diff --git a/BGL/include/CGAL/boost/graph/named_params_helper.h b/BGL/include/CGAL/boost/graph/named_params_helper.h
index e80cae78072..948de5dded6 100644
--- a/BGL/include/CGAL/boost/graph/named_params_helper.h
+++ b/BGL/include/CGAL/boost/graph/named_params_helper.h
@@ -336,7 +336,7 @@ struct Point_set_processing_3_np_helper
     return parameters::choose_parameter<Geom_traits>(parameters::get_parameter(np, internal_np::geom_traits));
   }
 
-  static constexpr bool has_normal_map(const PointRange&, const NamedParameters&)
+  static constexpr bool has_normal_map()
   {
     using CGAL::parameters::is_default_parameter;
     return !(is_default_parameter<NamedParameters, internal_np::normal_t>::value);
diff --git a/Point_set_3/include/CGAL/Point_set_3.h b/Point_set_3/include/CGAL/Point_set_3.h
index fc1da7fe601..539c75e7db6 100644
--- a/Point_set_3/include/CGAL/Point_set_3.h
+++ b/Point_set_3/include/CGAL/Point_set_3.h
@@ -1357,9 +1357,9 @@ struct Point_set_processing_3_np_helper<Point_set_3<Point, Vector>, NamedParamet
     return parameters::choose_parameter<Geom_traits>(parameters::get_parameter(np, internal_np::geom_traits));
   }
 
-  static constexpr bool has_normal_map(const Point_set_3<Point, Vector>&, const NamedParameters&)
+  static constexpr bool has_normal_map()
   {
-    return true;//either available in np, or in point set
+    return true; // either available in named parameters, and always available in Point_set_3 otherwise
   }
 
 };
diff --git a/Point_set_processing_3/include/CGAL/IO/read_ply_points.h b/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
index dd780cc6436..fad8715c3fc 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_ply_points.h
@@ -262,8 +262,8 @@ bool read_PLY(std::istream& is,
   NormalMap normal_map = NP_helper::get_normal_map(np);
 
   return read_PLY_with_properties(is, output,
-                                    make_ply_point_reader(point_map),
-                                    make_ply_normal_reader(normal_map));
+                                  make_ply_point_reader(point_map),
+                                  make_ply_normal_reader(normal_map));
 }
 
 /**
diff --git a/Point_set_processing_3/include/CGAL/IO/write_off_points.h b/Point_set_processing_3/include/CGAL/IO/write_off_points.h
index 2fb38456379..a3435090bb8 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_off_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_off_points.h
@@ -46,7 +46,7 @@ bool write_OFF_PSP(std::ostream& os,
   typedef typename NP_helper::Const_point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = NP_helper::has_normal_map(points, np);
+  bool has_normals = NP_helper::has_normal_map();
 
   PointMap point_map = NP_helper::get_const_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/IO/write_ply_points.h b/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
index d151871a541..38b361ff779 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_ply_points.h
@@ -201,7 +201,7 @@ bool write_PLY(std::ostream& os,
   typedef typename NP_helper::Const_point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = NP_helper::has_normal_map(points, np);
+  bool has_normals = NP_helper::has_normal_map();
 
   PointMap point_map = NP_helper::get_const_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h b/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
index b98ebb247df..73610c9545f 100644
--- a/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/write_xyz_points.h
@@ -47,7 +47,7 @@ bool write_XYZ_PSP(std::ostream& os,
   typedef typename NP_helper::Const_point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = NP_helper::has_normal_map(points, np);
+  bool has_normals = NP_helper::has_normal_map();
 
   PointMap point_map = NP_helper::get_const_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h b/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
index 5c1d2d7cf25..86fa5d23b19 100644
--- a/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
+++ b/Point_set_processing_3/include/CGAL/bilateral_smooth_point_set.h
@@ -278,7 +278,7 @@ bilateral_smooth_point_set(
   typedef typename Kernel::Point_3 Point_3;
   typedef typename Kernel::Vector_3 Vector_3;
 
