diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
index db03324b9fa..271329f689e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
@@ -58,9 +58,8 @@ namespace CGAL {
       using boost::choose_const_pmap;
       using boost::get_param;
       typename GetVertexPointMap<PolygonMesh, NamedParameters>::const_type
-        vpm = choose_const_pmap(get_param(np, CGAL::vertex_point),
-                                pmesh,
-                                CGAL::vertex_point);
+        vpm = choose_param(get_param(np, vertex_point),
+                           get_const_property_map(CGAL::vertex_point, pmesh));
 
       typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor halfedge_descriptor;
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
index f4ef8cc1b06..23bbab1291e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
@@ -139,7 +139,7 @@ compute_face_normal(typename boost::graph_traits<PolygonMesh>::face_descriptor f
 
   Vector normal = traits.construct_vector_3_object()(CGAL::NULL_VECTOR);
   sum_normals<Point>(pmesh, f
-    , choose_const_pmap(get_param(np, CGAL::vertex_point), pmesh, CGAL::vertex_point)
+    , choose_param(get_param(np, vertex_point), get_const_property_map(CGAL::vertex_point, pmesh))
     , normal
     , traits);
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/fair.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/fair.h
index 4af36f99d4f..eda485ca947 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/fair.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/fair.h
@@ -80,7 +80,7 @@ namespace internal {
   fairing does not fail, but the mesh gets shrinked to `CGAL::ORIGIN`.
 
   @tparam TriangleMesh a model of `FaceGraph` and `MutableFaceGraph`
-          that has an internal property map for `CGAL::vertex_point_t`
+  that has an internal property map for `CGAL::vertex_point_t`
   @tparam VertexRange a range of vertex descriptors of `TriangleMesh`, model of `Range`.
           Its iterator type is `InputIterator`.
   @tparam NamedParameters a sequence of \ref namedparameters
@@ -143,7 +143,8 @@ namespace internal {
     typedef CGAL::internal::Cotangent_weight_with_voronoi_area_fairing<TriangleMesh, VPMap>
       Default_Weight_calculator;
 
-    VPMap vpmap_ = choose_param(get_param(np, vertex_point), get(CGAL::vertex_point, tmesh));
+    VPMap vpmap_ = choose_param(get_param(np, vertex_point),
+                                get_property_map(vertex_point, tmesh));
 
     return internal::fair(tmesh, vertices,
       choose_param(get_param(np, sparse_linear_solver), Default_solver()),
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/measure.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/measure.h
index 3457888125b..a6617e9bc69 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/measure.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/measure.h
@@ -85,9 +85,8 @@ namespace Polygon_mesh_processing {
     using boost::get_param;
 
     typename GetVertexPointMap<PolygonMesh, NamedParameters>::const_type
-    vpm = choose_const_pmap(get_param(np, CGAL::vertex_point),
-                            pmesh,
-                            CGAL::vertex_point);
+    vpm = choose_param(get_param(np, vertex_point),
+                       get_const_property_map(CGAL::vertex_point, pmesh));
 
     return CGAL::approximate_sqrt(CGAL::squared_distance(get(vpm, source(h, pmesh)),
                                                          get(vpm, target(h, pmesh))));
@@ -231,9 +230,8 @@ namespace Polygon_mesh_processing {
     CGAL_precondition(boost::graph_traits<TriangleMesh>::null_face() != f);
 
     typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type
-    vpm = choose_const_pmap(get_param(np, CGAL::vertex_point),
-                            tmesh,
-                            CGAL::vertex_point);
+    vpm = choose_param(get_param(np, vertex_point),
+                       get_const_property_map(CGAL::vertex_point, tmesh));
 
     typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
     halfedge_descriptor hd = halfedge(f, tmesh);
@@ -416,9 +414,8 @@ namespace Polygon_mesh_processing {
     using boost::get_param;
 
     typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type
-      vpm = choose_const_pmap(get_param(np, CGAL::vertex_point),
-                              tmesh,
-                              CGAL::vertex_point);
+      vpm = choose_param(get_param(np, vertex_point),
+                         get_const_property_map(CGAL::vertex_point, tmesh));
     typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::Point_3
       origin(0, 0, 0);
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
index b3c487e2b23..db00ac1af78 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/orientation.h
@@ -96,9 +96,8 @@ bool is_outward_oriented(const PolygonMesh& pmesh,
 
