diff --git a/Surface_mesh_approximation/include/CGAL/vsa_approximation.h b/Surface_mesh_approximation/include/CGAL/vsa_approximation.h
index f5a27782df4..bb6ebc37aa5 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_approximation.h
@@ -447,7 +447,7 @@ public:
     for (std::size_t i = 0; i < nb_iterations; ++i) {
       // tag the whole surface
       BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-        put(fproxy_map,f, CGAL_VSA_INVALID_TAG);
+        put(fproxy_map, f, CGAL_VSA_INVALID_TAG);
 
       partition(proxies.begin(), proxies.end());
       fit(proxies.begin(), proxies.end());
@@ -506,7 +506,7 @@ public:
     BOOST_FOREACH(Proxy_wrapper &pxw, proxies)
       pxw.err = FT(0.0);
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
-      std::size_t pxidx = get(fproxy_map,f);
+      std::size_t pxidx = get(fproxy_map, f);
       proxies[pxidx].err += (*fit_error)(f, proxies[pxidx].px);
     }
 
@@ -570,7 +570,7 @@ public:
         static_cast<double>(num_faces(*m_pmesh)) / static_cast<double>(num_proxies));
       std::vector<FT> px_size(proxies.size(), FT(0.0));
       BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-        px_size[get(fproxy_map,f)] += FT(1.0);
+        px_size[get(fproxy_map, f)] += FT(1.0);
       FT residual(0.0);
       for (std::size_t i = 0; i < proxies.size(); ++i) {
         FT to_add = (residual + px_size[i]) / avg_facet;
@@ -673,7 +673,7 @@ public:
       // update merged proxies
       std::list<face_descriptor> merged_patch;
       BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
-        std::size_t px_idx = get(fproxy_map,f);
+        std::size_t px_idx = get(fproxy_map, f);
         if (px_idx == px_enlarged || px_idx == px_merged) {
           put(fproxy_map, f, px_enlarged);
           merged_patch.push_back(f);
@@ -728,8 +728,8 @@ public:
       proxies[i].idx = i;
     // keep facet proxy map valid
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
-      if (get(fproxy_map,f) > px1)
-        put(fproxy_map, f, get(fproxy_map,f)-1);
+      if (get(fproxy_map, f) > px1)
+        put(fproxy_map, f, get(fproxy_map, f) - 1);
     }
 
     FT err_merged(0.0);
@@ -755,7 +755,7 @@ public:
 
     std::vector<std::list<face_descriptor> > px_facets(proxies.size());
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-      px_facets[get(fproxy_map,f)].push_back(f);
+      px_facets[get(fproxy_map, f)].push_back(f);
 
     // find best merge
     MergedPair merged_set;
@@ -841,7 +841,7 @@ public:
       if (count >= n)
         break;
 
-      if (get(fproxy_map,f) == px_idx && f != proxies[px_idx].seed) {
+      if (get(fproxy_map, f) == px_idx && f != proxies[px_idx].seed) {
         put(fproxy_map, f, proxies.size());
         proxies.push_back(fit_new_proxy(f, proxies.size()));
         ++count;
@@ -927,7 +927,7 @@ public:
       return;
 
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-      if (get(fproxy_map,f) == px_idx)
+      if (get(fproxy_map, f) == px_idx)
         *out_itr++ = f;
   }
 
@@ -1231,7 +1231,7 @@ private:
   void fit(const ProxyWrapperIterator beg, const ProxyWrapperIterator end) {
     std::vector<std::list<face_descriptor> > px_facets(proxies.size());
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-      px_facets[get(fproxy_map,f)].push_back(f);
+      px_facets[get(fproxy_map, f)].push_back(f);
 
     // update proxy parameters and seed
     for (ProxyWrapperIterator pxw_itr = beg; pxw_itr != end; ++pxw_itr) {
@@ -1263,7 +1263,7 @@ private:
     face_descriptor fworst;
     bool first = true;
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
-      std::size_t px_idx = get(fproxy_map,f);
+      std::size_t px_idx = get(fproxy_map, f);
       if (px_idx != px_worst || f == proxies[px_idx].seed)
         continue;
 
