Add remesh_surface utility

include/deal.II/cgal/utilities.h

@@ -28,14 +28,19 @@
 #  include <CGAL/Mesh_criteria_3.h>
 #  include <CGAL/Mesh_triangulation_3.h>
 #  include <CGAL/Polygon_mesh_processing/corefinement.h>
+#  include <CGAL/Polygon_mesh_processing/remesh.h>
 #  include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
 #  include <CGAL/Polyhedral_mesh_domain_with_features_3.h>
 #  include <CGAL/Simple_cartesian.h>
 #  include <CGAL/Surface_mesh.h>
 #  include <CGAL/Triangulation_3.h>
+#  include <CGAL/boost/graph/copy_face_graph.h>
+#  include <CGAL/boost/graph/selection.h>
 #  include <CGAL/make_mesh_3.h>
 #  include <CGAL/make_surface_mesh.h>
+//#  include <CGAL/tetrahedral_remeshing.h> REQUIRES CGAL_VERSION>=5.1.5
 
+#  include <fstream>
 #  include <type_traits>
 
 
@@ -198,6 +203,56 @@ namespace CGALWrappers
     const CGAL::Surface_mesh<CGALPointType> &surface_mesh_2,
     const BooleanOperation &                 boolean_operation,
     CGAL::Surface_mesh<CGALPointType> &      output_surface_mesh);
+
+  /**
+   * Remesh a CGAL::Surface_mesh.
+   *
+   * The optional variable arguments @p cgal_args can be used to pass additional
+   * arguments to the CGAL::Mesh_criteria_3 class (see
+   * https://doc.cgal.org/latest/Mesh_3/index.html) for more information.
+   *
+   * The arguments allow fine control on the size, quality, and distribution of
+   * the cells of the final triangulation. CGAL uses named parameters for these
+   * arguments, i.e., they must be specified with the syntax
+   * `CGAL::parameters::parameter_name=parameter_value`. Accepted parameters
+   * are:
+   *
+   * - CGAL::parameters::facet_angle,
+   * - CGAL::parameters::facet_size,
+   * - CGAL::parameters::facet_distance,
+   * - CGAL::parameters::cell_radius_edge_ratio,
+   * - CGAL::parameters::cell_size;
+   *
+   * If the domain has 1-dimensional exposed features, the criteria includes a
+   * sizing field to guide the sampling of 1-dimensional features with
+   * protecting balls centers.
+   * - CGAL::parameters::edge_size.
+   *
+   * This utility should be exploited to improve the quality of a mesh coming
+   * from boolean operations. As an example, consider two CGAL::Surface_mesh
+   * objects describing two hyper_spheres that intersect non-trivially. After
+   * computing their corefinement and union with compute_boolean_operation(),
+   * the resulting mesh is the following:
+   *
+   * @image html boolean_union_hyper_spheres.png
+   *
+   * Clearly, elements (triangles) like the ones arising along the intersection
+   * of the two spheres should be avoided as they're quite degenerate and would
+   * decrease the accuracy of the results. A call to the present function will
+   * try to remesh the surface, according to the given named parameters, to
+   * improve its quality. In the present case, the result is the following:
+   *
+   * @image html boolean_union_hyper_spheres_remeshed.png
+   *
+   * @param surface_mesh The input CGAL::Surface_mesh.
+   * @param out_surface_mesh The output CGAL::Surface_mesh.
+   * @param cgal_args Optional CGAL named parameters.
+   */
+  template <typename CGALPointType, typename... Args>
+  void
+  remesh_surface(const CGAL::Surface_mesh<CGALPointType> &surface_mesh,
+                 CGAL::Surface_mesh<CGALPointType> &      out_surface_mesh,
+                 Args... cgal_args);
 } // namespace CGALWrappers
 
 #  ifndef DOXYGEN
@@ -330,6 +385,48 @@ namespace CGALWrappers
     Assert(res,
            ExcMessage("The boolean operation was not successfully computed."));
   }
+
+
+
+  template <typename CGALPointType, typename... Args>
+  void
+  remesh_surface(CGAL::Surface_mesh<CGALPointType> &cgal_mesh,
+                 Args... cgal_args)
+  {
+    using K           = CGAL::Exact_predicates_inexact_constructions_kernel;
+    using Mesh_domain = CGAL::Polyhedral_mesh_domain_with_features_3<K>;
+    // Polyhedron type
+    using Polyhedron = CGAL::Mesh_polyhedron_3<K>::type;
+    // Triangulation
+    using Tr = CGAL::Mesh_triangulation_3<Mesh_domain>::type;
+    using C3t3 =
+      CGAL::Mesh_complex_3_in_triangulation_3<Tr,
+                                              Mesh_domain::Corner_index,
+                                              Mesh_domain::Curve_index>;
+    // Criteria
+    using Mesh_criteria = CGAL::Mesh_criteria_3<Tr>;
+
+    Polyhedron poly;
+    CGAL::copy_face_graph(cgal_mesh, poly);
+    // Create a vector with only one element: the pointer to the
+    // polyhedron.
+    std::vector<Polyhedron *> poly_ptrs_vector(1, &poly);
+    // Create a polyhedral domain, with only one polyhedron,
+    // and no "bounding polyhedron", so the volumetric part of the
+    // domain will be empty.
+    Mesh_domain domain(poly_ptrs_vector.begin(), poly_ptrs_vector.end());
+    // Get sharp features
+    domain.detect_features(); // includes detection of borders
+    // Mesh criteria
+    Mesh_criteria criteria(cgal_args...);
+    // Mesh generation
+    C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain,
+                                        criteria,
+                                        CGAL::parameters::no_perturb(),
+                                        CGAL::parameters::no_exude());
+    cgal_mesh.clear();
+    CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, cgal_mesh);
+  }
 } // namespace CGALWrappers
 #  endif
 

