diff --git a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_class_interface_test.cpp b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_class_interface_test.cpp
index cfddead6989..51d0ff4f7c1 100644
--- a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_class_interface_test.cpp
+++ b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_class_interface_test.cpp
@@ -6,21 +6,22 @@
 #include <CGAL/IO/Polyhedron_iostream.h>
 
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
-#include <CGAL/VSA_metrics.h>
 #include <CGAL/VSA_approximation.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::FT FT;
 typedef Kernel::Point_3 Point_3;
 
-typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
-typedef Polyhedron_3::Facet_handle Facet_handle;
+typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
+typedef Polyhedron::Facet_handle Facet_handle;
 typedef boost::associative_property_map<std::map<Facet_handle, std::size_t> > FacetProxyMap;
+typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
-typedef CGAL::PlaneProxy<Polyhedron_3> PlaneProxy;
-typedef CGAL::L2Metric<Polyhedron_3> L2Metric;
-typedef CGAL::L2ProxyFitting<Polyhedron_3> L2ProxyFitting;
-typedef CGAL::VSA_approximation<Polyhedron_3, PlaneProxy, L2Metric, L2ProxyFitting> VSA;
+typedef CGAL::PlaneProxy<Polyhedron> PlaneProxy;
+typedef CGAL::L2Metric<Polyhedron> L2Metric;
+typedef CGAL::L2ProxyFitting<Polyhedron> L2ProxyFitting;
+typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap,
+  CGAL::Default, L2Metric, L2ProxyFitting> VSA;
 
 /**
  * This file tests the VSA class API and the L2 metric.
@@ -28,7 +29,7 @@ typedef CGAL::VSA_approximation<Polyhedron_3, PlaneProxy, L2Metric, L2ProxyFitti
  */
 int main()
 {
-  Polyhedron_3 mesh;
+  Polyhedron mesh;
   std::ifstream input("./data/sphere_iso.off");
   if (!input || !(input >> mesh) || mesh.empty()) {
     std::cerr << "Invalid off file." << std::endl;
@@ -37,20 +38,18 @@ int main()
 
   // facet area map
   std::map<Facet_handle, std::size_t> facet_index;
-  for (Polyhedron_3::Facet_iterator fitr = mesh.facets_begin();
+  for (Polyhedron::Facet_iterator fitr = mesh.facets_begin();
     fitr != mesh.facets_end(); ++fitr)
     facet_index.insert(std::pair<Facet_handle, std::size_t>(fitr, 0));
   FacetProxyMap proxy_pmap(facet_index);
 
-  L2Metric metric(mesh);
-  L2ProxyFitting proxy_fitting(mesh);
-
   // create VSA L2 metric approximation algorithm instance
   std::cout << "setup algorithm instance" << std::endl;
-  VSA l2_approx;
-  l2_approx.set_mesh(mesh);
-  l2_approx.set_error_metric(metric);
-  l2_approx.set_proxy_fitting(proxy_fitting);
+  VSA l2_approx(mesh,
+    get(boost::vertex_point, const_cast<Polyhedron &>(mesh)));
+  L2Metric metric(mesh);
+  L2ProxyFitting proxy_fitting(mesh);
+  l2_approx.set_metric(metric, proxy_fitting);
 
   // random init and run
   std::cout << "random init and run" << std::endl;
@@ -94,7 +93,7 @@ int main()
 
   // extract the approximation polyhedron
   std::cout << "meshing" << std::endl;
-  Polyhedron_3 out_mesh;
+  Polyhedron out_mesh;
   if (l2_approx.meshing(out_mesh, FT(0.5), true))
     std::cout << "manifold." << std::endl;
   else
@@ -110,7 +109,7 @@ int main()
   std::vector<Point_3> anchor_pos;
   l2_approx.get_anchor_points(std::back_inserter(anchor_pos));
 
