diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Cartesian_grid_3.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Cartesian_grid_3.h
index f3289d076d7..539310e1929 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Cartesian_grid_3.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Cartesian_grid_3.h
@@ -43,8 +43,6 @@ public:
   using Point_3 = typename Geom_traits::Point_3;
   using Vector_3 = typename Geom_traits::Vector_3;
 
-  using Vertex_descriptor = Isosurfacing::internal::Grid_topology_3::Vertex_descriptor;
-
 private:
   Bbox_3 m_bbox;
   Vector_3 m_spacing;
@@ -187,11 +185,6 @@ public:
               m_bbox.zmin() + z * x_coord(m_spacing));
   }
 
-  const Point_3& point(const Vertex_descriptor& v) const
-  {
-    return point(v[0], v[1], v[2]);
-  }
-
   /**
    * \brief gets the scalar value stored at the grid vertex described by a set of indices.
    *
@@ -208,11 +201,6 @@ public:
     return m_values[linear_index(x, y, z)];
   }
 
-  FT value(const Vertex_descriptor& v) const
-  {
-    return value(v[0], v[1], v[2]);
-  }
-
   /**
    * \brief gets the scalar value stored at the grid vertex described by a set of indices.
    *
@@ -231,11 +219,6 @@ public:
     return m_values[linear_index(x, y, z)];
   }
 
-  FT& value(const Vertex_descriptor& v)
-  {
-    return value(v[0], v[1], v[2]);
-  }
-
   /**
    * \brief gets the gradient stored at the grid vertex described by a set of indices.
    *
@@ -250,11 +233,6 @@ public:
     return m_gradients[linear_index(x, y, z)];
   }
 
-  const Vector_3& gradient(const Vertex_descriptor& v) const
-  {
-    return gradient(v[0], v[1], v[2]);
-  }
-
   /**
    * \brief gets the gradient stored at the grid vertex described by a set of indices.
    *
@@ -273,11 +251,6 @@ public:
     return m_gradients[linear_index(x, y, z)];
   }
 
-  Vector_3& gradient(const Vertex_descriptor& v)
-  {
-    return gradient(v[0], v[1], v[2]);
-  }
-
 private:
   std::size_t linear_index(const std::size_t x,
                            const std::size_t y,
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_domain_3.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_domain_3.h
index 7ef49301a94..5a39f3e3a05 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_domain_3.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_domain_3.h
@@ -34,7 +34,7 @@ namespace Isosurfacing {
  * \tparam Gradient the type of the gradient functor. It must be a model of `CopyConstructible` and implement
  *                  `GeomTraits::Vector_3 operator()(const GeomTraits::Point_3& point) const`.
  */
-#ifdef DOXYGEN_RUNNING // Allow more than a CGAL::Cartesian_grid_3
+#ifdef DOXYGEN_RUNNING // Allow more than a Cartesian_grid_3
 template <template <typename GeomTraits> class Cartesian_grid_3,
           typename Gradient = Zero_gradient>
 class Explicit_Cartesian_grid_domain_3;
@@ -69,7 +69,7 @@ using Explicit_Cartesian_grid_domain_3 =
  *
  * \return a new `Explicit_Cartesian_grid_domain_3`
  */
-#ifdef DOXYGEN_RUNNING // Allow more than CGAL::Cartesian_grid_3
+#ifdef DOXYGEN_RUNNING // Allow more than Cartesian_grid_3
 template <typename GeomTraits,
           typename Gradient = Zero_gradient>
 Explicit_Cartesian_grid_domain_3<Grid, Gradient>
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_gradient_3.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_gradient_3.h
index 87effc4ee89..ea59ea34c96 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_gradient_3.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/Explicit_Cartesian_grid_gradient_3.h
@@ -26,10 +26,15 @@ namespace Isosurfacing {
  *
  * \details The gradient at any point is calculated using trilinear interpolation.
  *
- * \tparam Grid must be a model of `CartesianGrid_3`.
+ * \tparam GeomTraits must be a model of `IsosurfacingTraits_3`.
  */
+#ifdef DOXYGEN_RUNNING // Allow more than just Cartesian_grid_3
+template <template <typename GeomTraits> class Cartesian_grid_3>
+class Explicit_Cartesian_grid_gradient_3
+#else
 template <typename Grid>
 class Explicit_Cartesian_grid_gradient_3
+#endif
 {
 public:
   using Geom_traits = typename Grid::Geom_traits;
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_function.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_function.h
index 2d6eb1ec345..072565d3593 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_function.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_function.h
@@ -38,7 +38,7 @@ public:
   // gets the value at vertex `v`
   FT operator()(const Vertex_descriptor& v) const
   {
-    return grid.value(v);
+    return grid.value(v[0], v[1], v[2]);
   }
 
 private:
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h
index c615e92408e..bbc090a2946 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h
@@ -33,7 +33,7 @@ public:
   // gets the position of vertex `v`
   decltype(auto) /*Point_3*/ operator()(const Vertex_descriptor& v) const
   {
-    return m_grid.point(v);
+    return m_grid.point(v[0], v[1], v[2]);
   }
 
 private: