diff --git a/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/PackageDescription.txt b/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/PackageDescription.txt
index 237b531d8bc..554729df485 100644
--- a/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/PackageDescription.txt
+++ b/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/PackageDescription.txt
@@ -35,17 +35,17 @@
 - `EfficientRANSACTraits`
 
 ## Main Classes ##
-- `CGAL::Shape_detection_3::Efficient_RANSAC<ERTraits>`
+- `CGAL::Shape_detection_3::Efficient_RANSAC<Traits>`
 - `CGAL::Shape_detection_3::Efficient_RANSAC_traits`
 
 ## Shape Interface ##
-- `CGAL::Shape_detection_3::Shape_base<ERTraits>`
+- `CGAL::Shape_detection_3::Shape_base<Traits>`
 
 ## Shape Classes ##
-- `CGAL::Shape_detection_3::Plane<ERTraits>`
-- `CGAL::Shape_detection_3::Sphere<ERTraits>`
-- `CGAL::Shape_detection_3::Cylinder<ERTraits>`
-- `CGAL::Shape_detection_3::Cone<ERTraits>`
-- `CGAL::Shape_detection_3::Torus<ERTraits>`
+- `CGAL::Shape_detection_3::Plane<Traits>`
+- `CGAL::Shape_detection_3::Sphere<Traits>`
+- `CGAL::Shape_detection_3::Cylinder<Traits>`
+- `CGAL::Shape_detection_3::Cone<Traits>`
+- `CGAL::Shape_detection_3::Torus<Traits>`
 */
 
diff --git a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_custom_shape.h b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_custom_shape.h
index 513a608bf63..a862246edf1 100644
--- a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_custom_shape.h
+++ b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_custom_shape.h
@@ -7,14 +7,14 @@
 My_Plane derives from Shape_base. The plane is represented by
 its normal vector and distance to the origin.
 */
-template <class ERTraits>
-class My_Plane : public CGAL::Shape_detection_3::Shape_base<ERTraits> {
+template <class Traits>
+class My_Plane : public CGAL::Shape_detection_3::Shape_base<Traits> {
 public:
-  typedef typename ERTraits::Geom_traits::FT FT;///< number type.
-  typedef typename ERTraits::Geom_traits::Point_3 Point;///< point type.
+  typedef typename Traits::Geom_traits::FT FT;///< number type.
+  typedef typename Traits::Geom_traits::Point_3 Point;///< point type.
 
 public:
-  My_Plane() : Shape_base<ERTraits>() {}
+  My_Plane() : Shape_base<Traits>() {}
 
   //  Computes squared Euclidean distance from query point to the shape.
   virtual FT squared_distance(const Point &p) const {
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
index a49aaac20b7..e5acc9c5c67 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
@@ -43,27 +43,27 @@ namespace CGAL {
    \brief Cone implements Shape_base.
     The cone is represented by its apex, the axis and the opening angle.
     This representation models an open infinite single-cone.
-    \tparam ERTraits a model of `EfficientRANSACTraits`
+    \tparam Traits a model of `EfficientRANSACTraits`
    \ingroup PkgPointSetShapeDetection3Shapes
    */
 
-  template <class ERTraits>
-  class Cone : public Shape_base<ERTraits> {
+  template <class Traits>
+  class Cone : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
      ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
      ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
      ///< property map to access the unoriented normal of an input point.
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point;///< point type.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector;///< vector type.
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Point_3 Point;///< point type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector;///< vector type.
     /// \endcond
 
 	
-    Cone() : Shape_base<ERTraits>() {}
+    Cone() : Shape_base<Traits>() {}
       
     /*!
       The opening angle between the axis and the surface of the cone.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
index 5ea37aa3e06..c2fa9af712d 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
@@ -42,28 +42,28 @@ namespace CGAL {
      \brief Cylinder implements Shape_base. The cylinder is represented
      by the axis, i.e. a point and direction, and the radius. The cylinder is
      unbounded, thus caps are not modelled.
-     \tparam ERTraits a model of `EfficientRANSACTraits`
+     \tparam Traits a model of `EfficientRANSACTraits`
      \ingroup PkgPointSetShapeDetection3Shapes
      */
-  template <class ERTraits>
-  class Cylinder : public Shape_base<ERTraits> {
+  template <class Traits>
+  class Cylinder : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
      ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
      ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
      ///< property map to access the unoriented normal of an input point.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector; ///< vector type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point; ///< point type.
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector; ///< vector type.
+    typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
     /// \endcond
 
