diff --git a/BGL/include/CGAL/boost/graph/named_params_helper.h b/BGL/include/CGAL/boost/graph/named_params_helper.h
index 158071c3f98..bf499143eb2 100644
--- a/BGL/include/CGAL/boost/graph/named_params_helper.h
+++ b/BGL/include/CGAL/boost/graph/named_params_helper.h
@@ -355,7 +355,7 @@ CGAL_DEF_GET_INITIALIZED_INDEX_MAP(face, typename boost::graph_traits<Graph>::fa
       friend void put(const DummyNormalMap&, const key_type&, const value_type&) { }
     };
 
-    typedef DummyNormalMap NoMap;
+    typedef DummyNormalMap NoMap; // public
     typedef typename internal_np::Lookup_named_param_def<
       internal_np::normal_t,
       NamedParameters,
@@ -367,6 +367,11 @@ CGAL_DEF_GET_INITIALIZED_INDEX_MAP(face, typename boost::graph_traits<Graph>::fa
       return parameters::choose_parameter<Point_map>(parameters::get_parameter(np, internal_np::point_map));
     }
 
+    static Point_map get_point_map(const NamedParameters& np)
+    {
+      return parameters::choose_parameter<Point_map>(parameters::get_parameter(np, internal_np::point_map));
+    }
+
     static Const_point_map get_const_point_map(const PointRange&, const NamedParameters& np)
     {
       return parameters::choose_parameter<Const_point_map>(parameters::get_parameter(np, internal_np::point_map));
@@ -377,6 +382,11 @@ CGAL_DEF_GET_INITIALIZED_INDEX_MAP(face, typename boost::graph_traits<Graph>::fa
       return parameters::choose_parameter<Normal_map>(parameters::get_parameter(np, internal_np::normal_map));
     }
 
+    static Normal_map get_normal_map(const NamedParameters& np)
+    {
+      return parameters::choose_parameter<Normal_map>(parameters::get_parameter(np, internal_np::normal_map));
+    }
+
     static Geom_traits get_geom_traits(const PointRange&, const NamedParameters& np)
     {
       return parameters::choose_parameter<Geom_traits>(parameters::get_parameter(np, internal_np::geom_traits));
@@ -397,67 +407,6 @@ CGAL_DEF_GET_INITIALIZED_INDEX_MAP(face, typename boost::graph_traits<Graph>::fa
       };
     };
 
-    namespace parameters
-    {
-      template <typename PointRange>
-      CGAL::parameters::Default_named_parameters
-      inline all_default(const PointRange&)
-      {
-        return CGAL::parameters::all_default();
-      }
-    }
-
-    template<typename PointRange>
-    class GetFT
-    {
-    public:
-      typedef typename Kernel_traits<
-        typename std::iterator_traits<
-          typename PointRange::iterator
-          >::value_type
-        >::Kernel::FT type;
-    };
-
-    template<typename PointRange, typename NamedParameters>
-    class GetK
-    {
-      typedef typename GetPointMap<PointRange, NamedParameters>::type Vpm;
-      typedef typename Kernel_traits<
-        typename boost::property_traits<Vpm>::value_type
-      >::Kernel Default_kernel;
-
-    public:
-      typedef typename internal_np::Lookup_named_param_def <
-        internal_np::geom_traits_t,
-        NamedParameters,
-        Default_kernel
-      > ::type  Kernel;
-    };
-
-    template<typename PointRange, typename NamedParameters>
-    class GetNormalMap
-    {
-      struct DummyNormalMap
-      {
-        typedef typename std::iterator_traits<typename PointRange::iterator>::value_type key_type;
-        typedef typename GetK<PointRange, NamedParameters>::Kernel::Vector_3 value_type;
-        typedef value_type reference;
-        typedef boost::read_write_property_map_tag category;
-
-        typedef DummyNormalMap Self;
-        friend value_type get(const Self&, const key_type&) { return CGAL::NULL_VECTOR; }
-        friend void put(const Self&, const key_type&, const value_type&) { }
-      };
-
-    public:
-      typedef DummyNormalMap NoMap;
-      typedef typename internal_np::Lookup_named_param_def <
-        internal_np::normal_t,
-        NamedParameters,
-        DummyNormalMap//default
-        > ::type  type;
-    };
-
     template<typename PlaneRange, typename NamedParameters>
     class GetPlaneMap
     {
diff --git a/Point_set_processing_3/include/CGAL/IO/read_off_points.h b/Point_set_processing_3/include/CGAL/IO/read_off_points.h
index cac9a61de93..9e7935232c5 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_off_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_off_points.h
@@ -92,16 +92,16 @@ bool read_OFF(std::istream& is,
   typedef Point_set_processing_3::Fake_point_range<OutputIteratorValueType> PointRange;
 
   // basic geometric types
-  typedef typename CGAL::GetPointMap<PointRange, CGAL_BGL_NP_CLASS>::type PointMap;
-  typedef typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::type NormalMap;
-  typedef typename Point_set_processing_3::GetK<PointRange, CGAL_BGL_NP_CLASS>::Kernel Kernel;
-  typedef typename Kernel::FT                                                          FT;
+  typedef Point_set_processing_3_np_helper<PointRange, CGAL_BGL_NP_CLASS> NP_helper;
+  typedef typename NP_helper::Point_map PointMap;
+  typedef typename NP_helper::Normal_map NormalMap;
+  typedef typename NP_helper::Geom_traits Kernel;
+  typedef typename Kernel::FT FT;
 
-  bool has_normals = !(boost::is_same<NormalMap,
-                       typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::NoMap>::value);
+  bool has_normals = !(boost::is_same<NormalMap, typename NP_helper::NoMap>::value);
 
-  PointMap point_map = choose_parameter<PointMap>(get_parameter(np, internal_np::point_map));
-  NormalMap normal_map = choose_parameter<NormalMap>(get_parameter(np, internal_np::normal_map));
+  PointMap point_map = NP_helper::get_point_map(np);
+  NormalMap normal_map = NP_helper::get_normal_map(np);
 
   // value_type_traits is a workaround as back_insert_iterator's value_type is void
   // typedef typename value_type_traits<OutputIterator>::type Enriched_point;
diff --git a/Point_set_processing_3/include/CGAL/IO/read_ply_points.h b/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
index 3a0170a0242..feaaa1c07f6 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
@@ -254,14 +254,14 @@ bool read_PLY(std::istream& is,
   typedef Point_set_processing_3::Fake_point_range<OutputIteratorValueType> PointRange;
 
   // basic geometric types
-  typedef typename CGAL::GetPointMap<PointRange, CGAL_BGL_NP_CLASS>::type PointMap;
-  typedef typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::type NormalMap;
+  typedef Point_set_processing_3_np_helper<PointRange, CGAL_BGL_NP_CLASS> NP_helper;
+  typedef typename NP_helper::Point_map PointMap;
+  typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = !(boost::is_same<NormalMap,
-                       typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::NoMap>::value);
+  bool has_normals = !(boost::is_same<NormalMap, typename NP_helper::NoMap>::value);
 
-  PointMap point_map = choose_parameter<PointMap>(get_parameter(np, internal_np::point_map));
-  NormalMap normal_map = choose_parameter<NormalMap>(get_parameter(np, internal_np::normal_map));
+  PointMap point_map = NP_helper::get_point_map(np);
+  NormalMap normal_map = NP_helper::get_normal_map(np);
 
   if(has_normals)
     return read_PLY_with_properties(is, output,
diff --git a/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h b/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
index 7fa9e7b6da2..abece867487 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
@@ -85,15 +85,15 @@ bool read_XYZ(std::istream& is,
   typedef Point_set_processing_3::Fake_point_range<OutputIteratorValueType> PointRange;
 
   // basic geometric types
-  typedef typename CGAL::GetPointMap<PointRange, CGAL_BGL_NP_CLASS>::type PointMap;
-  typedef typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::type NormalMap;
-  typedef typename Point_set_processing_3::GetK<PointRange, CGAL_BGL_NP_CLASS>::Kernel Kernel;
+  typedef Point_set_processing_3_np_helper<PointRange, CGAL_BGL_NP_CLASS> NP_helper;
+  typedef typename NP_helper::Point_map PointMap;
+  typedef typename NP_helper::Normal_map NormalMap;
+  typedef typename NP_helper::Geom_traits Kernel;
 
-  bool has_normals = !(boost::is_same<NormalMap,
-                       typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::NoMap>::value);
+  bool has_normals = !(boost::is_same<NormalMap, typename NP_helper::NoMap>::value);
 
-  PointMap point_map = choose_parameter<PointMap>(get_parameter(np, internal_np::point_map));
-  NormalMap normal_map = choose_parameter<NormalMap>(get_parameter(np, internal_np::normal_map));
+  PointMap point_map = NP_helper::get_point_map(np);
+  NormalMap normal_map = NP_helper::get_normal_map(np);
 
   // value_type_traits is a workaround as back_insert_iterator's value_type is void
   //typedef typename value_type_traits<OutputIterator>::type Enriched_point;
diff --git a/Point_set_processing_3/include/CGAL/IO/write_off_points.h b/Point_set_processing_3/include/CGAL/IO/write_off_points.h
index 7de17f726f0..658d7f2c9cb 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_off_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_off_points.h
@@ -44,13 +44,14 @@ bool write_OFF_PSP(std::ostream& os,
   using CGAL::parameters::is_default_parameter;
 
   // basic geometric types
-  typedef typename CGAL::GetPointMap<PointRange, CGAL_BGL_NP_CLASS>::type                         PointMap;
-  typedef typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::type      NormalMap;
+  typedef Point_set_processing_3_np_helper<PointRange, CGAL_BGL_NP_CLASS> NP_helper;
+  typedef typename NP_helper::Const_point_map PointMap;
+  typedef typename NP_helper::Normal_map NormalMap;
 
   const bool has_normals = !(is_default_parameter(get_parameter(np, internal_np::normal_map)));
 
-  PointMap point_map = choose_parameter<PointMap>(get_parameter(np, internal_np::point_map));
-  NormalMap normal_map = choose_parameter<NormalMap>(get_parameter(np, internal_np::normal_map));
+  PointMap point_map = NP_helper::get_const_point_map(points, np);
+  NormalMap normal_map = NP_helper::get_normal_map(points, np);
 
   CGAL_point_set_processing_precondition(points.begin() != points.end());
 
diff --git a/Point_set_processing_3/include/CGAL/IO/write_ply_points.h b/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
index 66eedccfac6..15e0d460ccc 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
@@ -201,8 +201,7 @@ bool write_PLY(std::ostream& os,
   typedef typename NP_helper::Const_point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = !(boost::is_same<NormalMap,
-                       typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::NoMap>::value);
+  bool has_normals = !(boost::is_same<NormalMap, typename NP_helper::NoMap>::value);
 
   PointMap point_map = NP_helper::get_const_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h b/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
index 9d7383cd83c..ff154a4e26b 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
@@ -43,15 +43,14 @@ bool write_XYZ_PSP(std::ostream& os,
   using CGAL::parameters::get_parameter;
 
   // basic geometric types
-  typedef typename CGAL::GetPointMap<PointRange, CGAL_BGL_NP_CLASS>::type                    PointMap;
-  typedef typename Point_set_processing_3::GetNormalMap<PointRange, CGAL_BGL_NP_CLASS>::type NormalMap;
+  typedef Point_set_processing_3_np_helper<PointRange, CGAL_BGL_NP_CLASS> NP_helper;
+  typedef typename NP_helper::Const_point_map PointMap;
+  typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = !(std::is_same<NormalMap,
-                                    typename Point_set_processing_3::GetNormalMap<
-                                      PointRange, CGAL_BGL_NP_CLASS>::NoMap>::value);
+  bool has_normals = !(boost::is_same<NormalMap, typename NP_helper::NoMap>::value);
 
-  PointMap point_map = choose_parameter<PointMap>(get_parameter(np, internal_np::point_map));
-  NormalMap normal_map = choose_parameter<NormalMap>(get_parameter(np, internal_np::normal_map));
+  PointMap point_map = NP_helper::get_const_point_map(points, np);
+  NormalMap normal_map = NP_helper::get_normal_map(points, np);
 
   CGAL_point_set_processing_precondition(points.begin() != points.end());
 
diff --git a/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h b/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
index 440685f4d9d..45d0675b81d 100644
--- a/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
+++ b/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
@@ -278,8 +278,7 @@ bilateral_smooth_point_set(
   typedef typename Kernel::Point_3 Point_3;
   typedef typename Kernel::Vector_3 Vector_3;
 
-  CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                              typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+  CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                             "Error: no normal map");
 
   typedef typename Kernel::FT FT;
diff --git a/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h b/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
index 6db7f9fd060..6d9b25d8a04 100644
--- a/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
+++ b/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
@@ -367,8 +367,7 @@ edge_aware_upsample_point_set(
   typedef typename NP_helper::Geom_traits Kernel;
 
 
-  CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                              typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+  CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                             "Error: no normal map");
 
   typedef typename Kernel::Point_3 Point;
diff --git a/Point_set_processing_3/include/CGAL/jet_estimate_normals.h b/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
index 91304a5790c..c2b7f68bb4f 100644
--- a/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
@@ -196,8 +196,7 @@ jet_estimate_normals(
   typedef typename Kernel::FT FT;
   typedef typename GetSvdTraits<NamedParameters>::type SvdTraits;
 
