diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
index 96508e14e87..b78f7465e96 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
@@ -29,11 +29,11 @@ public:
   FT compute_error(const TriangleMesh &tm, const face_descriptor &f, const Proxy &proxy) const;
 
   /// Computes and returns fitted proxy from a range of faces.
-  /// @tparam FaceRange range of
-  ///   `boost::graph_traits<TriangleMesh>::%face_descriptor`, model of `Range`.
-  ///   Its iterator type is `InputIterator`.
+  /// @tparam FaceRange a range of
+  ///   `boost::graph_traits<TriangleMesh>::%face_descriptor` model of `ConstRange`
+  ///   with iterator type being model of `InputIterator`.
   template <typename FaceRange>
-  Proxy fit_proxy(const TriangleMesh &tm, const FaceRange &faces) const;
+  Proxy fit_proxy(const FaceRange &faces, const TriangleMesh &tm) const;
 
   /// }
 
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_isotropic_metric_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_isotropic_metric_example.cpp
index b6bacd90828..af2d1448ff8 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_isotropic_metric_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_isotropic_metric_example.cpp
@@ -43,7 +43,7 @@ struct Compact_metric_point_proxy
   // template functor to compute a best-fit 
   // proxy from a range of faces
   template <typename FaceRange>
-  Proxy fit_proxy(const Polyhedron &tm, const FaceRange &faces) const {
+  Proxy fit_proxy(const FaceRange &faces, const Polyhedron &tm) const {
     (void)(tm);
     // fitting center
     Vector center = CGAL::NULL_VECTOR;
diff --git a/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
index 222976a0685..71c1a6ac8e4 100644
--- a/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
@@ -94,12 +94,12 @@ public:
   /*!
    * @brief Fits a proxy to a range of faces.
    * @tparam FaceRange range of face descriptors, model of Range.
-   * @param tm input triangle mesh
    * @param faces the range of faces to be fitted
+   * @param tm input triangle mesh
    * @return fitted proxy
    */
   template <typename FaceRange>
-  Proxy fit_proxy(const TriangleMesh &tm, const FaceRange &faces) const {
+  Proxy fit_proxy(const FaceRange &faces, const TriangleMesh &tm) const {
     (void)(tm);
     CGAL_assertion(!faces.empty());
 
diff --git a/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
index e2bab1f67f5..1174a8f521f 100644
--- a/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
@@ -100,12 +100,12 @@ public:
    * through the center of mass and is defined by the two principal
    * components of the integral covariance matrix.
    * @tparam FaceRange range of face descriptors, model of Range.
-   * @param tm input triangle mesh
    * @param faces the range of faces to be fitted
+   * @param tm input triangle mesh
    * @return fitted proxy
    */
   template <typename FaceRange>
-  Proxy fit_proxy(const TriangleMesh &tm, const FaceRange &faces) const {
+  Proxy fit_proxy(const FaceRange &faces, const TriangleMesh &tm) const {
     (void)(tm);
     CGAL_assertion(!faces.empty());
 
diff --git a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
index 93cda8b62b5..3c786bb95d2 100644
--- a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
@@ -1334,7 +1334,7 @@ private:
     CGAL_assertion(!px_patch.empty());
 
     // use Proxy_fitting functor to fit proxy parameters
-    const Proxy px = m_metric->fit_proxy(*m_ptm, px_patch);
+    const Proxy px = m_metric->fit_proxy(px_patch, *m_ptm);
 
     // find proxy seed and sum error
     face_descriptor seed = *px_patch.begin();
@@ -1374,7 +1374,7 @@ private:
   Proxy_wrapper fit_proxy_from_facet(const face_descriptor f, const std::size_t px_idx) {
     // fit proxy parameters
     std::vector<face_descriptor> fvec(1, f);
-    const Proxy px = m_metric->fit_proxy(*m_ptm, fvec);
+    const Proxy px = m_metric->fit_proxy(fvec, *m_ptm);
     const FT err = m_metric->compute_error(*m_ptm, f, px);
 
     // original proxy map should always be falid
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 dff47dab454..8393cdafc41 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
@@ -43,7 +43,7 @@ struct Compact_metric_point_proxy {
   // template functor to compute a best-fit 
   // proxy from a range of facets
   template <typename FaceRange>
-  Proxy fit_proxy(const Polyhedron &tm, const FaceRange &faces) const {
+  Proxy fit_proxy(const FaceRange &faces, const Polyhedron &tm) const {
     (void)(tm);
     // fitting center
     Vector center = CGAL::NULL_VECTOR;