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 d61ecad6b1d..fcf4bd653bf 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
@@ -241,6 +241,10 @@ namespace Point_set {
 
       const FT cos_value =
         m_scalar_product_2(query_normal, m_normal_of_best_fit);
+
+      if (cos_value < 0)
+        return false;
+
       const FT squared_cos_value = cos_value * cos_value;
 
       FT squared_cos_value_threshold =
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 3ac12c3dea7..613859165ee 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
@@ -287,6 +287,10 @@ namespace Polygon_mesh {
 
       const Vector_3 face_normal = get(m_face_normals, query);
       const FT cos_value = m_scalar_product_3(face_normal, m_normal_of_best_fit);
+
+      if (cos_value < 0)
+        return false;
+
       const FT squared_cos_value = cos_value * cos_value;
 
       FT squared_cos_value_threshold =
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 702cbaa0fb9..73f3d9cd4d5 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
@@ -244,6 +244,10 @@ namespace Segment_set {
 
       const FT cos_value =
         m_scalar_product(query_direction, m_direction_of_best_fit);
+
+      if (cos_value < 0)
+        return false;
+
       const FT squared_cos_value = cos_value * cos_value;
 
       FT squared_cos_value_threshold =