diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_approximation_and_extraction_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_approximation_and_extraction_example.cpp
index 399c7cf8075..6a3fca361b1 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_approximation_and_extraction_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_approximation_and_extraction_example.cpp
@@ -10,14 +10,14 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
-typedef Polyhedron::Facet_const_handle Facet_const_handle;
-typedef Polyhedron::Facet_const_iterator Facet_const_iterator;
-typedef std::map<Facet_const_handle, std::size_t> Facet_id_map;
+typedef Polyhedron::Facet_handle Facet_handle;
+typedef Polyhedron::Facet_iterator Facet_iterator;
+typedef std::map<Facet_handle, std::size_t> Facet_id_map;
 
 int main(int argc, char *argv[])
 {
   if (argc < 5)
-    return 0;
+    return EXIT_FAILURE;
 
   // create and read Polyhedron
   Polyhedron mesh;
@@ -29,9 +29,9 @@ int main(int argc, char *argv[])
 
   // create a property-map for facet proxy index map
   Facet_id_map facet_proxy_map;
-  for (Facet_const_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr)
-    facet_proxy_map.insert(std::pair<Facet_const_handle, std::size_t>(fitr, 0));
-  boost::associative_property_map<Facet_id_map> f_proxy_pmap(facet_proxy_map);
+  for (Facet_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr)
+    facet_proxy_map.insert(std::pair<Facet_handle, std::size_t>(fitr, 0));
+  boost::associative_property_map<Facet_id_map> proxy_pmap(facet_proxy_map);
 
   const std::size_t num_proxies = std::atoi(argv[3]);
   const std::size_t num_iterations = std::atoi(argv[4]);
@@ -42,7 +42,7 @@ int main(int argc, char *argv[])
     return EXIT_FAILURE;
 
   CGAL::vsa_approximate_and_extract(mesh,
-    f_proxy_pmap,
+    proxy_pmap,
     tris,
     anchor_pos,
     init,
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_extraction_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_extraction_example.cpp
index 76d10e76c33..14878f974cc 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_extraction_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_extraction_example.cpp
@@ -13,7 +13,7 @@ typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 int main(int argc, char *argv[])
 {
   if (argc < 5)
-    return 0;
+    return EXIT_FAILURE;
 
   // create and read Polyhedron
   Polyhedron mesh;
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_l2_metric_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_l2_metric_example.cpp
index ebc5d39838a..b19874938f8 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_l2_metric_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_l2_metric_example.cpp
@@ -23,7 +23,7 @@ typedef CGAL::PCAPlaneFitting<Polyhedron_3> PCAPlaneFitting;
 int main(int argc, char *argv[])
 {
   if (argc < 5)
-    return 0;
+    return EXIT_FAILURE;
   
   // read Polyhedron
   Polyhedron_3 mesh;
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
index 8101909ad5f..d03b7f71f07 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
@@ -14,12 +14,12 @@ typedef Kernel::FT FT;
 typedef Kernel::Vector_3 Vector_3;
 typedef Kernel::Point_3 Point_3;
 typedef Polyhedron::Facet_handle Facet_handle;
-typedef Polyhedron::Facet_const_handle Facet_const_handle;
-typedef Polyhedron::Halfedge_const_handle Halfedge_const_handle;
-typedef Polyhedron::Facet_const_iterator Facet_const_iterator;
-typedef boost::associative_property_map<std::map<Facet_const_handle, Vector_3> > FacetNormalMap;
-typedef boost::associative_property_map<std::map<Facet_const_handle, FT> > FacetAreaMap;
-typedef boost::associative_property_map<std::map<Facet_const_handle, Point_3> > FacetCenterMap;
+typedef Polyhedron::Halfedge_handle Halfedge_handle;
+typedef Polyhedron::Facet_iterator Facet_iterator;
+typedef boost::associative_property_map<std::map<Facet_handle, Vector_3> > FacetNormalMap;
+typedef boost::associative_property_map<std::map<Facet_handle, FT> > FacetAreaMap;
+typedef boost::associative_property_map<std::map<Facet_handle, Point_3> > FacetCenterMap;
+typedef std::map<Facet_handle, std::size_t> Facet_id_map;
 
 struct PointProxy {
   Facet_handle seed;
@@ -32,7 +32,7 @@ struct CompactMetric {
   CompactMetric(const FacetCenterMap &_center_pmap)
     : center_pmap(_center_pmap) {}
 