-  CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                              typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+  CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                             "Error: no normal map");
   CGAL_static_assertion_msg(!(boost::is_same<SvdTraits,
                               typename GetSvdTraits<NamedParameters>::NoTraits>::value),
diff --git a/Point_set_processing_3/include/CGAL/mst_orient_normals.h b/Point_set_processing_3/include/CGAL/mst_orient_normals.h
index c16cf95afb9..a0c38a5c47b 100644
--- a/Point_set_processing_3/include/CGAL/mst_orient_normals.h
+++ b/Point_set_processing_3/include/CGAL/mst_orient_normals.h
@@ -617,8 +617,7 @@ mst_orient_normals(
     typedef typename NP_helper::Geom_traits Kernel;
     typedef typename Point_set_processing_3::GetIsConstrainedMap<PointRange, NamedParameters>::type ConstrainedMap;
 
-    CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                                typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+    CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                               "Error: no normal map");
 
     PointMap point_map = NP_helper::get_point_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/pca_estimate_normals.h b/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
index a4011bde4c5..5db5769c599 100644
--- a/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
@@ -168,8 +168,7 @@ pca_estimate_normals(
   typedef typename NP_helper::Geom_traits Kernel;
   typedef typename Kernel::FT FT;
 
-  CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                              typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+  CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                             "Error: no normal map");
 
   PointMap point_map = NP_helper::get_point_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/scanline_orient_normals.h b/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
index 520ca3dcc1e..2b314612c8d 100644
--- a/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
+++ b/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
@@ -478,9 +478,7 @@ void scanline_orient_normals (PointRange& points, const NamedParameters& np = pa
     <internal_np::scanline_id_t, NamedParameters, No_map>::type;
   using Fallback_scanline_ID = Boolean_tag<std::is_same<ScanlineIDMap, No_map>::value>;
 
-  CGAL_static_assertion_msg(!(std::is_same<NormalMap,
-                              typename Point_set_processing_3::GetNormalMap
-                              <PointRange, NamedParameters>::NoMap>::value),
+  CGAL_static_assertion_msg(!(std::is_same<NormalMap, typename NP_helper::NoMap>::value),
                             "Error: no normal map");
 
   PointMap point_map = NP_helper::get_point_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/structure_point_set.h b/Point_set_processing_3/include/CGAL/structure_point_set.h
index 4b7d318add0..5b01d11f8b6 100644
--- a/Point_set_processing_3/include/CGAL/structure_point_set.h
+++ b/Point_set_processing_3/include/CGAL/structure_point_set.h
@@ -233,8 +233,7 @@ public:
     typedef typename Point_set_processing_3::GetPlaneMap<PlaneRange, NamedParameters>::type PlaneMap;
     typedef typename Point_set_processing_3::GetPlaneIndexMap<NamedParameters>::type PlaneIndexMap;
 
-    CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                                typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+    CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                               "Error: no normal map");
     CGAL_static_assertion_msg(!(boost::is_same<PlaneIndexMap,
                                 typename Point_set_processing_3::GetPlaneIndexMap<NamedParameters>::NoMap>::value),
diff --git a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
index 3f6cf27075c..6fdc2570e76 100644
--- a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
@@ -321,8 +321,7 @@ vcm_estimate_normals_internal (PointRange& points,
     typedef typename NP_helper::Geom_traits Kernel;
     typedef typename GetDiagonalizeTraits<NamedParameters, double, 3>::type DiagonalizeTraits;
 
-    CGAL_static_assertion_msg(!(boost::is_same<NormalMap,
-                                typename Point_set_processing_3::GetNormalMap<PointRange, NamedParameters>::NoMap>::value),
+    CGAL_static_assertion_msg(!(boost::is_same<NormalMap, typename NP_helper::NoMap>::value),
                               "Error: no normal map");
 
     PointMap point_map = NP_helper::get_point_map(points, np);
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/simplify_polyline.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/simplify_polyline.h
index d5e39611018..974cc8a520c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/simplify_polyline.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/simplify_polyline.h
@@ -45,7 +45,7 @@ void simplify_polyline(const PointRangeIn& input,
 
   typedef typename GetPointMap<PointRangeIn, NamedParametersIn>::type Point_map_in;
   typedef typename GetPointMap<PointRangeOut, NamedParametersOut>::type Point_map_out;
-  typedef typename Point_set_processing_3::GetK<PointRangeIn, NamedParametersIn>::Kernel Kernel;
+  typedef typename Point_set_processing_3_np_helper<PointRangeIn, NamedParametersIn>::Geom_traits Kernel;
 
   Point_map_in in_pm = choose_parameter<Point_map_in>(get_parameter(np_in, internal_np::point_map));
   Point_map_out out_pm = choose_parameter<Point_map_out>(get_parameter(np_out, internal_np::point_map));