diff --git a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
index 35ee486a392..313cbb3e33d 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation.h
@@ -318,7 +318,7 @@ void vsa_approximate(
   typedef CGAL::PlaneProxy<TriangleMesh> PlaneProxy;
   typedef CGAL::L21Metric<PlaneProxy, FacetNormalMap, FacetAreaMap> L21Metric;
   typedef CGAL::L21ProxyFitting<PlaneProxy, FacetNormalMap, FacetAreaMap> L21ProxyFitting;
-  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, VertexPointMap, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
+  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
 
   VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
   // construct facet normal & area map
@@ -339,7 +339,7 @@ void vsa_approximate(
 
   vsa_approximate(tm,
     f_proxy_pmap,
-    L21ApproximationTrait(tm, point_pmap, normal_pmap, area_pmap),
+    L21ApproximationTrait(tm, normal_pmap, area_pmap),
     init,
     number_of_segments,
     number_of_iterations);
@@ -389,7 +389,7 @@ void vsa_extract(
   typedef CGAL::L21Metric<PlaneProxy, FacetNormalMap, FacetAreaMap> L21Metric;
   typedef CGAL::L21ProxyFitting<PlaneProxy, FacetNormalMap, FacetAreaMap> L21ProxyFitting;
   typedef CGAL::PlaneFitting<TriangleMesh> PlaneFitting;
-  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, VertexPointMap, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
+  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
 
   VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
   // construct facet normal & area map
@@ -418,7 +418,7 @@ void vsa_extract(
     tris,
     pos,
     PlaneFitting(tm),
-    L21ApproximationTrait(tm, point_pmap, normal_pmap, area_pmap),
+    L21ApproximationTrait(tm, normal_pmap, area_pmap),
     init,
     number_of_segments,
     number_of_iterations);
@@ -474,7 +474,7 @@ void vsa_approximate_and_extract(
   typedef CGAL::L21Metric<PlaneProxy, FacetNormalMap, FacetAreaMap> L21Metric;
   typedef CGAL::L21ProxyFitting<PlaneProxy, FacetNormalMap, FacetAreaMap> L21ProxyFitting;
   typedef CGAL::PlaneFitting<TriangleMesh> PlaneFitting;
-  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, VertexPointMap, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
+  typedef CGAL::L21ApproximationTrait<PlaneProxy, TriangleMesh, L21Metric, L21ProxyFitting, FacetNormalMap, FacetAreaMap> L21ApproximationTrait;
 
   VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
   // construct facet normal & area map
@@ -493,7 +493,7 @@ void vsa_approximate_and_extract(
   FacetNormalMap normal_pmap(facet_normals);
   FacetAreaMap area_pmap(facet_areas);
 
-  L21ApproximationTrait app_trait(tm, point_pmap, normal_pmap, area_pmap);
+  L21ApproximationTrait app_trait(tm, normal_pmap, area_pmap);
   vsa_approximate_and_extract(tm,
     f_proxy_pmap,
     tris,
diff --git a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
index 202883db974..a44fc91dad3 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
@@ -177,7 +177,6 @@ template<typename PlaneProxy,
   typename TriangleMesh,
   typename L21ErrorMetric,
   typename L21ProxyFitting,
-  typename VertexPointMap,
   typename FacetNormalMap,
   typename FacetAreaMap>
 struct L21ApproximationTrait
@@ -189,11 +188,9 @@ struct L21ApproximationTrait
 
   L21ApproximationTrait(
     const TriangleMesh &_mesh,
-    const VertexPointMap &_point_pmap,
     const FacetNormalMap &_facet_normal_map,
     const FacetAreaMap &_facet_area_map)
     : mesh(_mesh),
-    point_pmap(_point_pmap),
     normal_pmap(_facet_normal_map),
     area_pmap(_facet_area_map) {}
 
@@ -210,7 +207,6 @@ struct L21ApproximationTrait
 
 private:
   const TriangleMesh &mesh;
-  const VertexPointMap point_pmap;
   const FacetNormalMap normal_pmap;
   const FacetAreaMap area_pmap;
 };