utilities.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2022 - 2023 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.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_cgal_utilities_h
#define dealii_cgal_utilities_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/exceptions.h>
 
#include <deal.II/cgal/additional_data.h>
 
#ifdef DEAL_II_WITH_CGAL
#  include <deal.II/base/quadrature_lib.h>
 
#  include <deal.II/grid/tria.h>
 
#  include <boost/hana.hpp>
 
#  include <CGAL/Cartesian.h>
#  include <CGAL/Complex_2_in_triangulation_3.h>
#  include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#  include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#  include <CGAL/Kernel_traits.h>
#  include <CGAL/Mesh_complex_3_in_triangulation_3.h>
#  include <CGAL/Mesh_criteria_3.h>
#  include <CGAL/Mesh_triangulation_3.h>
// Disable a warnung that we get with gcc-13 about a potential unitialized
// usage of an <anonymous> lambda function in this external CGAL header.
DEAL_II_DISABLE_EXTRA_DIAGNOSTICS
#  include <CGAL/Polygon_mesh_processing/corefinement.h>
DEAL_II_ENABLE_EXTRA_DIAGNOSTICS
#  include <CGAL/Polygon_mesh_processing/measure.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/convex_hull_3.h>
#  include <CGAL/make_mesh_3.h>
#  include <CGAL/make_surface_mesh.h>
#  include <deal.II/cgal/surface_mesh.h>
 
#  include <fstream>
#  include <limits>
#  include <type_traits>
 
 
 
DEAL_II_NAMESPACE_OPEN
namespace CGALWrappers
{
#  ifdef CGAL_CONCURRENT_MESH_3
  using ConcurrencyTag = CGAL::Parallel_tag;
#  else
  using ConcurrencyTag = CGAL::Sequential_tag;
#  endif
 
  enum class BooleanOperation
  {
    compute_corefinement = 1 << 0,
 
    compute_difference = 1 << 1,
 
    compute_intersection = 1 << 2,
 
    compute_union = 1 << 3,
  };
 
 
 
  template <typename C3t3>
  void
  cgal_surface_mesh_to_cgal_triangulation(
    CGAL::Surface_mesh<typename C3t3::Point::Point> &surface_mesh,
    C3t3 &                                           triangulation,
    const AdditionalData<3> &data = AdditionalData<3>{});
 
  template <typename CGALPointType>
  void
  compute_boolean_operation(
    const CGAL::Surface_mesh<CGALPointType> &surface_mesh_1,
    const CGAL::Surface_mesh<CGALPointType> &surface_mesh_2,
    const BooleanOperation &                 boolean_operation,
    CGAL::Surface_mesh<CGALPointType> &      output_surface_mesh);
 
  template <typename CGALTriangulationType>
  ::Quadrature<CGALTriangulationType::Point::Ambient_dimension::value>
  compute_quadrature(const CGALTriangulationType &tria,
                     const unsigned int           degree);
 
  template <int dim0, int dim1, int spacedim>
  ::Quadrature<spacedim>
  compute_quadrature_on_boolean_operation(
    const typename ::Triangulation<dim0, spacedim>::cell_iterator &cell0,
    const typename ::Triangulation<dim1, spacedim>::cell_iterator &cell1,
    const unsigned int                                                   degree,
    const BooleanOperation &       bool_op,
    const Mapping<dim0, spacedim> &mapping0 =
      (ReferenceCells::get_hypercube<dim0>()
         .template get_default_linear_mapping<dim0, spacedim>()),
    const Mapping<dim1, spacedim> &mapping1 =
      (ReferenceCells::get_hypercube<dim1>()
         .template get_default_linear_mapping<dim1, spacedim>()));
 
  template <int dim0, int dim1, int spacedim>
  ::Quadrature<spacedim>
  compute_quadrature_on_intersection(
    const typename ::Triangulation<dim0, spacedim>::cell_iterator &cell0,
    const typename ::Triangulation<dim1, spacedim>::cell_iterator &cell1,
    const unsigned int                                                   degree,
    const Mapping<dim0, spacedim> &mapping0,
    const Mapping<dim1, spacedim> &mapping1);
 
  template <typename CGALPointType>
  void
  remesh_surface(CGAL::Surface_mesh<CGALPointType> &surface_mesh,
                 const AdditionalData<3> &          data = AdditionalData<3>{});
} // namespace CGALWrappers
 
