_traits<GT,TP>::sort_primitives(PrimitiveIterator first,
+AABB_traits<GT,P>::sort_primitives(PrimitiveIterator first,
                                     PrimitiveIterator last,
                                     const Bounding_box& bbox) const
 {
@@ -225,10 +229,10 @@ AABB_traits<GT,TP>::sort_primitives(PrimitiveIterator first,
   }
 }
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 template<typename ConstPrimitiveIterator>
-typename AABB_traits<GT,TP>::Bounding_box
-AABB_traits<GT,TP>::compute_bbox(ConstPrimitiveIterator first,
+typename AABB_traits<GT,P>::Bounding_box
+AABB_traits<GT,P>::compute_bbox(ConstPrimitiveIterator first,
                                  ConstPrimitiveIterator last) const
 {
   Bounding_box bbox = compute_bbox(*first);
@@ -240,10 +244,10 @@ AABB_traits<GT,TP>::compute_bbox(ConstPrimitiveIterator first,
 }
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 template<typename Query>
 bool
-AABB_traits<GT,TP>::do_intersect(const Query& q,
+AABB_traits<GT,P>::do_intersect(const Query& q,
                                  const Bounding_box& bbox) const
 {
   // AABB tree package call
@@ -252,26 +256,26 @@ AABB_traits<GT,TP>::do_intersect(const Query& q,
 }
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 template<typename Query>
 bool
-AABB_traits<GT,TP>::do_intersect(const Query& q,
-                                 const Primitive& pr) const
+AABB_traits<GT,P>::do_intersect(const Query& q,
+                                 const P& pr) const
 {
-  return GT().do_intersect_3_object()(q, pr.data());
+  return GT().do_intersect_3_object()(q, pr.object());
 }
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 template<typename Query>
 bool
-AABB_traits<GT,TP>::intersection(const Query& q,
-                                 const Primitive& pr,
+AABB_traits<GT,P>::intersection(const Query& q,
+                                 const P& pr,
                                  Intersection& intersection) const
 {
   // TODO: implement a real intersection construction method
   // do_intersect is needed here because we construct intersection between
-  // pr.data().supporting_plane() and q
+  // pr.object().supporting_plane() and q
   if ( ! do_intersect(q,pr) )
   {
     return false;
@@ -279,7 +283,8 @@ AABB_traits<GT,TP>::intersection(const Query& q,
 
   // AABB tree package call
   // TODO: extend kernel
-  Object intersection_obj = CGAL::intersection(pr.data(), q);
+  Object o = pr.object();
+  CGAL::Object intersection_obj = CGAL::intersection(o, q);
 
   return CGAL::assign(intersection, intersection_obj);
 }
@@ -287,15 +292,15 @@ AABB_traits<GT,TP>::intersection(const Query& q,
 
 // PA: CAREFUL: the ad-hoc code here must be removed.
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::intersection(const Sphere& sphere,
-                                 const Primitive& pr,
+AABB_traits<GT,P>::intersection(const Sphere& sphere,
+                                 const P& pr,
                                  Projection& projected) const
 {
-  typedef typename TP::Data Triangle_3;
+  typedef typename P::Object Triangle_3;
 
-  const Triangle_3 triangle = pr.data();
+  const Triangle_3 triangle = pr.object();
   projected = triangle.supporting_plane().projection(sphere.center());
 
   // If point is projected outside sphere, return false
@@ -318,9 +323,9 @@ AABB_traits<GT,TP>::intersection(const Sphere& sphere,
 }
 
 
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::is_smaller(const Sphere& a, const Sphere& b) const
+AABB_traits<GT,P>::is_smaller(const Sphere& a, const Sphere& b) const
 {
   CGAL_precondition(a.center() == b.center());
 
@@ -333,9 +338,9 @@ AABB_traits<GT,TP>::is_smaller(const Sphere& a, const Sphere& b) const
 //-------------------------------------------------------
 // Private methods
 //-------------------------------------------------------
-template<typename GT, typename TP>
-typename AABB_traits<GT,TP>::Axis
-AABB_traits<GT,TP>::longest_axis(const Bounding_box& bbox) const
+template<typename GT, typename P>
+typename AABB_traits<GT,P>::Axis
+AABB_traits<GT,P>::longest_axis(const Bounding_box& bbox) const
 {
   const double dx = bbox.xmax() - bbox.xmin();
   const double dy = bbox.ymax() - bbox.ymin();
@@ -366,9 +371,9 @@ AABB_traits<GT,TP>::longest_axis(const Bounding_box& bbox) const
 }
 