-  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+  CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
   typedef typename Kernel::FT FT;
 
diff --git a/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h b/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
index 7bcb43eaf8f..507418d45b8 100644
--- a/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
+++ b/Point_set_processing_3/include/CGAL/edge_aware_upsample_point_set.h
@@ -367,7 +367,7 @@ edge_aware_upsample_point_set(
   typedef typename NP_helper::Geom_traits Kernel;
 
 
-  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+  CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
   typedef typename Kernel::Point_3 Point;
   typedef typename Kernel::Vector_3 Vector;
diff --git a/Point_set_processing_3/include/CGAL/jet_estimate_normals.h b/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
index 092c479c53d..da74d6e93ee 100644
--- a/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/jet_estimate_normals.h
@@ -196,7 +196,7 @@ jet_estimate_normals(
   typedef typename Kernel::FT FT;
   typedef typename GetSvdTraits<NamedParameters>::type SvdTraits;
 
-  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+  CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
   CGAL_static_assertion_msg(!(boost::is_same<SvdTraits,
                               typename GetSvdTraits<NamedParameters>::NoTraits>::value),
                             "Error: no SVD traits");
diff --git a/Point_set_processing_3/include/CGAL/mst_orient_normals.h b/Point_set_processing_3/include/CGAL/mst_orient_normals.h
index 18be66609e5..909dc37a63d 100644
--- a/Point_set_processing_3/include/CGAL/mst_orient_normals.h
+++ b/Point_set_processing_3/include/CGAL/mst_orient_normals.h
@@ -631,7 +631,7 @@ mst_orient_normals(
     typedef typename NP_helper::Geom_traits Kernel;
     typedef typename Point_set_processing_3::GetIsConstrainedMap<PointRange, NamedParameters>::type ConstrainedMap;
 
-    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+    CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
     PointMap point_map = NP_helper::get_point_map(points, np);
     NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/pca_estimate_normals.h b/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
index 9c4f5cde3e6..8447ae952ff 100644
--- a/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/pca_estimate_normals.h
@@ -168,7 +168,7 @@ pca_estimate_normals(
   typedef typename NP_helper::Geom_traits Kernel;
   typedef typename Kernel::FT FT;
 
-  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+  CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
   PointMap point_map = NP_helper::get_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/scanline_orient_normals.h b/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
index 272ce021158..02f956f2416 100644
--- a/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
+++ b/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
@@ -478,7 +478,7 @@ void scanline_orient_normals (PointRange& points, const NamedParameters& np = pa
     <internal_np::scanline_id_t, NamedParameters, No_map>::type;
   using Fallback_scanline_ID = Boolean_tag<std::is_same<ScanlineIDMap, No_map>::value>;
 
-  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+  CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
   PointMap point_map = NP_helper::get_point_map(points, np);
   NormalMap normal_map = NP_helper::get_normal_map(points, np);
diff --git a/Point_set_processing_3/include/CGAL/structure_point_set.h b/Point_set_processing_3/include/CGAL/structure_point_set.h
index 5930d4b08f0..f0a9fc34c86 100644
--- a/Point_set_processing_3/include/CGAL/structure_point_set.h
+++ b/Point_set_processing_3/include/CGAL/structure_point_set.h
@@ -234,7 +234,7 @@ public:
     typedef typename Point_set_processing_3::GetPlaneMap<PlaneRange, NamedParameters>::type PlaneMap;
     typedef typename Point_set_processing_3::GetPlaneIndexMap<NamedParameters>::type PlaneIndexMap;
 
-    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+    CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
     CGAL_static_assertion_msg((!is_default_parameter<NamedParameters, internal_np::plane_index_t>::value),
                               "Error: no plane index map");
 
diff --git a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
index de0c26d68f6..5b69f3ef0f9 100644
--- a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
@@ -321,7 +321,7 @@ vcm_estimate_normals_internal (PointRange& points,
     typedef typename NP_helper::Geom_traits Kernel;
     typedef typename GetDiagonalizeTraits<NamedParameters, double, 3>::type DiagonalizeTraits;
 
-    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
+    CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
 
     PointMap point_map = NP_helper::get_point_map(points, np);
     NormalMap normal_map = NP_helper::get_normal_map(points, np);