-    typedef typename ERTraits::Geom_traits::Line_3 Line; ///< line type.
+    typedef typename Traits::Geom_traits::Line_3 Line; ///< line type.
 
   public:
-    Cylinder() : Shape_base<ERTraits>() {}
+    Cylinder() : Shape_base<Traits>() {}
 
     /*!
       Axis of the cylinder.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
index d60eda1a94f..d7dedba6325 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
@@ -60,10 +60,10 @@ this classes enables to detect subset of connected points lying on the surface o
 Each input point is assigned to either none or at most one detected primitive
 shape. The implementation follows \cgalCite{Schnabel07}.
 
-\tparam ERTraits a model of `EfficientRANSACTraits`
+\tparam Traits a model of `EfficientRANSACTraits`
 
 */
-  template <class ERTraits>
+  template <class Traits>
   class Efficient_RANSAC {
   public:
 
@@ -88,16 +88,16 @@ shape. The implementation follows \cgalCite{Schnabel07}.
 
     /// \name Types 
     /// @{    
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
     ///< random access iterator for input data.
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point; ///< point type.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector; ///< vector type.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector; ///< vector type.
+    typedef typename Traits::Point_pmap Point_pmap;
     ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
     ///< property map to access the unoriented normal of an input point
-    typedef Shape_base<ERTraits> Shape; ///< shape type.
+    typedef Shape_base<Traits> Shape; ///< shape type.
 
 #ifdef DOXYGEN_RUNNING
     typedef unspecified_type Shape_range;
@@ -141,9 +141,9 @@ shape. The implementation follows \cgalCite{Schnabel07}.
     /// @}
 
   private:
-    typedef internal::Octree<internal::DirectPointAccessor<ERTraits> >
+    typedef internal::Octree<internal::DirectPointAccessor<Traits> >
       Direct_octree;
-    typedef internal::Octree<internal::IndexedPointAccessor<ERTraits> >
+    typedef internal::Octree<internal::IndexedPointAccessor<Traits> >
       Indexed_octree;
     //--------------------------------------------typedef
 
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
index be898fbc816..b7a01c97e1f 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
@@ -39,7 +39,7 @@ extern int scoreTime;
 namespace CGAL {
   namespace Shape_detection_3 {
   
-    template<class ERTraits> 
+    template<class Traits> 
     class Efficient_RANSAC;
     
   namespace internal {
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
index 54093089470..4b13bad04ec 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
@@ -32,27 +32,27 @@ namespace CGAL {
     /*!
      \ingroup PkgPointSetShapeDetection3Shapes
      \brief Plane implements Shape_base. The plane is represented by the normal vector and the distance to the origin.
-     \tparam ERTraits a model of `EfficientRANSACTraits`
+     \tparam Traits a model of `EfficientRANSACTraits`
      */
-  template <class ERTraits>
-  class Plane : public Shape_base<ERTraits> {
+  template <class Traits>
+  class Plane : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
      ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
      ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
      ///< property map to access the unoriented normal of an input point.
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point; ///< point type.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector;
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector;
     /// \endcond
 
-    typedef typename ERTraits::Geom_traits::Plane_3 Plane_3;///< plane type for conversion operator.
+    typedef typename Traits::Geom_traits::Plane_3 Plane_3;///< plane type for conversion operator.
 
   public:
-    Plane() : Shape_base<ERTraits>() {}
+    Plane() : Shape_base<Traits>() {}
 
     /*!
       Conversion operator to Plane_3 type.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
index 905e8ed306b..cbdea0facdf 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
@@ -56,7 +56,7 @@ namespace CGAL {
             identify the inliers from the input data and to extract the largest
             cluster of spatially neighbored points.
      */
-  template <class ERTraits>
+  template <class Traits>
   class Shape_base {
     /// \cond SKIP_IN_MANUAL
     template <class T>
@@ -67,19 +67,19 @@ namespace CGAL {
 
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
       ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
       ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
       ///< property map to access the unoriented normal of an input point.
-    typedef Shape_base<ERTraits> Shape;
+    typedef Shape_base<Traits> Shape;
       ///< own type.
     /// \endcond
 
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point; ///< point type.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector; ///< vector type.
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector; ///< vector type.
 
