diff --git a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
index 7f344e37230..478cedf5340 100644
--- a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
+++ b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
@@ -258,7 +258,7 @@ CGAL_add_named_parameter(minimum_region_size_t, minimum_region_size, minimum_reg
 CGAL_add_named_parameter(sphere_radius_t, sphere_radius, sphere_radius)
 CGAL_add_named_parameter(k_neighbors_t, k_neighbors, k_neighbors)
 CGAL_add_named_parameter(item_map_t, item_map, item_map)
-CGAL_add_named_parameter(cosine_value_t, cosine_value, cosine_value)
+CGAL_add_named_parameter(cosine_of_maxium_angle_t, cosine_of_maxium_angle, cosine_of_maxium_angle)
 CGAL_add_named_parameter(minimum_radius_t, minimum_radius, minimum_radius)
 CGAL_add_named_parameter(maximum_radius_t, maximum_radius, maximum_radius)
 
diff --git a/Shape_detection/include/CGAL/Polygon_mesh_processing/region_growing.h b/Shape_detection/include/CGAL/Polygon_mesh_processing/region_growing.h
index 0d3357c3fde..fdd9ee64d47 100644
--- a/Shape_detection/include/CGAL/Polygon_mesh_processing/region_growing.h
+++ b/Shape_detection/include/CGAL/Polygon_mesh_processing/region_growing.h
@@ -53,9 +53,9 @@ namespace Polygon_mesh_processing {
                             such that they are considered part of the same region}
       \cgalParamType{`GeomTraits::FT` with `GeomTraits` being the type of the parameter `geom_traits`}
       \cgalParamDefault{25 degrees}
-      \cgalParamExtra{this parameter and `cosine_value` are exclusive}
+      \cgalParamExtra{this parameter and `cosine_of_maxium_angle` are exclusive}
     \cgalParamNEnd
-    \cgalParamNBegin{cosine_value}
+    \cgalParamNBegin{cosine_of_maxium_angle}
       \cgalParamDescription{The maximum angle, given as a cosine, between the normal of the supporting planes of adjacent faces
                             such that they are considered part of the same region}
       \cgalParamType{`GeomTraits::FT` with `GeomTraits` being the type of the parameter `geom_traits`}
@@ -157,7 +157,7 @@ region_growing_of_planes_on_faces(const PolygonMesh& mesh,
       \cgalParamDescription{the maximum distance from a point to a line such that it is considered part of the region of the line}
       \cgalParamType{`GeomTraits::FT` with `GeomTraits` being the type of the parameter `geom_traits`}
       \cgalParamDefault{1}
-      \cgalParamExtra{this parameter and `cosine_value` are exclusive}
+      \cgalParamExtra{this parameter and `cosine_of_maxium_angle` are exclusive}
     \cgalParamNEnd
     \cgalParamNBegin{maximum_angle}
       \cgalParamDescription{the maximum angle in degrees between two adjacent segments
@@ -165,7 +165,7 @@ region_growing_of_planes_on_faces(const PolygonMesh& mesh,
       \cgalParamType{`GeomTraits::FT` with `GeomTraits` being the type of the parameter `geom_traits`}
       \cgalParamDefault{25 degrees}
     \cgalParamNEnd
-    \cgalParamNBegin{cosine_value}
+    \cgalParamNBegin{cosine_of_maxium_angle}
       \cgalParamDescription{The maximum angle, given as a cosine, between two adjacent segments
                             such that they are considered part of the same region}
       \cgalParamType{`GeomTraits::FT` with `GeomTraits` being the type of the parameter `geom_traits`}
@@ -204,8 +204,7 @@ detect_corners_of_regions(
   using parameters::get_parameter;
   using parameters::is_default_parameter;
 
-  typedef typename GetGeomTraits<PolygonMesh, CGAL_NP_CLASS>::type  Traits;
-
+  using Traits = typename GetGeomTraits<PolygonMesh, CGAL_NP_CLASS>::type;
   using Graph_traits = boost::graph_traits<PolygonMesh>;
   using halfedge_descriptor = typename Graph_traits::halfedge_descriptor;
   using edge_descriptor = typename Graph_traits::edge_descriptor;
@@ -213,7 +212,7 @@ detect_corners_of_regions(
   using vertex_descriptor = typename Graph_traits::vertex_descriptor;
 
   using Default_ecm = typename boost::template property_map<PolygonMesh, CGAL::dynamic_edge_property_t<bool> >::type;
-  using Ecm = internal_np::Lookup_named_param_def <
+  using Ecm = typename internal_np::Lookup_named_param_def <
                 internal_np::edge_is_constrained_t,
                 CGAL_NP_CLASS,
                 Default_ecm
@@ -238,6 +237,7 @@ detect_corners_of_regions(
     halfedge_descriptor h = halfedge(e, mesh);
     face_descriptor f1 = face(h, mesh);
     face_descriptor f2 = face(opposite(h, mesh), mesh);
+    // an edge is constrained if it is a border edge or if the regions assigned to the two faces are different
     if (f1 == Graph_traits::null_face() || f2 == Graph_traits::null_face() || get(region_map,f1)!=get(region_map,f2))
       put(ecm, e, true);
   }
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_circle_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_circle_fit_region.h
index 05d8d4e9149..0aca9432166 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_circle_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_circle_fit_region.h
@@ -129,7 +129,7 @@ namespace Point_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -168,7 +168,7 @@ namespace Point_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
@@ -198,7 +198,7 @@ namespace Point_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
 