#  ifndef DOXYGEN
// Template implementations
namespace CGALWrappers
{
  template <typename C3t3>
  void
  cgal_surface_mesh_to_cgal_triangulation(
    CGAL::Surface_mesh<typename C3t3::Point::Point> &surface_mesh,
    C3t3 &                                           triangulation,
    const AdditionalData<3> &                        data)
  {
    using CGALPointType = typename C3t3::Point::Point;
    Assert(CGAL::is_closed(surface_mesh),
           ExcMessage("The surface mesh must be closed."));
 
    using K           = typename CGAL::Kernel_traits<CGALPointType>::Kernel;
    using Mesh_domain = CGAL::Polyhedral_mesh_domain_with_features_3<
      K,
      CGAL::Surface_mesh<CGALPointType>>;
    using Tr = typename CGAL::
      Mesh_triangulation_3<Mesh_domain, CGAL::Default, ConcurrencyTag>::type;
    using Mesh_criteria = CGAL::Mesh_criteria_3<Tr>;
 
    CGAL::Polygon_mesh_processing::triangulate_faces(surface_mesh);
    Mesh_domain domain(surface_mesh);
    domain.detect_features();
    Mesh_criteria criteria(CGAL::parameters::facet_size  = data.facet_size,
                           CGAL::parameters::facet_angle = data.facet_angle,
                           CGAL::parameters::facet_distance =
                             data.facet_distance,
                           CGAL::parameters::cell_radius_edge_ratio =
                             data.cell_radius_edge_ratio,
                           CGAL::parameters::cell_size = data.cell_size);
    // Mesh generation
    triangulation = CGAL::make_mesh_3<C3t3>(domain,
                                            criteria,
                                            CGAL::parameters::no_perturb(),
                                            CGAL::parameters::no_exude());
  }
 
 
 
  template <typename CGALPointType>
  void
  compute_boolean_operation(
    const CGAL::Surface_mesh<CGALPointType> &surface_mesh_1,
    const CGAL::Surface_mesh<CGALPointType> &surface_mesh_2,
    const BooleanOperation &                 boolean_operation,
    CGAL::Surface_mesh<CGALPointType> &      output_surface_mesh)
  {
    Assert(output_surface_mesh.is_empty(),
           ExcMessage(
             "output_surface_mesh must be empty upon calling this function"));
    Assert(CGAL::is_closed(surface_mesh_1),
           ExcMessage(
             "The input surface_mesh_1 must be a closed surface mesh."));
    Assert(CGAL::is_closed(surface_mesh_2),
           ExcMessage(
             "The input surface_mesh_2 must be a closed surface mesh."));
    Assert(CGAL::is_triangle_mesh(surface_mesh_1),
           ExcMessage("The first CGAL mesh must be triangulated."));
    Assert(CGAL::is_triangle_mesh(surface_mesh_2),
           ExcMessage("The second CGAL mesh must be triangulated."));
 
    bool res      = false;
    auto surf_1   = surface_mesh_1;
    auto surf_2   = surface_mesh_2;
    namespace PMP = CGAL::Polygon_mesh_processing;
    switch (boolean_operation)
      {
        case BooleanOperation::compute_union:
          res = PMP::corefine_and_compute_union(surf_1,
                                                surf_2,
                                                output_surface_mesh);
          break;
        case BooleanOperation::compute_intersection:
          res = PMP::corefine_and_compute_intersection(surf_1,
                                                       surf_2,
                                                       output_surface_mesh);
          break;
        case BooleanOperation::compute_difference:
          res = PMP::corefine_and_compute_difference(surf_1,
                                                     surf_2,
                                                     output_surface_mesh);
          break;
        case BooleanOperation::compute_corefinement:
          PMP::corefine(surf_1,
                        surf_2); // both surfaces are corefined
          output_surface_mesh = std::move(surf_1);
          res                 = true;
          break;
        default:
          output_surface_mesh.clear();
          break;
      }
    (void)res;
    Assert(res,
           ExcMessage("The boolean operation was not successfully computed."));
  }
 
