diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h
index 7d80d7f9737..a9b8df207e2 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h
@@ -10,14 +10,10 @@ It is nested within the `ErrorMetric` and `ProxyFitting` concepts.
 
 class Proxy {
 public:
-  /// Triangle mesh facet descriptor.
-  typedef unspecified_type facet_descriptor;
-
   /// @name Data members
   /// @{
 
-  /// Data member to store the proxy seed.
-  facet_descriptor seed;
+  /// Anything to store the proxy shape parameters.
 
   /// }
 };
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 9ec4cb294ce..72188ba794a 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
@@ -25,7 +25,6 @@ typedef boost::associative_property_map<std::map<Facet_handle, Point> > FacetCen
 
 // proxy
 struct PointProxy {
-  Facet_handle seed;
   Point center;
 };
 
diff --git a/Surface_mesh_approximation/include/CGAL/VSA_approximation.h b/Surface_mesh_approximation/include/CGAL/VSA_approximation.h
index 429c9c16de1..cbf56017185 100644
--- a/Surface_mesh_approximation/include/CGAL/VSA_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/VSA_approximation.h
@@ -53,7 +53,7 @@ class VSA_approximation {
       typename boost::property_traits<VertexPointMap>::value_type
     >::Kernel >::type GeomTraits;
   typedef typename CGAL::Default::Get<Proxy_,
-    CGAL::PlaneProxy<TriangleMesh, GeomTraits> >::type Proxy;
+    CGAL::PlaneProxy<GeomTraits> >::type Proxy;
   typedef typename CGAL::Default::Get<ErrorMetric_,
     CGAL::L21Metric<TriangleMesh, VertexPointMap, GeomTraits, Proxy> >::type ErrorMetric;
   typedef typename CGAL::Default::Get<ProxyFitting_,
diff --git a/Surface_mesh_approximation/include/CGAL/VSA_metrics.h b/Surface_mesh_approximation/include/CGAL/VSA_metrics.h
index 47fae7889a4..e827cf91ef8 100644
--- a/Surface_mesh_approximation/include/CGAL/VSA_metrics.h
+++ b/Surface_mesh_approximation/include/CGAL/VSA_metrics.h
@@ -20,20 +20,15 @@ namespace CGAL
  *
  * \cgalModels `Proxy`
  *
- * @tparam TriangleMesh a triangle `FaceGraph`
  * @tparam GeomTraits geometric traits
  */
-template<typename TriangleMesh,
-  typename GeomTraits = typename TriangleMesh::Traits>
+template <typename GeomTraits>
 class PlaneProxy
 {
   typedef typename GeomTraits::Vector_3 Vector_3;
   typedef typename GeomTraits::Plane_3 Plane_3;
-  typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
 
 public:
-  // The proxy seed.
-  face_descriptor seed;
   // The proxy normal used in the `L21Metric`.
   Vector_3 normal;
   // The fitting plane of the proxy used in the `L2Metric`.
@@ -54,11 +49,11 @@ public:
  * @tparam GeomTraits geometric traits
  * @tparam PlaneProxy a model of `PlaneProxy`
  */
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename VertexPointMap
     = typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
   typename GeomTraits = typename TriangleMesh::Traits,
-  typename PlaneProxy = CGAL::PlaneProxy<TriangleMesh, GeomTraits> >
+  typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
 class L21Metric
 {
   typedef typename GeomTraits::FT FT;
@@ -116,7 +111,7 @@ private:
 };
 
 // specialization
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename GeomTraits,
   typename PlaneProxy>
 class L21Metric<TriangleMesh,
@@ -194,11 +189,11 @@ private:
  * @tparam GeomTraits geometric traits
  * @tparam PlaneProxy a model of `PlaneProxy`
  */
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename VertexPointMap
     = typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
   typename GeomTraits = typename TriangleMesh::Traits,
-  typename PlaneProxy = CGAL::PlaneProxy<TriangleMesh, GeomTraits> >
+  typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
 class L21ProxyFitting
 {
   typedef typename GeomTraits::FT FT;
@@ -238,7 +233,7 @@ public:
   }
 
   // returns the proxy fitted from the facets from beg to end.
-  template<typename FacetIterator>
+  template <typename FacetIterator>
   Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
@@ -268,7 +263,7 @@ private:
 };
 