@@ -1278,7 +1278,7 @@ private:
     if (first)
       return false;
 
-    put(fproxy_map,fworst, proxies.size());
+    put(fproxy_map, fworst, proxies.size());
     proxies.push_back(fit_new_proxy(fworst, proxies.size()));
 
     return true;
@@ -1366,7 +1366,7 @@ private:
     proxies.clear();
     proxies.push_back(fit_new_proxy(*(faces(*m_pmesh).first), proxies.size()));
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-      put(fproxy_map,f, 0);
+      put(fproxy_map, f, 0);
   }
 
   /*!
@@ -1377,7 +1377,7 @@ private:
     // fit proxy planes, areas, normals
     std::vector<std::list<face_descriptor> > px_facets(proxies.size());
     BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
-      px_facets[get(fproxy_map,f)].push_back(f);
+      px_facets[get(fproxy_map, f)].push_back(f);
 
     BOOST_FOREACH(const std::list<face_descriptor> &px_patch, px_facets) {
       Plane_3 fit_plane = if_pca_plane ? 
@@ -1413,7 +1413,7 @@ private:
       BOOST_FOREACH(halfedge_descriptor h, halfedges_around_target(vtx, *m_pmesh)) {
         if (CGAL::is_border_edge(h, *m_pmesh))
           ++border_count;
-        else if (get(fproxy_map,face(h, *m_pmesh)) != get(fproxy_map, face(opposite(h, *m_pmesh), *m_pmesh)))
+        else if (get(fproxy_map, face(h, *m_pmesh)) != get(fproxy_map, face(opposite(h, *m_pmesh), *m_pmesh)))
           ++border_count;
       }
       if (border_count >= 3)
@@ -1564,7 +1564,7 @@ private:
     BOOST_FOREACH(vertex_descriptor v, vertices(*m_pmesh)) {
       sg_vertex_descriptor sgv = add_vertex(gmain);
       global_vanchor_map[sgv] = get(vanchor_map, v);
-      global_vtag_map[sgv] = get(vanchor_map,v);
+      global_vtag_map[sgv] = get(vanchor_map, v);
       vmap.insert(std::pair<vertex_descriptor, sg_vertex_descriptor>(v, sgv));
     }
     BOOST_FOREACH(edge_descriptor e, edges(*m_pmesh)) {
diff --git a/Surface_mesh_approximation/include/CGAL/vsa_metrics.h b/Surface_mesh_approximation/include/CGAL/vsa_metrics.h
index e14a28fbc4d..ce7b54107ca 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_metrics.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_metrics.h
@@ -74,47 +74,44 @@ class L21_metric
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L21_metric(const TriangleMesh &tm, const VertexPointMap &point_pmap)
-    : normal_pmap(), area_pmap() {
+  L21_metric(const TriangleMesh &tm, const VertexPointMap &vpoint_map) {
     GeomTraits traits;
     scalar_product_functor = traits.compute_scalar_product_3_object();
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
     
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(tm));
     // construct internal facet normal & area map
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
-      FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
-      put(area_pmap, f, area);
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
   // returns L21 error of a facet f to a proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    Vector_3 v = sum_functor(get(normal_pmap, f), scale_functor(px.normal, FT(-1)));
-    return get(area_pmap, f) * scalar_product_functor(v, v);
+    Vector_3 v = sum_functor(get(fnormal_map, f), scale_functor(px.normal, FT(-1.0)));
+    return get(farea_map, f) * scalar_product_functor(v, v);
   }
 
 private:
-  FacetNormalMap normal_pmap;
-  FacetAreaMap area_pmap;
+  Face_normal_map fnormal_map;
+  Face_area_map farea_map;
   Construct_scaled_vector_3 scale_functor;
   Compute_scalar_product_3 scalar_product_functor;
   Construct_sum_of_vectors_3 sum_functor;
@@ -145,49 +142,46 @@ class L21_metric<TriangleMesh,
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L21_metric(const TriangleMesh &tm)
-    : normal_pmap(), area_pmap() {
+  L21_metric(const TriangleMesh &tm) {
     GeomTraits traits;
     scalar_product_functor = traits.compute_scalar_product_3_object();
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
 
