diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetric.h b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetric.h
index da6c320f90b..94b4b4b4656 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetric.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetric.h
@@ -2,19 +2,18 @@
 \ingroup PkgTSMAConcepts
 \cgalConcept
 
-The concept `ErrorMetric` is requied to operate on a facet and a proxy, returns the fitting error.
-It is used in the functions `vsa_mesh_approximation()` and `vsa_mesh_segmentation()`.
+The concept `ErrorMetric` computes the fitting error of a face to a `Proxy`, used in CGAL::VSA::Mesh_approximation.
 
-\cgalHasModel `L21Metric`
-\cgalHasModel `L2Metric`
+\cgalHasModel `CGAL::VSA::L21_metric`
+\cgalHasModel `CGAL::VSA::L2_metric`
 */
 
 class ErrorMetric {
 public:
   /// A number type model of `Field` and `RealEmbeddable`
   typedef unspecified_type FT;
-  /// Triangle mesh facet descriptor.
-  typedef unspecified_type facet_descriptor;
+  /// Triangle mesh face descriptor.
+  typedef unspecified_type face_descriptor;
   /// Parametrized shape proxy.
   typedef unspecified_type Proxy;
 
@@ -22,8 +21,8 @@ public:
   /// A model of this concept must provide:
   /// @{
 
-  /// returns the fitting error of a facet f to the proxy px.
-  FT operator()(const facet_descriptor &f, const Proxy &px) const;
+  /// returns the fitting error of a face f to the proxy px.
+  FT operator()(const face_descriptor &f, const Proxy &px) const;
 
   /// }
 };
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 61a01b62927..fe415ae95ec 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/Proxy.h
@@ -2,10 +2,11 @@
 \ingroup PkgTSMAConcepts
 \cgalConcept
 
-The concept `Proxy` describes the primitive shape used in the Variational Shape Approximation algorithm.
-It is nested within the `ErrorMetric` and `ProxyFitting` concepts.
+The concept `Proxy` describes the primitive shape, nested within the `ErrorMetric` and `ProxyFitting` concepts.
 
-\cgalHasModel `Plane_proxy`
+It can contain anything to store the primitive shape parameters.
+
+\cgalHasModel `CGAL::VSA::Plane_proxy`
 */
 
 class Proxy {
diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ProxyFitting.h b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ProxyFitting.h
index 9bf69ca0984..a1655700b9f 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ProxyFitting.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ProxyFitting.h
@@ -2,11 +2,10 @@
 \ingroup PkgTSMAConcepts
 \cgalConcept
 
-The concept `ProxyFitting` is required to fit a shape `Proxy` from a range of facets.
-It is used in the functions `vsa_mesh_approximation()`.
+The concept `ProxyFitting` fits a shape primitive `Proxy` from a range of facets, used in CGAL::VSA::Mesh_approximation.
 
-\cgalHasModel `L21ProxyFitting`
-\cgalHasModel `L2ProxyFitting`
+\cgalHasModel `CGAL::VSA::L21_proxy_fitting`
+\cgalHasModel `CGAL::VSA::L2_proxy_fitting`
 */
 
 class ProxyFitting {
@@ -18,9 +17,9 @@ public:
   /// A model of this concept must provide:
   /// @{
 
-  /// returns the fitting proxy from a range of facets.
-  template<FacetsIterator>
-  Proxy operator()(const FacetsIterator &beg, const FacetsIterator &end) const;
+  /// returns the fitted proxy from a range of facets.
+  template <typename FacetIterator>
+  Proxy operator()(const FacetIterator &beg, const FacetIterator &end) const;
 
   /// }
 };