   //VertexPointMap
   typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::const_type VPMap;
-  VPMap vpmap = choose_const_pmap(get_param(np, boost::vertex_point),
-                                  pmesh,
-                                  boost::vertex_point);
+  VPMap vpmap = choose_param(get_param(np, vertex_point),
+                             get_const_property_map(vertex_point, pmesh));
   //Kernel
   typedef typename GetGeomTraits<PolygonMesh, NamedParameters>::type Kernel;
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/refine.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/refine.h
index a3978d5072d..af754e2609c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/refine.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/refine.h
@@ -84,9 +84,8 @@ namespace Polygon_mesh_processing {
     CGAL_precondition(is_triangle_mesh(tmesh) );
 
     typedef typename GetVertexPointMap<TriangleMesh,NamedParameters>::type VPmap;
-    VPmap vpm = choose_pmap(get_param(np, boost::vertex_point),
-                            tmesh,
-                            boost::vertex_point);
+    VPmap vpm = choose_param(get_param(np, vertex_point),
+                             get_property_map(vertex_point, tmesh));
 
     internal::Refine_Polyhedron_3<TriangleMesh, VPmap> refine_functor(tmesh, vpm);
     refine_functor.refine(faces,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
index 4e6cde6a2f7..fdc0dc57b14 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh.h
@@ -141,9 +141,8 @@ void isotropic_remeshing(const FaceRange& faces
   typedef typename GetGeomTraits<PM, NamedParameters>::type GT;
 
   typedef typename GetVertexPointMap<PM, NamedParameters>::type VPMap;
-  VPMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                            pmesh,
-                            boost::vertex_point);
+  VPMap vpmap = choose_param(get_param(np, vertex_point),
+                             get_property_map(vertex_point, pmesh));
 
   typedef typename GetFaceIndexMap<PM, NamedParameters>::type FIMap;
   FIMap fimap = choose_param(get_param(np, face_index),
@@ -311,13 +310,12 @@ void split_long_edges(const EdgeRange& edges
 
   typedef typename GetGeomTraits<PM, NamedParameters>::type GT;
   typedef typename GetVertexPointMap<PM, NamedParameters>::type VPMap;
-  VPMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                            pmesh,
-                            boost::vertex_point);
+  VPMap vpmap = choose_param(get_param(np, vertex_point),
+                             get_property_map(vertex_point, pmesh));
 
   typedef typename GetFaceIndexMap<PM, NamedParameters>::type FIMap;
   FIMap fimap = choose_param(get_param(np, face_index),
-    get_property_map(face_index, pmesh));
+                             get_property_map(face_index, pmesh));
 
   typedef typename boost::lookup_named_param_def <
         CGAL::edge_is_constrained_t,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
index 9163f9b0c0e..ca823fdd92c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
@@ -163,9 +163,8 @@ std::size_t remove_null_edges(
   typedef typename GT::vertex_descriptor vertex_descriptor;
 
   typedef typename GetVertexPointMap<TM, NamedParameters>::type VertexPointMap;
-  VertexPointMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                                     tmesh,
-                                     boost::vertex_point);
+  VertexPointMap vpmap = choose_param(get_param(np, vertex_point),
+                                      get_property_map(vertex_point, tmesh));
   typedef typename GetGeomTraits<TM, NamedParameters>::type Traits;
   Traits traits = choose_param(get_param(np, geom_traits), Traits());
 