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(tm));
     
     // construct internal facet normal & area map
-    VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
+    VertexPointMap vpoint_map = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
-      FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
-          put(area_pmap, f, area);
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
   // returns L21 error of a facet f to a proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    Vector_3 v = sum_functor(get(normal_pmap, f), scale_functor(px.normal, FT(-1)));
-    return get(area_pmap, f) * scalar_product_functor(v, v);
+    Vector_3 v = sum_functor(get(fnormal_map, f), scale_functor(px.normal, FT(-1.0)));
+    return get(farea_map, f) * scalar_product_functor(v, v);
   }
 
 private:
-  FacetNormalMap normal_pmap;
-  FacetAreaMap area_pmap;
+  Face_normal_map fnormal_map;
+  Face_area_map farea_map;
   Construct_scaled_vector_3 scale_functor;
   Compute_scalar_product_3 scalar_product_functor;
   Construct_sum_of_vectors_3 sum_functor;
@@ -215,43 +209,40 @@ class L21_metric<TriangleMesh,
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L21_metric(const TriangleMesh &tm, const VertexPointMap &point_pmap)
-    : normal_pmap() {
+  L21_metric(const TriangleMesh &tm, const VertexPointMap &vpoint_map) {
     GeomTraits traits;
     scalar_product_functor = traits.compute_scalar_product_3_object();
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
 
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
     
     // construct internal facet normal map
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
-      FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
     }
   }
 
   // returns L21 error of a facet f to a proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    Vector_3 v = sum_functor(get(normal_pmap,f), scale_functor(px.normal, FT(-1)));
+    Vector_3 v = sum_functor(get(fnormal_map,f), scale_functor(px.normal, FT(-1.0)));
     return scalar_product_functor(v, v);
   }
 
 private:
-  FacetNormalMap normal_pmap;
+  Face_normal_map fnormal_map;
   Construct_scaled_vector_3 scale_functor;
   Compute_scalar_product_3 scalar_product_functor;
   Construct_sum_of_vectors_3 sum_functor;
@@ -280,43 +271,41 @@ class L21_metric<TriangleMesh,
   typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L21_metric(const TriangleMesh &tm)
-    : normal_pmap() {
+  L21_metric(const TriangleMesh &tm) {
     GeomTraits traits;
     scalar_product_functor = traits.compute_scalar_product_3_object();
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
 
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
     
     // construct internal facet normal map
-    VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
+    VertexPointMap vpoint_map = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
     }
   }
 
   // returns L21 error of a facet f to a proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    Vector_3 v = sum_functor(get(normal_pmap,f), scale_functor(px.normal, FT(-1)));
+    Vector_3 v = sum_functor(get(fnormal_map,f), scale_functor(px.normal, FT(-1.0)));
     return scalar_product_functor(v, v);
   }
 
 private:
-  FacetNormalMap normal_pmap;
+  Face_normal_map fnormal_map;
   Construct_scaled_vector_3 scale_functor;
   Compute_scalar_product_3 scalar_product_functor;
   Construct_sum_of_vectors_3 sum_functor;
@@ -354,35 +343,32 @@ class L21_proxy_fitting
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor.
-  L21_proxy_fitting(const TriangleMesh &tm, const VertexPointMap &point_pmap)
-    : normal_pmap(), area_pmap() {
+  L21_proxy_fitting(const TriangleMesh &tm, const VertexPointMap &vpoint_map) {
     GeomTraits traits;
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
 
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(tm));
     