-  std::vector<Polyhedron_3::Vertex_handle> anchor_vtx;
+  std::vector<Polyhedron::Vertex_handle> anchor_vtx;
   l2_approx.get_anchor_vertices(std::back_inserter(anchor_vtx));
 
   std::vector<int> tris;
diff --git a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_correctness_test.cpp b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_correctness_test.cpp
index 1fa7e5dc6c6..e4f4ccb07b3 100644
--- a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_correctness_test.cpp
+++ b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_correctness_test.cpp
@@ -6,34 +6,34 @@
 #include <CGAL/IO/Polyhedron_iostream.h>
 
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
-#include <CGAL/VSA_metrics.h>
 #include <CGAL/VSA_approximation.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::FT FT;
 typedef Kernel::Point_3 Point_3;
-typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
+typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
+typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
-typedef CGAL::PlaneProxy<Polyhedron_3> PlaneProxy;
-typedef CGAL::L21Metric<Polyhedron_3> L21Metric;
-typedef CGAL::L21ProxyFitting<Polyhedron_3> L21ProxyFitting;
-typedef CGAL::VSA_approximation<Polyhedron_3, PlaneProxy, L21Metric, L21ProxyFitting> VSAL21;
+typedef CGAL::L21Metric<Polyhedron> L21Metric;
+typedef CGAL::L21ProxyFitting<Polyhedron> L21ProxyFitting;
+typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap> VSAL21;
 
 bool test_shape(const char *file_name, const std::size_t target_num_proxies)
 {
-  Polyhedron_3 mesh;
+  Polyhedron mesh;
   std::ifstream input(file_name);
   if (!input || !(input >> mesh) || mesh.empty()) {
     std::cerr << "Invalid off file." << std::endl;
     return false;
   }
 
+  // algorithm instance
+  VSAL21 vsa_l21(mesh,
+    get(boost::vertex_point, const_cast<Polyhedron &>(mesh)));
+
   L21Metric l21_metric(mesh);
   L21ProxyFitting l21_fitting(mesh);
-
-  // algorithm instance
-  VSAL21 vsa_l21(l21_metric, l21_fitting);
-  vsa_l21.set_mesh(mesh);
+  vsa_l21.set_metric(l21_metric, l21_fitting);
 
   // approximation, init from error, drop to the target error incrementally
   // should reach targeted number of proxies gradually
@@ -51,7 +51,7 @@ bool test_shape(const char *file_name, const std::size_t target_num_proxies)
   }
 
   // meshing, should be manifold
-  Polyhedron_3 mesh_out;
+  Polyhedron mesh_out;
   if (!vsa_l21.meshing(mesh_out)) {
     std::cout << "incremental reaching meshing non-manifold" << std::endl;
     return false;
diff --git a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_error_decrease_test.cpp b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_error_decrease_test.cpp
index 27b845e6248..98464a7f068 100644
--- a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_error_decrease_test.cpp
+++ b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_error_decrease_test.cpp
@@ -6,17 +6,17 @@
 #include <CGAL/IO/Polyhedron_iostream.h>
 
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
-#include <CGAL/VSA_metrics.h>
 #include <CGAL/VSA_approximation.h>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::FT FT;
-typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
+typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
+typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
-typedef CGAL::PlaneProxy<Polyhedron_3> PlaneProxy;
-typedef CGAL::L21Metric<Polyhedron_3> L21Metric;
-typedef CGAL::L21ProxyFitting<Polyhedron_3> L21ProxyFitting;
-typedef CGAL::VSA_approximation<Polyhedron_3, PlaneProxy, L21Metric, L21ProxyFitting> VSAL21;
+typedef CGAL::PlaneProxy<Polyhedron> PlaneProxy;
+typedef CGAL::L21Metric<Polyhedron> L21Metric;
+typedef CGAL::L21ProxyFitting<Polyhedron> L21ProxyFitting;
+typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap> VSAL21;
 
 bool check_strict_ordering(const std::vector<FT> &error)
 {
@@ -37,19 +37,20 @@ bool check_strict_ordering(const std::vector<FT> &error)
  */
 int main()
 {
-  Polyhedron_3 mesh;
+  Polyhedron mesh;
   std::ifstream input("./data/sphere_iso.off");
   if (!input || !(input >> mesh) || mesh.empty()) {
     std::cerr << "Invalid off file." << std::endl;
     return EXIT_FAILURE;
   }
 
