diff --git a/Polygon_mesh_processing/doc/Polygon_mesh_processing/Concepts/PMPSizingField.h b/Polygon_mesh_processing/doc/Polygon_mesh_processing/Concepts/PMPSizingField.h
index 5b90dddfbc9..d672f19bb06 100644
--- a/Polygon_mesh_processing/doc/Polygon_mesh_processing/Concepts/PMPSizingField.h
+++ b/Polygon_mesh_processing/doc/Polygon_mesh_processing/Concepts/PMPSizingField.h
@@ -31,6 +31,9 @@ typedef unspecified_type FT;
 /// @name Functions
 /// @{
 
+/// a function that returns the sizing value at `v`.
+FT at(const vertex_descriptor v) const;
+
 /// a function controlling edge split and edge collapse,
 /// returning the ratio of the current edge length and the local target edge length between
 /// the points of `va` and `vb` in case the current edge is too long, and `std::nullopt` otherwise.
@@ -47,7 +50,8 @@ Point_3 split_placement(const halfedge_descriptor h,
                         const PolygonMesh& pmesh) const;
 
 /// a function that updates the sizing field value at the vertex `v`.
-void update(const vertex_descriptor v, const PolygonMesh& pmesh);
+void update(const vertex_descriptor v,
+            const PolygonMesh& pmesh);
 
 /// @}
 };
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Adaptive_sizing_field.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Adaptive_sizing_field.h
index 91e04160d11..cf46db6d919 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Adaptive_sizing_field.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Adaptive_sizing_field.h
@@ -214,7 +214,7 @@ private:
   }
 
 public:
-  FT get_sizing(const vertex_descriptor v) const
+  FT at(const vertex_descriptor v) const
   {
     CGAL_assertion(get(m_vertex_sizing_map, v));
     return get(m_vertex_sizing_map, v);
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Uniform_sizing_field.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Uniform_sizing_field.h
index d73b318f8c1..00ea4a39dcb 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Uniform_sizing_field.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Uniform_sizing_field.h
@@ -68,7 +68,8 @@ public:
   *        the input mesh.
   */
   Uniform_sizing_field<PolygonMesh, VPMap>(const FT size, const VPMap& vpmap)
-    : m_sq_short( CGAL::square(4./5. * size))
+    : m_size(size)
+    , m_sq_short( CGAL::square(4./5. * size))
     , m_sq_long(  CGAL::square(4./3. * size))
     , m_vpmap(vpmap)
   {}
@@ -100,6 +101,11 @@ private:
   }
 
 public:
+  FT at(const vertex_descriptor /* v */) const
+  {
+    return m_size;
+  }
+
   std::optional<FT> is_too_long(const vertex_descriptor va, const vertex_descriptor vb) const
   {
     const FT sqlen = sqlength(va, vb);
@@ -130,6 +136,7 @@ public:
   {}
 
 private:
+  const FT m_size;
   const FT m_sq_short;
   const FT m_sq_long;
   const VPMap m_vpmap;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Sizing_field_base.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Sizing_field_base.h
index 3835f180358..1f70c251aca 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Sizing_field_base.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Sizing_field_base.h
@@ -60,6 +60,7 @@ public:
   typedef typename K::FT                                        FT;
 
 public:
+  virtual FT at(const vertex_descriptor v) const;
   virtual std::optional<FT> is_too_long(const vertex_descriptor va,
                                         const vertex_descriptor vb) const = 0;
   virtual std::optional<FT> is_too_short(const halfedge_descriptor h,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
index 83fdd5ff37f..6693524324a 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/tangential_relaxation.h
@@ -288,9 +288,9 @@ void tangential_relaxation(const VertexRange& vertices,
 
             const double tri_area = gt_area(get(vpm, v), get(vpm, v1), get(vpm, v2));
             const double face_weight = tri_area
-                                       / (1. / 3. * (sizing.get_sizing(v)
-                                                   + sizing.get_sizing(v1)
-                                                   + sizing.get_sizing(v2)));
+                                       / (1. / 3. * (sizing.at(v)
+                                                   + sizing.at(v1)
+                                                   + sizing.at(v2)));
             weight += face_weight;
 
             const Point_3 centroid = gt_centroid(get(vpm, v), get(vpm, v1), get(vpm, v2));