     Shape_base() :
     m_is_valid(false),
@@ -274,12 +274,12 @@ namespace CGAL {
     std::size_t connected_component_kdTree(std::vector<std::size_t> &indices,
                                            FT cluster_epsilon) {
       typedef typename CGAL::Search_traits_3<
-        typename ERTraits::Geom_traits> Traits_base;
+        typename Traits::Geom_traits> Traits_base;
       typedef typename boost::tuple<Point,int> Point_and_int;
       typedef typename CGAL::Search_traits_adapter<Point_and_int,
-        CGAL::Nth_of_tuple_property_map<0, Point_and_int>, Traits_base> Traits;
-      typedef typename CGAL::Kd_tree<Traits> Kd_Tree;
-      typedef typename CGAL::Fuzzy_sphere<Traits> Fuzzy_sphere;
+        CGAL::Nth_of_tuple_property_map<0, Point_and_int>, Traits_base> Search_traits;
+      typedef typename CGAL::Kd_tree<Search_traits> Kd_Tree;
+      typedef typename CGAL::Fuzzy_sphere<Search_traits> Fuzzy_sphere;
 
       m_has_connected_component = true;
       
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
index 21feb7697b7..fb56d0ca434 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
@@ -33,30 +33,30 @@ namespace CGAL {
     /*!
      \ingroup PkgPointSetShapeDetection3Shapes
      \brief Sphere implements Shape_base. The sphere is represented by its center and the radius.
-     \tparam ERTraits a model of `EfficientRANSACTraits`
+     \tparam Traits a model of `EfficientRANSACTraits`
      */
-  template <class ERTraits>
-  class Sphere : public Shape_base<ERTraits> {
+  template <class Traits>
+  class Sphere : public Shape_base<Traits> {
   public:    
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
       ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
       ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
       ///< property map to access the unoriented normal of an input point.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector;
+    typedef typename Traits::Geom_traits::Vector_3 Vector;
       ///< vector type.
-    typedef typename ERTraits::Geom_traits::Sphere_3 Sphere_3;
+    typedef typename Traits::Geom_traits::Sphere_3 Sphere_3;
       ///< sphere type.
-    typedef typename ERTraits::Geom_traits::FT FT;
+    typedef typename Traits::Geom_traits::FT FT;
       ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point;
+    typedef typename Traits::Geom_traits::Point_3 Point;
       ///< point type.
     /// \endcond
 
   public:
-    Sphere() : Shape_base<ERTraits>() {}
+    Sphere() : Shape_base<Traits>() {}
 
     /*!
       Conversion operator to convert to common Sphere_3 type.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
index cb584754bc4..6639e029df4 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
@@ -36,28 +36,28 @@ namespace CGAL {
       \ingroup PkgPointSetShapeDetection3Shapes
       \brief Torus implements Shape_base. The torus is represented by the
       symmetry axis, its center on the axis and the major and minor radii.
-      \tparam ERTraits a model of `EfficientRANSACTraits`
+      \tparam Traits a model of `EfficientRANSACTraits`
      */
-  template <class ERTraits>
-  class Torus : public Shape_base<ERTraits> {
+  template <class Traits>
+  class Torus : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename ERTraits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_iterator Input_iterator;
      ///< random access iterator for input data.
-    typedef typename ERTraits::Point_pmap Point_pmap;
+    typedef typename Traits::Point_pmap Point_pmap;
      ///< property map to access the location of an input point.
-    typedef typename ERTraits::Normal_pmap Normal_pmap;
+    typedef typename Traits::Normal_pmap Normal_pmap;
      ///< property map to access the unoriented normal of an input point.
-    typedef typename ERTraits::Geom_traits::FT FT; ///< number type.
-    typedef typename ERTraits::Geom_traits::Point_3 Point; ///< point type.
-    typedef typename ERTraits::Geom_traits::Vector_3 Vector; ///< vector type.
-    typedef typename ERTraits::Geom_traits::Point_2 Point_2;
+    typedef typename Traits::Geom_traits::FT FT; ///< number type.
+    typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
+    typedef typename Traits::Geom_traits::Vector_3 Vector; ///< vector type.
+    typedef typename Traits::Geom_traits::Point_2 Point_2;
      ///< 2D point type used during construction.
-    typedef typename ERTraits::Geom_traits::Circle_2 Circle;
+    typedef typename Traits::Geom_traits::Circle_2 Circle;
      ///< cricle type used during construction.
     /// \endcond
 
-    Torus() : Shape_base<ERTraits>() {}
+    Torus() : Shape_base<Traits>() {}
       
     /*!
       Direction of symmetry axis.