 
 
  template <typename CGALTriangulationType>
  ::Quadrature<CGALTriangulationType::Point::Ambient_dimension::value>
  compute_quadrature(const CGALTriangulationType &tria,
                     const unsigned int           degree)
  {
    Assert(tria.is_valid(), ExcMessage("The triangulation is not valid."));
    Assert(CGALTriangulationType::Point::Ambient_dimension::value == 3,
           ExcNotImplemented());
    Assert(degree > 0,
           ExcMessage("The degree of the Quadrature formula is not positive."));
 
    constexpr int spacedim =
      CGALTriangulationType::Point::Ambient_dimension::value;
    std::vector<std::array<::Point<spacedim>, spacedim + 1>>
      vec_of_simplices; // tets
 
    std::array<::Point<spacedim>, spacedim + 1> simplex;
    for (const auto &f : tria.finite_cell_handles())
      {
        for (unsigned int i = 0; i < (spacedim + 1); ++i)
          {
            simplex[i] =
              cgal_point_to_dealii_point<spacedim>(f->vertex(i)->point());
          }
 
        vec_of_simplices.push_back(simplex);
      }
 
    return QGaussSimplex<spacedim>(degree).mapped_quadrature(vec_of_simplices);
  }
 
 
 
  template <int dim0, int dim1, int spacedim>
  ::Quadrature<spacedim>
  compute_quadrature_on_boolean_operation(
    const typename ::Triangulation<dim0, spacedim>::cell_iterator &cell0,
    const typename ::Triangulation<dim1, spacedim>::cell_iterator &cell1,
    const unsigned int                                                   degree,
    const BooleanOperation &       bool_op,
    const Mapping<dim0, spacedim> &mapping0,
    const Mapping<dim1, spacedim> &mapping1)
  {
    Assert(dim0 == 3 && dim1 == 3 && spacedim == 3,
           ExcNotImplemented("2d geometries are not yet supported."));
    if (dim1 > dim0)
      {
        return compute_quadrature_on_boolean_operation(
          cell1,
          cell0,
          degree,
          bool_op,
          mapping1,
          mapping0); // This function works for dim1<=dim0, so swap them if this
                     // is not the case.
      }
    if (bool_op == BooleanOperation::compute_intersection)
      {
        return compute_quadrature_on_intersection(
          cell0, cell1, degree, mapping0, mapping1);
      }
    else
      {
        using K         = CGAL::Exact_predicates_inexact_constructions_kernel;
        using CGALPoint = CGAL::Point_3<K>;
        using CGALTriangulation = CGAL::Triangulation_3<K>;
        CGAL::Surface_mesh<CGALPoint> surface_1, surface_2, out_surface;
        dealii_cell_to_cgal_surface_mesh(cell0, mapping0, surface_1);
        dealii_cell_to_cgal_surface_mesh(cell1, mapping1, surface_2);
        // They have to be triangle meshes
        CGAL::Polygon_mesh_processing::triangulate_faces(surface_1);
        CGAL::Polygon_mesh_processing::triangulate_faces(surface_2);
        Assert(CGAL::is_triangle_mesh(surface_1) &&
                 CGAL::is_triangle_mesh(surface_2),
               ExcMessage("The surface must be a triangle mesh."));
        compute_boolean_operation(surface_1, surface_2, bool_op, out_surface);
 
        CGALTriangulation tria;
        tria.insert(out_surface.points().begin(), out_surface.points().end());
        return compute_quadrature(tria, degree);
      }
  }
 
 
 
  template <int dim0, int dim1, int spacedim>
  ::Quadrature<spacedim>
  compute_quadrature_on_intersection(
    const typename ::Triangulation<dim0, spacedim>::cell_iterator &cell0,
    const typename ::Triangulation<dim1, spacedim>::cell_iterator &cell1,
    const unsigned int                                                   degree,
    const Mapping<dim0, spacedim> &mapping0,
    const Mapping<dim1, spacedim> &mapping1)
  {
    Assert(dim0 == 3 && dim1 == 3 && spacedim == 3,
           ExcNotImplemented("2d geometries are not yet supported."));
    using K         = CGAL::Exact_predicates_inexact_constructions_kernel;
    using CGALPoint = CGAL::Point_3<K>;
    using CGALTriangulation = CGAL::Triangulation_3<K>;
 
    CGAL::Surface_mesh<CGALPoint> surface_1, surface_2, out_surface;
    dealii_cell_to_cgal_surface_mesh(cell0, mapping0, surface_1);
    dealii_cell_to_cgal_surface_mesh(cell1, mapping1, surface_2);
    // They have to be triangle meshes
    CGAL::Polygon_mesh_processing::triangulate_faces(surface_1);
    CGAL::Polygon_mesh_processing::triangulate_faces(surface_2);
 
    compute_boolean_operation(surface_1,
                              surface_2,
                              BooleanOperation::compute_intersection,
                              out_surface);
    CGAL::Surface_mesh<CGALPoint> dummy;
    CGALTriangulation             tr;
    CGAL::convex_hull_3(out_surface.points().begin(),
                        out_surface.points().end(),
                        dummy);
    tr.insert(dummy.points().begin(), dummy.points().end());
    return compute_quadrature(tr, degree);
  }
 