tests/cgal/cgal_remesh_surface.cc

@@ -0,0 +1,90 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2022 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+// Remesh the union of two deal.II hyper_spheres in order to avoid bad
+// triangles.
+
+#include <deal.II/base/config.h>
+
+#include <deal.II/base/point.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/cgal/surface_mesh.h>
+#include <deal.II/cgal/triangulation.h>
+#include <deal.II/cgal/utilities.h>
+#include <string.h>
+
+#include "../tests.h"
+
+using namespace CGALWrappers;
+using K         = CGAL::Exact_predicates_inexact_constructions_kernel;
+using CGALPoint = CGAL::Point_3<K>;
+using CGALMesh  = CGAL::Surface_mesh<CGALPoint>;
+
+template <int dim, int spacedim>
+void
+test()
+{
+  deallog << "dim= " << dim << ",\t spacedim= " << spacedim << std::endl;
+
+  Triangulation<spacedim> tria0, tria1;
+  Triangulation<2, 3>     tria_out;
+  GridOut                 go;
+  CGALMesh                surface_mesh0, surface_mesh1, out_mesh;
+
+  GridGenerator::hyper_ball(tria0, {0., 0., 0.}, 0.4);
+  GridGenerator::hyper_ball(tria1, {0.3, 0.3, 0.3}, 0.4);
+  tria0.refine_global(3);
+  tria1.refine_global(3);
+
+  // Move to CGAL surfaces
+  dealii_tria_to_cgal_surface_mesh(tria0, surface_mesh0);
+  dealii_tria_to_cgal_surface_mesh(tria1, surface_mesh1);
+
+  // close the surfaces
+  CGAL::Polygon_mesh_processing::stitch_borders(surface_mesh0);
+  CGAL::Polygon_mesh_processing::stitch_borders(surface_mesh1);
+
+  CGAL::Polygon_mesh_processing::triangulate_faces(surface_mesh0);
+  CGAL::Polygon_mesh_processing::triangulate_faces(surface_mesh1);
+
+  compute_boolean_operation(surface_mesh0,
+                            surface_mesh1,
+                            BooleanOperation::compute_union,
+                            out_mesh);
+
+  remesh_surface<CGALPoint>(out_mesh,
+                            CGAL::parameters::edge_size      = 0.02,
+                            CGAL::parameters::facet_angle    = 25,
+                            CGAL::parameters::facet_size     = 0.05,
+                            CGAL::parameters::facet_distance = 0.05);
+
+  //  Now back to deal.II
+  cgal_surface_mesh_to_dealii_triangulation(out_mesh, tria_out);
+  std::ofstream out_name_spheres("remeshed_union_spheres.vtk");
+  go.write_vtk(tria_out, out_name_spheres);
+  deallog << "OK" << std::endl;
+}
+
+int
+main()
+{
+  initlog();
+  test<3, 3>();
+}

tests/cgal/cgal_remesh_surface.output

@@ -0,0 +1,3 @@
+
+DEAL::dim= 3,	 spacedim= 3
+DEAL::OK

tests/cgal/cgal_surface_mesh_05.cc

@@ -70,10 +70,10 @@ test()
                             out_mesh);
   // Now back to deal.II
   cgal_surface_mesh_to_dealii_triangulation(out_mesh, tria_out);
-  std::ofstream out_name_spheres("boolean_triangulation_spheres.vtk");
+  std::ofstream out_name_spheres("boolean_intersection_hyper_spheres.vtk");
   go.write_vtk(tria_out, out_name_spheres);
   deallog << "OK" << std::endl;
-  remove("tria_out.vtk");
+  remove("boolean_intersection_hyper_spheres.vtk");
 
   // Clear everything
   tria0.clear();
@@ -106,10 +106,10 @@ test()
                             out_mesh);
   // Now back to deal.II
   cgal_surface_mesh_to_dealii_triangulation(out_mesh, tria_out);
-  std::ofstream out_name_cubes("boolean_triangulation_cubes.vtk");
+  std::ofstream out_name_cubes("boolean_intersection_cubes.vtk");
   go.write_vtk(tria_out, out_name_cubes);
-  remove("tria_out.vtk");
   deallog << "OK" << std::endl;
+  remove("boolean_intersection_cubes.vtk");
 }
 
 int