@@ -485,9 +484,8 @@ std::size_t remove_degenerate_faces(TriangleMesh& tmesh,
   typedef typename GT::vertex_descriptor vertex_descriptor;
 
   typedef typename GetVertexPointMap<TM, NamedParameters>::type VertexPointMap;
-  VertexPointMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                                     tmesh,
-                                     boost::vertex_point);
+  VertexPointMap vpmap = choose_param(get_param(np, vertex_point),
+                                      get_property_map(vertex_point, tmesh));
   typedef typename GetGeomTraits<TM, NamedParameters>::type Traits;
   Traits traits = choose_param(get_param(np, geom_traits), Traits());
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
index 7edcef02eea..246295a20e0 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
@@ -306,9 +306,8 @@ self_intersections( const FaceRange& face_range,
   );
 
   typedef typename GetVertexPointMap<TM, NamedParameters>::const_type VertexPointMap;
-  VertexPointMap vpmap = choose_const_pmap(get_param(np, boost::vertex_point),
-                                           tmesh,
-                                           boost::vertex_point);
+  VertexPointMap vpmap = choose_param(get_param(np, vertex_point),
+                                      get_const_property_map(vertex_point, tmesh));
 
   BOOST_FOREACH(face_descriptor f, face_range)
   {
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
index 6e2e99702f1..402ff0b8b3e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/stitch_borders.h
@@ -304,9 +304,8 @@ void stitch_borders(PolygonMesh& pmesh,
   using boost::get_param;
 
   typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::const_type VPMap;
-  VPMap vpm = choose_const_pmap(get_param(np, boost::vertex_point),
-                                pmesh,
-                                boost::vertex_point);
+  VPMap vpm = choose_param(get_param(np, vertex_point),
+                           get_const_property_map(vertex_point, pmesh));
 
   internal::Naive_border_stitching_modifier<PolygonMesh, VPMap, HalfedgePairsRange>
     modifier(hedge_pairs_to_stitch, vpm);
@@ -356,9 +355,8 @@ void stitch_borders(PolygonMesh& pmesh, const CGAL_PMP_NP_CLASS& np)
   std::vector< std::pair<halfedge_descriptor, halfedge_descriptor> > hedge_pairs_to_stitch;
 
   typedef typename GetVertexPointMap<PolygonMesh, CGAL_PMP_NP_CLASS>::const_type VPMap;
-  VPMap vpm = choose_const_pmap(get_param(np, boost::vertex_point),
-                                pmesh,
-                                boost::vertex_point);
+  VPMap vpm = choose_param(get_param(np, vertex_point),
+                           get_const_property_map(vertex_point, pmesh));
 
   internal::detect_duplicated_boundary_edges(pmesh,
     std::back_inserter(hedge_pairs_to_stitch),
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_faces.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_faces.h
index 76687bfc123..0704bad66ff 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_faces.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_faces.h
@@ -329,9 +329,8 @@ bool  triangulate_face(typename boost::graph_traits<PolygonMesh>::face_descripto
 
   //VertexPointMap
   typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type VPMap;
-  VPMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                            pmesh,
-                            boost::vertex_point);
+  VPMap vpmap = choose_param(get_param(np, vertex_point),
+                             get_property_map(vertex_point, pmesh));
   //Kernel
   typedef typename GetGeomTraits<PolygonMesh, NamedParameters>::type Kernel;
 
@@ -379,9 +378,8 @@ bool triangulate_faces(FaceRange face_range,
 
   //VertexPointMap
   typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type VPMap;
-  VPMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
-                            pmesh,
-                            boost::vertex_point);
+  VPMap vpmap = choose_param(get_param(np, vertex_point),
+                             get_property_map(vertex_point, pmesh));
   //Kernel
   typedef typename GetGeomTraits<PolygonMesh, NamedParameters>::type Kernel;
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_hole.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_hole.h
index f03f7d10735..551f9e3726d 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_hole.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/triangulate_hole.h
@@ -98,7 +98,7 @@ namespace Polygon_mesh_processing {
     return internal::triangulate_hole_polygon_mesh(pmesh,
       border_halfedge,
       out,
-      choose_param(get_param(np, vertex_point), get(CGAL::vertex_point, pmesh)),
+      choose_param(get_param(np, vertex_point), get_property_map(vertex_point, pmesh)),
       use_dt3,
       choose_param(get_param(np, geom_traits), typename GetGeomTraits<PolygonMesh,NamedParameters>::type()))
       .first;