     // construct internal facet normal & area map
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
-      FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
-      put(area_pmap, f, area);
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
@@ -395,7 +381,7 @@ public:
     Vector_3 norm = CGAL::NULL_VECTOR;
     for (FacetIterator fitr = beg; fitr != end; ++fitr) {
       norm = sum_functor(norm,
-                         scale_functor(get(normal_pmap, *fitr), get(area_pmap, *fitr)));
+        scale_functor(get(fnormal_map, *fitr), get(farea_map, *fitr)));
     }
     norm = scale_functor(norm,
       FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
@@ -408,8 +394,8 @@ public:
   }
 
 private:
-  FacetNormalMap normal_pmap;
-  FacetAreaMap area_pmap;
+  Face_normal_map fnormal_map;
+  Face_area_map farea_map;
   Construct_scaled_vector_3 scale_functor;
   Construct_sum_of_vectors_3 sum_functor;
 };
@@ -436,35 +422,33 @@ class L21_proxy_fitting<TriangleMesh,
 
   typedef CGAL::internal::face_property_t<Vector_3> Face_normal_tag;
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type FacetNormalMap;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_normal_tag >::type Face_normal_map;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor.
-  L21_proxy_fitting(const TriangleMesh &tm)
-    : normal_pmap(), area_pmap() {
+  L21_proxy_fitting(const TriangleMesh &tm) {
     GeomTraits traits;
     sum_functor = traits.construct_sum_of_vectors_3_object();
     scale_functor = traits.construct_scaled_vector_3_object();
 
-    normal_pmap = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
-                                               const_cast<TriangleMesh&>(tm));
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-                                               const_cast<TriangleMesh&>(tm));
+    fnormal_map = CGAL::internal::add_property(Face_normal_tag("VSA-face_normal"),
+      const_cast<TriangleMesh &>(tm));
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(tm));
+
     // construct internal facet normal & area map
-    VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
+    VertexPointMap vpoint_map = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
     BOOST_FOREACH(face_descriptor f, faces(tm)) {
       const halfedge_descriptor he = halfedge(f, tm);
-      const Point_3 &p0 = point_pmap[source(he, tm)];
-      const Point_3 &p1 = point_pmap[target(he, tm)];
-      const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
-      Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
-      put(normal_pmap, f, normal);
-      FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
-      put(area_pmap, f, area);
+      const Point_3 &p0 = vpoint_map[source(he, tm)];
+      const Point_3 &p1 = vpoint_map[target(he, tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, tm), tm)];
+      put(fnormal_map, f, CGAL::unit_normal(p0, p1, p2));
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
@@ -477,7 +461,7 @@ public:
     Vector_3 norm = CGAL::NULL_VECTOR;
     for (FacetIterator fitr = beg; fitr != end; ++fitr) {
       norm = sum_functor(norm,
-                         scale_functor(get(normal_pmap, *fitr), get(area_pmap, *fitr)));
+                         scale_functor(get(fnormal_map, *fitr), get(farea_map, *fitr)));
     }
     norm = scale_functor(norm,
       FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
@@ -490,8 +474,8 @@ public:
   }
 
 private:
-  FacetNormalMap normal_pmap;
-  FacetAreaMap area_pmap;
+  Face_normal_map fnormal_map;
+  Face_area_map farea_map;
   Construct_scaled_vector_3 scale_functor;
   Construct_sum_of_vectors_3 sum_functor;
 };
@@ -524,34 +508,33 @@ class L2_metric
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
 
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L2_metric(const TriangleMesh &tm, const VertexPointMap &_point_pmap)
-    : mesh(&tm), area_pmap(), point_pmap(_point_pmap) {
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-      const_cast<TriangleMesh &>(*mesh));
+  L2_metric(const TriangleMesh &tm_, const VertexPointMap &vpoint_map_)
+    : tm(&tm_), vpoint_map(vpoint_map_) {
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(*tm));
 