 
 
  template <typename CGALPointType>
  void
  remesh_surface(CGAL::Surface_mesh<CGALPointType> &cgal_mesh,
                 const AdditionalData<3> &          data)
  {
    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
    const double default_value_edge_size = std::numeric_limits<double>::max();
    if (data.edge_size > 0 &&
        std::abs(data.edge_size - default_value_edge_size) > 1e-12)
      {
        Mesh_criteria criteria(CGAL::parameters::edge_size   = data.edge_size,
                               CGAL::parameters::facet_size  = data.facet_size,
                               CGAL::parameters::facet_angle = data.facet_angle,
                               CGAL::parameters::facet_distance =
                                 data.facet_distance,
                               CGAL::parameters::cell_radius_edge_ratio =
                                 data.cell_radius_edge_ratio,
                               CGAL::parameters::cell_size = data.cell_size);
        // 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);
      }
    else if (std::abs(data.edge_size - default_value_edge_size) <= 1e-12)
      {
        Mesh_criteria criteria(CGAL::parameters::facet_size  = data.facet_size,
                               CGAL::parameters::facet_angle = data.facet_angle,
                               CGAL::parameters::facet_distance =
                                 data.facet_distance,
                               CGAL::parameters::cell_radius_edge_ratio =
                                 data.cell_radius_edge_ratio,
                               CGAL::parameters::cell_size = data.cell_size);
        // 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);
      }
    else
      {
        Assert(false, ExcInternalError());
      }
  }
 
 
 
  template <int spacedim>
  void
  resort_dealii_vertices_to_cgal_order(const unsigned int            structdim,
                                       std::vector<Point<spacedim>> &vertices)
  {
    if (ReferenceCell::n_vertices_to_type(structdim, vertices.size()) ==
        ReferenceCells::Quadrilateral)
      std::swap(vertices[2], vertices[3]);
  }
 
 
 
  template <int dim, int spacedim>
  std::vector<Point<spacedim>>
  get_vertices_in_cgal_order(
    const typename ::Triangulation<dim, spacedim>::cell_iterator &cell,
    const Mapping<dim, spacedim> &                                      mapping)
  {
    // Elements have to be rectangular or simplices
    const unsigned int n_vertices = cell->n_vertices();
    Assert((n_vertices == ReferenceCells::get_hypercube<dim>().n_vertices()) ||
             (n_vertices == ReferenceCells::get_simplex<dim>().n_vertices()),
           ExcNotImplemented());
 
    std::vector<Point<spacedim>> ordered_vertices(n_vertices);
    std::copy_n(mapping.get_vertices(cell).begin(),
                n_vertices,
                ordered_vertices.begin());
 
    resort_dealii_vertices_to_cgal_order(dim, ordered_vertices);
 
    return ordered_vertices;
  }
 
 
 
  template <int dim, int spacedim>
  std::vector<Point<spacedim>>
  get_vertices_in_cgal_order(
    const typename ::Triangulation<dim, spacedim>::cell_iterator &cell,
    const unsigned int                                                  face_no,
    const Mapping<dim, spacedim> &                                      mapping)
  {
    // Elements have to be rectangular or simplices
    const unsigned int n_vertices = cell->face(face_no)->n_vertices();
    Assert(
      (n_vertices == ReferenceCells::get_hypercube<dim - 1>().n_vertices()) ||
        (n_vertices == ReferenceCells::get_simplex<dim - 1>().n_vertices()),
      ExcNotImplemented());
 
    std::vector<Point<spacedim>> ordered_vertices(n_vertices);
    std::copy_n(mapping.get_vertices(cell, face_no).begin(),
                n_vertices,
                ordered_vertices.begin());
 
    resort_dealii_vertices_to_cgal_order(dim - 1, ordered_vertices);
 
    return ordered_vertices;
  }
 
 
 
} // namespace CGALWrappers
#  endif
 
DEAL_II_NAMESPACE_CLOSE
 
#endif
#endif