-  FT operator()(const Facet_const_handle &f, const PointProxy &px) const {
+  FT operator()(const Facet_handle &f, const PointProxy &px) const {
     return FT(std::sqrt(CGAL::to_double(
       CGAL::squared_distance(center_pmap[f], px.center))));
   }
@@ -43,15 +43,11 @@ struct CompactMetric {
 struct PointProxyFitting {
   typedef PointProxy Proxy;
 
-  PointProxyFitting(const FacetCenterMap &_center_pmap,
-    const FacetAreaMap &_area_pmap)
-    : center_pmap(_center_pmap),
-    area_pmap(_area_pmap) {}
+  PointProxyFitting(const FacetCenterMap &_center_pmap, const FacetAreaMap &_area_pmap)
+    : center_pmap(_center_pmap), area_pmap(_area_pmap) {}
 
   template<typename FacetIterator>
   PointProxy operator()(const FacetIterator beg, const FacetIterator end) const {
-    CGAL_assertion(beg != end);
-
     // fitting center
     Vector_3 center = CGAL::NULL_VECTOR;
     FT area(0);
@@ -75,7 +71,7 @@ struct PointProxyFitting {
 int main(int argc, char *argv[])
 {
   if (argc < 5)
-    return 0;
+    return EXIT_FAILURE;
 
   // create and read Polyhedron
   Polyhedron mesh;
@@ -86,26 +82,25 @@ int main(int argc, char *argv[])
   }
 
   // construct facet normal & area map
-  std::map<Facet_const_handle, FT> facet_areas;
-  std::map<Facet_const_handle, Point_3> facet_centers;
-  for(Facet_const_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr) {
-    const Halfedge_const_handle he = fitr->halfedge();
-    const Point_3 p1 = he->opposite()->vertex()->point();
-    const Point_3 p2 = he->vertex()->point();
-    const Point_3 p3 = he->next()->vertex()->point();
-    FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p1, p2, p3))));
-    facet_areas.insert(std::pair<Facet_const_handle, FT>(fitr, area));
-    facet_centers.insert(std::pair<Facet_const_handle, Point_3>(fitr, CGAL::centroid(p1, p2, p3)));
+  std::map<Facet_handle, FT> facet_areas;
+  std::map<Facet_handle, Point_3> facet_centers;
+  for(Facet_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr) {
+    const Halfedge_handle he = fitr->halfedge();
+    const Point_3 &p0 = he->opposite()->vertex()->point();
+    const Point_3 &p1 = he->vertex()->point();
+    const Point_3 &p2 = he->next()->vertex()->point();
+    FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
+    facet_areas.insert(std::pair<Facet_handle, FT>(fitr, area));
+    facet_centers.insert(std::pair<Facet_handle, Point_3>(fitr, CGAL::centroid(p0, p1, p2)));
   }
   FacetAreaMap area_pmap(facet_areas);
   FacetCenterMap center_pmap(facet_centers);
 
   // create a property-map for segment-ids
-  typedef std::map<Facet_const_handle, std::size_t> Facet_id_map;
-  Facet_id_map internal_facet_id_map;
-  for (Facet_const_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr)
-    internal_facet_id_map.insert(std::pair<Facet_const_handle, std::size_t>(fitr, 0));
-  boost::associative_property_map<Facet_id_map> proxy_patch_map(internal_facet_id_map);
+  Facet_id_map facet_proxy_map;
+  for (Facet_iterator fitr = mesh.facets_begin(); fitr != mesh.facets_end(); ++fitr)
+    facet_proxy_map.insert(std::pair<Facet_handle, std::size_t>(fitr, 0));
+  boost::associative_property_map<Facet_id_map> proxy_pmap(facet_proxy_map);
 
   const std::size_t num_proxies = std::atoi(argv[3]);
   const std::size_t num_iterations = std::atoi(argv[4]);
@@ -114,7 +109,7 @@ int main(int argc, char *argv[])
     return EXIT_FAILURE;
 
   CGAL::vsa_approximate(mesh,
-    proxy_patch_map,
+    proxy_pmap,
     CompactMetric(center_pmap),
     PointProxyFitting(center_pmap, area_pmap),
     init,