 // PA: ad-hoc code to be removed
-template<typename GT, typename TP>
+template<typename GT, typename P>
 bool
-AABB_traits<GT,TP>::is_inside_triangle_3(Point_3& p,
+AABB_traits<GT,P>::is_inside_triangle_3(Point_3& p,
                                          const Triangle_3& t) const
 {
   typedef typename GT::Vector_3 Vector;
diff --git a/AABB_tree/include/CGAL/AABB_tree.h b/AABB_tree/include/CGAL/AABB_tree.h
index 04487146151..788dee9bdaf 100644
--- a/AABB_tree/include/CGAL/AABB_tree.h
+++ b/AABB_tree/include/CGAL/AABB_tree.h
@@ -23,7 +23,7 @@
 
 #include <vector>
 #include <iterator>
-#include <CGAL/AABB_tree/AABB_node.h>
+#include <CGAL/AABB_node.h>
 #include <boost/mpl/vector.hpp>
 #include <boost/utility/enable_if.hpp>
 #include <boost/mpl/contains.hpp>
@@ -43,8 +43,8 @@ public:
   typedef typename AABBTraits::Primitive Primitive;
   typedef typename AABBTraits::Bounding_box Bounding_box;
   typedef typename AABBTraits::Projection_query Projection_query;
-  typedef typename AABBTraits::Projection_type Projection_type;
-  typedef typename AABBTraits::Intersection_type Intersection_type;
+  typedef typename AABBTraits::Projection Projection;
+  typedef typename AABBTraits::Intersection Intersection;
 
   /**
    * @brief Constructor
@@ -77,27 +77,27 @@ public:
 
   template<typename Query>
   bool any_intersection(const Query& q,
-                        Intersection_type& intersection) const;
+                        Intersection& intersection) const;
 
   template<typename Query, typename OutputIterator>
   bool any_intersected_primitive(const Query& q,
                                  Primitive& pr) const;
 
-  Projection_type closest_point(const Projection_query& q,
-                                const Projection_type& hint) const;
+  Projection closest_point(const Projection_query& q,
+                                const Projection& hint) const;
 
 
   //////////////////////////////////////////////
   //TODO: document this
-  Bounding_box root_bbox() const { return p_root_->bounding_box(); }
-  bool is_empty() const { return data_.empty(); }
-  size_t size() const { return data_.size(); }
+  Bounding_box root_bbox() const { return m_p_root->bounding_box(); }
+  bool is_empty() const { return m_data.empty(); }
+  size_t size() const { return m_data.size(); }
 
   /// generic traversal of tree
   template <class Query, class Traversal_traits>
   void traversal(const Query& q, Traversal_traits& traits) const
   {
-    p_root_->template traversal<Traversal_traits,Query>(q, traits, data_.size());
+    m_p_root->template traversal<Traversal_traits,Query>(q, traits, m_data.size());
   }
   //////////////////////////////////////////////
 
@@ -116,14 +116,14 @@ private:
   {
   public:
     First_intersection_traits()
-      : is_found_(false)
-      , result_() {}
+      : m_is_found(false)
+      , m_result() {}
 
-    bool go_further() const { return !is_found_; }
+    bool go_further() const { return !m_is_found; }
 
     void intersection(const Query& q, const Primitive& primitive)
     {
-      is_found_ = AABBTraits().intersection(q, primitive, result_);
+      m_is_found = AABBTraits().intersection(q, primitive, m_result);
     }
 
     bool do_intersect(const Query& q, const Node& node) const
@@ -131,12 +131,12 @@ private:
       return AABBTraits().do_intersect(q, node.bounding_box());
     }
 
-    Intersection_type result() const { return result_; }
-    bool is_intersection_found() const { return is_found_; }
+    Intersection result() const { return m_result; }
+    bool is_intersection_found() const { return m_is_found; }
 
   private:
-    bool is_found_;
-    Intersection_type result_;
+    bool m_is_found;
+    Intersection m_result;
   };
 
 
@@ -169,7 +169,7 @@ private:
     int intersection_number() const { return intersection_nb_; }
 
   private:
-    Intersection_type intersection_;
+    Intersection intersection_;
     int intersection_nb_;
   };
 
@@ -201,7 +201,7 @@ private:
     }
 
   private:
-    Intersection_type intersection_;
+    Intersection intersection_;
     Output_iterator out_it_;
   };
 
@@ -233,7 +233,7 @@ private:
     }
 
   private:
-    Intersection_type intersection_;
+    Intersection intersection_;
     Output_iterator out_it_;
   };
 
