diff --git a/BGL/include/CGAL/boost/graph/named_params_helper.h b/BGL/include/CGAL/boost/graph/named_params_helper.h
index 303ab8c9ba1..b70872a7334 100644
--- a/BGL/include/CGAL/boost/graph/named_params_helper.h
+++ b/BGL/include/CGAL/boost/graph/named_params_helper.h
@@ -335,10 +335,10 @@ 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()
+  static constexpr bool has_normal_map(const PointRange&, const NamedParameters&)
   {
-    return !std::is_same< typename internal_np::Get_param<typename NamedParameters::base, internal_np::normal_t>::type,
-                            internal_np::Param_not_found> ::value;
+    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 304cf589d5f..c48e0ad463c 100644
--- a/Point_set_3/include/CGAL/Point_set_3.h
+++ b/Point_set_3/include/CGAL/Point_set_3.h
@@ -465,8 +465,9 @@ public:
     \note Properties of the added point other than its normal vector
     are initialized to their default value.
 
-    \note A normal property must have been added to the point set
-    before using this method.
+    \note If not already added, a normal property is automatically
+    added to the point set when using this method. The default value
+    for normal vectors is `CGAL::NULL_VECTOR`.
 
     \note If a reallocation happens, all iterators, pointers and
     references related to the container are invalidated.  Otherwise,
@@ -479,8 +480,7 @@ public:
   iterator insert (const Point& p, const Vector& n)
   {
     iterator out = insert (p);
-    CGAL_assertion(has_normal_map());
-    m_normals[size()-1] = n;
+    normal_map()[size()-1] = n;
     return out;
   }
 
@@ -550,17 +550,17 @@ public:
   /*!
     \brief returns a reference to the normal corresponding to `index`.
 
-    \note The normal property must have been added to the point set
-    before calling this method (see `add_normal_map()`).
+    \note If not already added, a normal property is automatically
+    added to the point set (see `add_normal_map()`).
   */
-  Vector& normal (const Index& index) { return m_normals[index]; }
+  Vector& normal (const Index& index) { return normal_map()[index]; }
   /*!
     \brief returns a constant reference to the normal corresponding to `index`.
 
-    \note The normal property must have been added to the point set
-    before calling this method (see `add_normal_map()`).
+    \note If not already added, a normal property is automatically
+    added to the point set (see `add_normal_map()`).
   */
-  const Vector& normal (const Index& index) const { return m_normals[index]; }
+  const Vector& normal (const Index& index) const { return normal_map()[index]; }
 
   /// @}
 
@@ -869,11 +869,14 @@ public:
   /*!
     \brief returns the property map of the normal property.
 
-    \note The normal property must have been added to the point set
-    before calling this method (see `add_normal_map()`).
+    \note If the normal property has not been added yet to the point set
+    before calling this method, the property map is automatically added
+    with `add_normal_map()`.
   */
   Vector_map normal_map ()
   {
+    if (!m_normals)
+      add_normal_map();
     return m_normals;
   }
   /*!
@@ -982,7 +985,7 @@ public:
   inline parameters() const
   {
     return CGAL::parameters::point_map (m_points).
-      normal_map (m_normals).
+      normal_map (normal_map()).
       geom_traits (typename Kernel_traits<Point>::Kernel());
   }
 
@@ -1036,7 +1039,7 @@ public:
   */
   Vector_range normals () const
   {
-    return this->range<Vector> (m_normals);
+    return this->range<Vector> (normal_map());
   }
 
   /// @}
@@ -1354,11 +1357,18 @@ 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()
+  static bool has_normal_map(const Point_set_3<Point, Vector>& ps, const NamedParameters&)
   {
-    return true;
+    if (ps.has_normal_map())
+      return true;
+    using CGAL::parameters::is_default_parameter;
+    return !(is_default_parameter<NamedParameters, internal_np::normal_t>::value);
   }
 
+  static constexpr bool has_normal_map(Point_set_3<Point, Vector>&, const NamedParameters&)
+  {
+    return true; // either available in named parameters, and always available in Point_set_3 otherwise
+  }
 };
 /// \endcond
 
diff --git a/Point_set_processing_3/include/CGAL/IO/read_off_points.h b/Point_set_processing_3/include/CGAL/IO/read_off_points.h
index e002a834c5f..660601cb985 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_off_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_off_points.h
@@ -97,8 +97,6 @@ bool read_OFF(std::istream& is,
   typedef typename NP_helper::Geom_traits Kernel;
   typedef typename Kernel::FT FT;
 