 // specialization
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename GeomTraits,
   typename PlaneProxy>
 class L21ProxyFitting<TriangleMesh,
@@ -315,7 +310,7 @@ public:
   }
 
   // returns the proxy fitted from the facets from beg to end.
-  template<typename FacetIterator>
+  template <typename FacetIterator>
   Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
@@ -358,11 +353,11 @@ private:
  * @tparam GeomTraits geometric traits
  * @tparam PlaneProxy a model of `PlaneProxy`
  */
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename VertexPointMap
     = typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
   typename GeomTraits = typename TriangleMesh::Traits,
-  typename PlaneProxy = CGAL::PlaneProxy<TriangleMesh, GeomTraits> >
+  typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
 class L2Metric
 {
   typedef typename GeomTraits::FT FT;
@@ -414,7 +409,7 @@ private:
 };
 
 // specialization
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename GeomTraits,
   typename PlaneProxy>
 class L2Metric<TriangleMesh,
@@ -487,11 +482,11 @@ private:
  * @tparam GeomTraits geometric traits
  * @tparam PlaneProxy a model of `PlaneProxy`
  */
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename VertexPointMap
     = typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
   typename GeomTraits = typename TriangleMesh::Traits,
-  typename PlaneProxy = CGAL::PlaneProxy<TriangleMesh, GeomTraits> >
+  typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
 class L2ProxyFitting
 {
   typedef typename GeomTraits::Point_3 Point_3;
@@ -507,7 +502,7 @@ public:
     : mesh(&_mesh), point_pmap(_point_pmap) {}
 
   // returns the proxy fitted from a range of facets.
-  template<typename FacetIterator>
+  template <typename FacetIterator>
   Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
@@ -539,7 +534,7 @@ private:
 /*!
  * Specialization.
  */
-template<typename TriangleMesh,
+template <typename TriangleMesh,
   typename GeomTraits,
   typename PlaneProxy>
 class L2ProxyFitting<TriangleMesh,
@@ -564,7 +559,7 @@ public:
     point_pmap(get(boost::vertex_point, const_cast<TriangleMesh &>(_mesh))) {}
 
   // returns the proxy fitted from a range of facets.
-  template<typename FacetIterator>
+  template <typename FacetIterator>
   Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
diff --git a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
index 7ba58d65fdd..b775336c10e 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
@@ -78,7 +78,7 @@ bool vsa_mesh_approximation(const TriangleMesh &tm_in,
     get(boost::vertex_point, const_cast<TriangleMesh &>(tm_in)));
     // get_property_map(vertex_point, tm_in));
 
-  typedef CGAL::PlaneProxy<TriangleMesh> PlaneProxy;
+  typedef CGAL::PlaneProxy<GeomTraits> PlaneProxy;
   typedef CGAL::L21Metric<TriangleMesh> L21Metric;
   typedef CGAL::L21ProxyFitting<TriangleMesh> L21ProxyFitting;
   typedef CGAL::VSA_approximation<TriangleMesh, VPMap,
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 51d0ff4f7c1..d16131211d1 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
@@ -17,7 +17,7 @@ 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> PlaneProxy;
+typedef CGAL::PlaneProxy<Kernel> PlaneProxy;
 typedef CGAL::L2Metric<Polyhedron> L2Metric;
 typedef CGAL::L2ProxyFitting<Polyhedron> L2ProxyFitting;
 typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap,
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 98464a7f068..693ef72ff0a 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
@@ -13,7 +13,6 @@ typedef Kernel::FT FT;
 typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
-typedef CGAL::PlaneProxy<Polyhedron> PlaneProxy;
 typedef CGAL::L21Metric<Polyhedron> L21Metric;
 typedef CGAL::L21ProxyFitting<Polyhedron> L21ProxyFitting;
 typedef CGAL::VSA_approximation<Polyhedron, VertexPointMap> VSAL21;
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 23858230434..460f6e1fb5e 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
@@ -23,7 +23,6 @@ typedef boost::associative_property_map<std::map<Facet_handle, Point_3> > FacetC
 typedef boost::property_map<Polyhedron, boost::vertex_point_t>::type VertexPointMap;
 
 struct PointProxy {
-  Facet_handle seed;
   Point_3 center;
 };