+  // algorithm instance
+  VSAL21 vsa_l21(mesh,
+    get(boost::vertex_point, const_cast<Polyhedron &>(mesh)));
+
   L21Metric l21_metric(mesh);
   L21ProxyFitting l21_fitting(mesh);
-
-  // algorithm instance
-  VSAL21 vsa_l21(l21_metric, l21_fitting);
-  vsa_l21.set_mesh(mesh);
+  vsa_l21.set_metric(l21_metric, l21_fitting);
 
   vsa_l21.init_proxies(100, VSAL21::RandomInit);
   std::vector<FT> error;
diff --git a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_metric_test.cpp b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_metric_test.cpp
index 9b8b5ffecdf..23858230434 100644
--- a/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_metric_test.cpp
+++ b/Surface_mesh_approximation/test/Surface_mesh_approximation/vsa_metric_test.cpp
@@ -14,12 +14,13 @@ typedef Kernel::FT FT;
 typedef Kernel::Vector_3 Vector_3;
 typedef Kernel::Point_3 Point_3;
 
-typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
-typedef Polyhedron_3::Facet_handle Facet_handle;
-typedef Polyhedron_3::Halfedge_handle Halfedge_handle;
-typedef Polyhedron_3::Facet_iterator Facet_iterator;
+typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
+typedef Polyhedron::Facet_handle Facet_handle;
+typedef Polyhedron::Halfedge_handle Halfedge_handle;
+typedef Polyhedron::Facet_iterator Facet_iterator;
 typedef boost::associative_property_map<std::map<Facet_handle, FT> > FacetAreaMap;
 typedef boost::associative_property_map<std::map<Facet_handle, Point_3> > FacetCenterMap;
+typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
 struct PointProxy {
   Facet_handle seed;
@@ -67,14 +68,15 @@ struct PointProxyFitting {
   const FacetCenterMap center_pmap;
   const FacetAreaMap area_pmap;
 };
-typedef CGAL::VSA_approximation<Polyhedron_3, PointProxy, CompactMetric, PointProxyFitting> CompactVSA;
+typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap,
+  PointProxy, CompactMetric, PointProxyFitting> CompactVSA;
 
 /**
  * This file tests the user defined metric.
  */
 int main()
 {
-  Polyhedron_3 mesh;
+  Polyhedron mesh;
   std::ifstream input("./data/cube_meshed_open.off");
   if (!input || !(input >> mesh) || mesh.empty()) {
     std::cerr << "Invalid off file." << std::endl;
@@ -96,15 +98,14 @@ int main()
   FacetAreaMap area_pmap(facet_areas);
   FacetCenterMap center_pmap(facet_centers);
 
-  CompactMetric metric(center_pmap);
-  PointProxyFitting proxy_fitting(center_pmap, area_pmap);
-
   // create compact metric approximation algorithm instance
   std::cout << "create compact vas instance" << std::endl;
-  CompactVSA compact_approx;
-  compact_approx.set_mesh(mesh);
-  compact_approx.set_error_metric(metric);
-  compact_approx.set_proxy_fitting(proxy_fitting);
+  CompactVSA compact_approx(mesh,
+    get(boost::vertex_point, const_cast<Polyhedron &>(mesh)));
+
+  CompactMetric metric(center_pmap);
+  PointProxyFitting proxy_fitting(center_pmap, area_pmap);
+  compact_approx.set_metric(metric, proxy_fitting);
 
   std::cout << "random init and run" << std::endl;
   compact_approx.init_proxies(20, CompactVSA::RandomInit);
@@ -115,7 +116,7 @@ int main()
 
   // extract the approximation polyhedron
   std::cout << "meshing" << std::endl;
-  Polyhedron_3 out_mesh;
+  Polyhedron out_mesh;
   if (compact_approx.meshing(out_mesh))
     std::cout << "manifold." << std::endl;
   else