-  bool has_normals = NP_helper::has_normal_map();
-
   PointMap point_map = NP_helper::get_point_map(np);
   NormalMap normal_map = NP_helper::get_normal_map(np);
 
@@ -182,8 +180,7 @@ bool read_OFF(std::istream& is,
 
         Enriched_point pwn;
         put(point_map,  pwn, point);  // point_map[&pwn] = point
-        if (has_normals)
-          put(normal_map, pwn, normal); // normal_map[&pwn] = normal
+        put(normal_map, pwn, normal); // normal_map[&pwn] = normal
 
         *output++ = pwn;
         ++pointsRead;
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 282ad59d4a3..93cf9c91356 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
@@ -257,17 +257,12 @@ bool read_PLY(std::istream& is,
   typedef typename NP_helper::Point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  bool has_normals = NP_helper::has_normal_map();
-
   PointMap point_map = NP_helper::get_point_map(np);
   NormalMap normal_map = NP_helper::get_normal_map(np);
 
-  if(has_normals)
-    return read_PLY_with_properties(is, output,
-                                    make_ply_point_reader(point_map),
-                                    make_ply_normal_reader(normal_map));
-  // else
-  return read_PLY_with_properties(is, output, make_ply_point_reader(point_map));
+  return read_PLY_with_properties(is, output,
+                                  make_ply_point_reader(point_map),
+                                  make_ply_normal_reader(normal_map));
 }
 
 /**
diff --git a/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h b/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
index caf7e062a5e..b930b167d09 100644
--- a/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
+++ b/Point_set_processing_3/include/CGAL/IO/read_xyz_points.h
@@ -89,8 +89,6 @@ bool read_XYZ(std::istream& is,
   typedef typename NP_helper::Normal_map NormalMap;
   typedef typename NP_helper::Geom_traits Kernel;
 
-  bool has_normals = NP_helper::has_normal_map();
-
   PointMap point_map = NP_helper::get_point_map(np);
   NormalMap normal_map = NP_helper::get_normal_map(np);
 
@@ -155,8 +153,7 @@ bool read_XYZ(std::istream& is,
         Enriched_point pwn;
         put(point_map,  pwn, point);  // point_map[pwn] = point
 
-        if (has_normals)
-          put(normal_map, pwn, normal); // normal_map[pwn] = normal
+        put(normal_map, pwn, normal); // normal_map[pwn] = normal
 
         *output++ = pwn;
         continue;
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 0be0e4183a3..d5411b67fd9 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
@@ -45,7 +45,7 @@ bool write_OFF_PSP(std::ostream& os,
   typedef typename NP_helper::Const_point_map PointMap;
   typedef typename NP_helper::Normal_map NormalMap;
 
-  const bool has_normals = !(is_default_parameter<CGAL_NP_CLASS, internal_np::normal_t>::value);
+  const bool has_normals = NP_helper::has_normal_map(points, np);
 
   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 6dca998ae72..525bc159023 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();
+  const bool has_normals = NP_helper::has_normal_map(points, np);
 
   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 2f2cc0ae701..43875b1a5d8 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
@@ -46,7 +46,7 @@ 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();
+  const bool has_normals = NP_helper::has_normal_map(points, np);
 
   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 396d9cdb0e0..6588d5f32f2 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 bf4b589d788..c74414b6cb2 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 30a7f34d48c..d808a6ee46f 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
   CGAL_static_assertion_msg(!(std::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 2a284b2e859..aa576df9f80 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 4d5e04b9491..897ade8967c 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 62c0ea1f76d..2623dbc112c 100644
--- a/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
+++ b/Point_set_processing_3/include/CGAL/scanline_orient_normals.h
@@ -479,7 +479,7 @@ 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+  CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 f2d9bd447c3..b421f811b4b 100644
--- a/Point_set_processing_3/include/CGAL/structure_point_set.h
+++ b/Point_set_processing_3/include/CGAL/structure_point_set.h
@@ -233,7 +233,7 @@ public:
     typedef typename Point_set_processing_3::GetPlaneMap<PlaneRange, NamedParameters>::type PlaneMap;
     typedef typename Point_set_processing_3::GetPlaneIndexMap<NamedParameters>::type PlaneIndexMap;
 
-    CGAL_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "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 bf7a7f5225c..b85d68cc9e9 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_static_assertion_msg(NP_helper::has_normal_map(), "Error: no normal map");
+    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");
 
     PointMap point_map = NP_helper::get_point_map(points, np);
     NormalMap normal_map = NP_helper::get_normal_map(points, np);