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_cylinder_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_cylinder_fit_region.h
index 59c9992656b..c1224eaeb1c 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_cylinder_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_cylinder_fit_region.h
@@ -128,7 +128,7 @@ namespace Point_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -167,7 +167,7 @@ namespace Point_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
@@ -197,7 +197,7 @@ namespace Point_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
 
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_line_fit_region.h
index 064b75421aa..6f04d915753 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_line_fit_region.h
@@ -118,7 +118,7 @@ namespace Point_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -145,7 +145,7 @@ namespace Point_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
     */
     template<typename CGAL_NP_TEMPLATE_PARAMETERS>
@@ -174,7 +174,7 @@ namespace Point_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
     }
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_plane_fit_region.h
index 89b234bae07..b1fe82d706f 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_plane_fit_region.h
@@ -119,7 +119,7 @@ namespace Point_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -146,7 +146,7 @@ namespace Point_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
     */
     template<typename CGAL_NP_TEMPLATE_PARAMETERS>
@@ -175,7 +175,7 @@ namespace Point_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
     }
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h
index d2689ca1a9e..68285b5777b 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h
@@ -118,7 +118,7 @@ namespace Point_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -157,7 +157,7 @@ namespace Point_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
@@ -187,7 +187,7 @@ namespace Point_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
 
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Polygon_mesh/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Polygon_mesh/Least_squares_plane_fit_region.h
index bbdbeeb0dce..8a3e133c0b9 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Polygon_mesh/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Polygon_mesh/Least_squares_plane_fit_region.h
@@ -118,7 +118,7 @@ namespace Polygon_mesh {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -143,7 +143,7 @@ namespace Polygon_mesh {
       \pre `faces(tmesh).size() > 0`
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
     */
     template<typename CGAL_NP_TEMPLATE_PARAMETERS>
@@ -176,7 +176,7 @@ namespace Polygon_mesh {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
     }
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h
index 171dc0b7e38..70b2aa0026d 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h
@@ -128,7 +128,7 @@ namespace Segment_set {
           \cgalParamType{`GeomTraits::FT`}
           \cgalParamDefault{25 degrees}
         \cgalParamNEnd
-        \cgalParamNBegin{cosine_value}
+        \cgalParamNBegin{cosine_of_maxium_angle}
           \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
           this parameter can be used instead of the `maximum_angle`}
           \cgalParamType{`GeomTraits::FT`}
@@ -152,7 +152,7 @@ namespace Segment_set {
 
       \pre `maximum_distance >= 0`
       \pre `maximum_angle >= 0 && maximum_angle <= 90`
-      \pre `cosine_value >= 0 && cosine_value <= 1`
+      \pre `cosine_of_maxium_angle >= 0 && cosine_of_maxium_angle <= 1`
       \pre `minimum_region_size > 0`
     */
     template<typename NamedParameters = parameters::Default_named_parameters>
@@ -182,7 +182,7 @@ namespace Segment_set {
       const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
         (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
       const FT cos_value = parameters::choose_parameter(
-        parameters::get_parameter(np, internal_np::cosine_value), default_cos_value);
+        parameters::get_parameter(np, internal_np::cosine_of_maxium_angle), default_cos_value);
       CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
       m_cos_value_threshold = cos_value;
     }
diff --git a/Shape_detection/test/Shape_detection/test_validity_sampled_data.cpp b/Shape_detection/test/Shape_detection/test_validity_sampled_data.cpp
index 3f65401eb3e..58424b53aa8 100644
--- a/Shape_detection/test/Shape_detection/test_validity_sampled_data.cpp
+++ b/Shape_detection/test/Shape_detection/test_validity_sampled_data.cpp
@@ -122,7 +122,7 @@ void test_copied_point_cloud (const Point_set& original_points, std::size_t nb)
   RG_region rg_region (
     CGAL::parameters::
     maximum_distance(parameters.epsilon).
-    cosine_value(parameters.normal_threshold).
+    cosine_of_maxium_angle(parameters.normal_threshold).
     minimum_region_size(parameters.min_points));
   Region_growing region_growing (points, rg_query, rg_region);
   std::size_t nb_detected = 0;