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 9ebac1bcafa3..c4cca891a9e0 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
@@ -16,9 +16,10 @@
 
 #include <CGAL/Isosurfacing_3/internal/Isosurfacing_domain_3.h>
 #include <CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_function.h>
-#include <CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h>
+#include <CGAL/Isosurfacing_3/internal/Implicit_Cartesian_grid_geometry_3.h>
 #include <CGAL/Isosurfacing_3/internal/Grid_topology_3.h>
 #include <CGAL/Isosurfacing_3/Zero_gradient.h>
+#include <CGAL/Bbox_3.h>
 
 namespace CGAL {
 namespace Isosurfacing {
@@ -44,7 +45,7 @@ using Explicit_Cartesian_grid_domain_3 = unspecified_type;
 template <typename Grid,
           typename Gradient = Zero_gradient,
           typename Topology = internal::Grid_topology_3,
-          typename Geometry = internal::Explicit_Cartesian_grid_geometry_3<Grid>,
+          typename Geometry = internal::Implicit_Cartesian_grid_geometry_3<typename Grid::Geom_traits>,
           typename Function = internal::Explicit_Cartesian_grid_function<Grid> >
 using Explicit_Cartesian_grid_domain_3 =
   internal::Isosurfacing_domain_3<typename Grid::Geom_traits,
@@ -96,8 +97,11 @@ create_explicit_Cartesian_grid_domain(const Grid& grid,
   const std::size_t size_j = grid.ydim();
   const std::size_t size_k = grid.zdim();
 
+  const Bbox_3& bbox = grid.bbox();
+  const typename Geometry::Vector_3 offset{bbox.xmin(), bbox.ymin(), bbox.zmin()};
+
   const Topology topo { size_i, size_j, size_k };
-  const Geometry geom { grid };
+  const Geometry geom { offset, grid.spacing() };
   const Function func { grid };
 
   return Domain{ topo, geom, func, grad, grid.geom_traits() };
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
deleted file mode 100644
index bbc090a29461..000000000000
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/Explicit_Cartesian_grid_geometry_3.h
+++ /dev/null
@@ -1,47 +0,0 @@
-// Copyright (c) 2022-2023 INRIA Sophia-Antipolis (France).
-// All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org).
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
-//
-// Author(s)     : Julian Stahl
-
-#ifndef CGAL_ISOSURFACING_3_INTERNAL_EXPLICIT_CARTESIAN_GRID_GEOMETRY_3_H
-#define CGAL_ISOSURFACING_3_INTERNAL_EXPLICIT_CARTESIAN_GRID_GEOMETRY_3_H
-
-#include <CGAL/license/Isosurfacing_3.h>
-
-#include <CGAL/Isosurfacing_3/internal/Grid_topology_3.h>
-
-namespace CGAL {
-namespace Isosurfacing {
-namespace internal {
-
-template <typename Grid>
-class Explicit_Cartesian_grid_geometry_3
-{
-  using Vertex_descriptor = typename Grid_topology_3::Vertex_descriptor;
-
-public:
-  Explicit_Cartesian_grid_geometry_3(const Grid& grid)
-    : m_grid{grid}
-  { }
-
-  // gets the position of vertex `v`
-  decltype(auto) /*Point_3*/ operator()(const Vertex_descriptor& v) const
-  {
-    return m_grid.point(v[0], v[1], v[2]);
-  }
-
-private:
-  const Grid& m_grid;
-};
-
-} // namespace internal
-} // namespace Isosurfacing
-} // namespace CGAL
-
-#endif // CGAL_ISOSURFACING_3_INTERNAL_EXPLICIT_CARTESIAN_GRID_GEOMETRY_3_H