-    BOOST_FOREACH(face_descriptor f, faces(*mesh)) {
-      const halfedge_descriptor he = halfedge(f, *mesh);
-      const Point_3 &p0 = point_pmap[source(he, *mesh)];
-      const Point_3 &p1 = point_pmap[target(he, *mesh)];
-      const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
-      put(area_pmap, f,
-        std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
+    BOOST_FOREACH(face_descriptor f, faces(*tm)) {
+      const halfedge_descriptor he = halfedge(f, *tm);
+      const Point_3 &p0 = vpoint_map[source(he, *tm)];
+      const Point_3 &p1 = vpoint_map[target(he, *tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
   // returns l2 fitting error from facet f to proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    halfedge_descriptor he = halfedge(f, *mesh);
-    const Point_3 &p0 = point_pmap[source(he, *mesh)];
-    const Point_3 &p1 = point_pmap[target(he, *mesh)];
-    const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
+    halfedge_descriptor he = halfedge(f, *tm);
+    const Point_3 &p0 = vpoint_map[source(he, *tm)];
+    const Point_3 &p1 = vpoint_map[target(he, *tm)];
+    const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
     const FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
     const FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
     const FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
@@ -559,13 +542,13 @@ public:
     const FT d1(std::sqrt(CGAL::to_double(sq_d1)));
     const FT d2(std::sqrt(CGAL::to_double(sq_d2)));
 
-    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(area_pmap, f) / FT(6.0);
+    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(farea_map, f) / FT(6.0);
   }
 
 private:
-  const TriangleMesh *mesh;
-  const VertexPointMap point_pmap;
-  FacetAreaMap area_pmap;
+  const TriangleMesh *tm;
+  const VertexPointMap vpoint_map;
+  Face_area_map farea_map;
 };
 
 // specialization
@@ -586,34 +569,33 @@ class L2_metric<TriangleMesh,
   typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
 
   typedef CGAL::internal::face_property_t<FT> Face_area_tag;
-  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type FacetAreaMap;
+  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;
 
 public:
   // type required by `ErrorMetric` concept
   typedef PlaneProxy Proxy;
 
   // constructor
-  L2_metric(const TriangleMesh &tm)
-    : mesh(&tm), area_pmap(),
-    point_pmap(get(boost::vertex_point, const_cast<TriangleMesh &>(tm))) {
-    area_pmap = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
-      const_cast<TriangleMesh &>(*mesh));
-    BOOST_FOREACH(face_descriptor f, faces(*mesh)) {
-      const halfedge_descriptor he = halfedge(f, *mesh);
-      const Point_3 &p0 = point_pmap[source(he, *mesh)];
-      const Point_3 &p1 = point_pmap[target(he, *mesh)];
-      const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
-      put(area_pmap, f,
-        std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
+  L2_metric(const TriangleMesh &tm_)
+    : tm(&tm_), vpoint_map(get(boost::vertex_point, const_cast<TriangleMesh &>(tm_))) {
+    farea_map = CGAL::internal::add_property(Face_area_tag("VSA-face_area"),
+      const_cast<TriangleMesh &>(*tm));
+
+    BOOST_FOREACH(face_descriptor f, faces(*tm)) {
+      const halfedge_descriptor he = halfedge(f, *tm);
+      const Point_3 &p0 = vpoint_map[source(he, *tm)];
+      const Point_3 &p1 = vpoint_map[target(he, *tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
+      put(farea_map, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
     }
   }
 
   // returns l2 fitting error from facet f to proxy px.
   FT operator()(const face_descriptor &f, const Proxy &px) const {
-    halfedge_descriptor he = halfedge(f, *mesh);
-    const Point_3 &p0 = point_pmap[source(he, *mesh)];
-    const Point_3 &p1 = point_pmap[target(he, *mesh)];
-    const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
+    halfedge_descriptor he = halfedge(f, *tm);
+    const Point_3 &p0 = vpoint_map[source(he, *tm)];
+    const Point_3 &p1 = vpoint_map[target(he, *tm)];
+    const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
     const FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
     const FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
     const FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
@@ -621,13 +603,13 @@ public:
     const FT d1(std::sqrt(CGAL::to_double(sq_d1)));
     const FT d2(std::sqrt(CGAL::to_double(sq_d2)));
 
-    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(area_pmap, f) / FT(6);
+    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(farea_map, f) / FT(6);
   }
 
 private:
-  const TriangleMesh *mesh;
-  const VertexPointMap point_pmap;
-  FacetAreaMap area_pmap;
+  const TriangleMesh *tm;
+  const VertexPointMap vpoint_map;
+  Face_area_map farea_map;
 };
 
 /*!
@@ -661,8 +643,8 @@ public:
   typedef PlaneProxy Proxy;
 
   // construct L2 proxy fitting functor from a triangle mesh and the vertex point map.
-  L2_proxy_fitting(const TriangleMesh &_mesh, const VertexPointMap &_point_pmap)
-    : mesh(&_mesh), point_pmap(_point_pmap) {}
+  L2_proxy_fitting(const TriangleMesh &tm_, const VertexPointMap &vpoint_map_)
+    : tm(&tm_), vpoint_map(vpoint_map_) {}
 
   // returns proxy fitted from range of facets.
   template <typename FacetIterator>
@@ -671,10 +653,10 @@ public:
 
     std::list<Triangle_3> tris;
     for (FacetIterator fitr = beg; fitr != end; ++fitr) {
-      halfedge_descriptor he = halfedge(*fitr, *mesh);
-      const Point_3 &p0 = point_pmap[source(he, *mesh)];
-      const Point_3 &p1 = point_pmap[target(he, *mesh)];
-      const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
+      halfedge_descriptor he = halfedge(*fitr, *tm);
+      const Point_3 &p0 = vpoint_map[source(he, *tm)];
+      const Point_3 &p1 = vpoint_map[target(he, *tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
       tris.push_back(Triangle_3(p0, p1, p2));
     }
 
@@ -690,8 +672,8 @@ public:
   }
 
 private:
-  const TriangleMesh *mesh;
-  const VertexPointMap point_pmap;
+  const TriangleMesh *tm;
+  const VertexPointMap vpoint_map;
 };
 
 // specialization.
@@ -715,9 +697,8 @@ public:
   typedef PlaneProxy Proxy;
 
   // construct L2 proxy fitting functor from a triangle mesh.
-  L2_proxy_fitting(const TriangleMesh &_mesh)
-    : mesh(&_mesh),
-    point_pmap(get(boost::vertex_point, const_cast<TriangleMesh &>(_mesh))) {}
+  L2_proxy_fitting(const TriangleMesh &tm_)
+    : tm(&tm_), vpoint_map(get(boost::vertex_point, const_cast<TriangleMesh &>(tm_))) {}
 
   // returns the proxy fitted from a range of facets.
   template <typename FacetIterator>
@@ -726,10 +707,10 @@ public:
 
     std::list<Triangle_3> tris;
     for (FacetIterator fitr = beg; fitr != end; ++fitr) {
-      halfedge_descriptor he = halfedge(*fitr, *mesh);
-      const Point_3 &p0 = point_pmap[source(he, *mesh)];
-      const Point_3 &p1 = point_pmap[target(he, *mesh)];
-      const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
+      halfedge_descriptor he = halfedge(*fitr, *tm);
+      const Point_3 &p0 = vpoint_map[source(he, *tm)];
+      const Point_3 &p1 = vpoint_map[target(he, *tm)];
+      const Point_3 &p2 = vpoint_map[target(next(he, *tm), *tm)];
       tris.push_back(Triangle_3(p0, p1, p2));
     }
 
@@ -745,8 +726,8 @@ public:
   }
 
 private:
-  const TriangleMesh *mesh;
-  const VertexPointMap point_pmap;
+  const TriangleMesh *tm;
+  const VertexPointMap vpoint_map;
 };
 
 } // end namespace VSA