@@ -244,7 +244,7 @@ private:
   {
   public:
     Projecting_traits(const Projection_query& query,
-                      const Projection_type& hint)
+                      const Projection& hint)
       : projection_(hint)
       , center_(query)
       , sphere_(AABBTraits().sphere(query,hint))         { }
@@ -256,7 +256,7 @@ private:
       // We don't use q here because it is embedded in sphere_ and we don't
       // want to compute sphere everytime
 
-      Projection_type projection;
+      Projection projection;
       if ( AABBTraits().intersection(sphere_, primitive, projection) )
       {
         const Sphere sphere = AABBTraits().sphere(center_, projection);
@@ -273,10 +273,10 @@ private:
       return AABBTraits().do_intersect(sphere_, node.bounding_box());
     }
 
-    Projection_type projection() const { return projection_; }
+    Projection projection() const { return projection_; }
 
   private:
-    Projection_type projection_;
+    Projection projection_;
     Projection_query center_;
     Sphere sphere_;
   };
@@ -284,9 +284,9 @@ private:
 
 private:
   // set of input primitives (halfedge or face handles)
-  std::vector<Primitive> data_;
+  std::vector<Primitive> m_data;
   // single root node
-  Node* p_root_;
+  Node* m_p_root;
 
 private:
   // Disabled copy constructor & assignment operator
@@ -300,26 +300,26 @@ template<typename Tr>
 template<typename ConstPrimitiveIterator>
 AABB_tree<Tr>::AABB_tree(ConstPrimitiveIterator first,
                          ConstPrimitiveIterator beyond)
-: data_()
-, p_root_(NULL)
+: m_data()
+, m_p_root(NULL)
 {
   // Insert each primitive into tree
   // TODO: get number of elements to reserve space ?
   while ( first != beyond )
   {
-    data_.push_back(Primitive(first));
+    m_data.push_back(Primitive(first));
     ++first;
   }
 
-  p_root_ = new Node[data_.size()-1]();
-  p_root_->expand(data_.begin(), data_.end(), data_.size());
+  m_p_root = new Node[m_data.size()-1]();
+  m_p_root->expand(m_data.begin(), m_data.end(), m_data.size());
 }
 
 
 template<typename Tr>
 AABB_tree<Tr>::~AABB_tree()
 {
-  delete[] p_root_;
+  delete[] m_p_root;
 }
 
 
@@ -353,8 +353,8 @@ AABB_tree<Tr>::number_of_intersections(const Query& query) const
 template<typename Tr>
 template<typename Query, typename OutputIterator>
 OutputIterator
-AABB_tree<Tr>::intersected_primitives(const Query& query,
-                                      OutputIterator out) const
+AABB_tree<Tr>::all_intersected_primitives(const Query& query,
+                                          OutputIterator out) const
 {
   typedef Listing_primitive_traits<Query, OutputIterator> Traversal_traits;
   Traversal_traits traversal_traits(out);
@@ -363,8 +363,6 @@ AABB_tree<Tr>::intersected_primitives(const Query& query,
   return out;
 }
 
-
-
 template<typename Tr>
 template<typename Query, typename OutputIterator>
 OutputIterator
@@ -383,7 +381,7 @@ template<typename Tr>
 template<typename Query>
 bool
 AABB_tree<Tr>::any_intersection(const Query& query,
-                                Intersection_type& intersection) const
+                                Intersection& intersection) const
 {
   typedef First_intersection_traits<Query> Traversal_traits;
   Traversal_traits traversal_traits;
@@ -396,9 +394,9 @@ AABB_tree<Tr>::any_intersection(const Query& query,
 
 
 template<typename Tr>
-typename AABB_tree<Tr>::Projection_type
+typename AABB_tree<Tr>::Projection
 AABB_tree<Tr>::closest_point(const Projection_query& query,
-                             const Projection_type& hint) const
+                             const Projection& hint) const
 {
   Projecting_traits traversal_traits(query,hint);
 
diff --git a/AABB_tree/test/AABB_tree/data/anchor.off b/AABB_tree/test/AABB_tree/data/anchor.off
new file mode 100644
index 00000000000..748f2902ece
--- /dev/null
+++ b/AABB_tree/test/AABB_tree/data/anchor.off
@@ -0,0 +1,1571 @@
+OFF 
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diff --git a/AABB_tree/test/AABB_tree/data/cube.off b/AABB_tree/test/AABB_tree/data/cube.off
new file mode 100644
index 00000000000..c78d6c7d357
--- /dev/null
+++ b/AABB_tree/test/AABB_tree/data/cube.off
@@ -0,0 +1,22 @@
+OFF
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