build_mesh_from_cell_complex.h

/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
 *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
 *    Author(s):       Siargey Kachanovich
 *
 *    Copyright (C) 2019 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef IO_BUILD_MESH_FROM_CELL_COMPLEX_H_
#define IO_BUILD_MESH_FROM_CELL_COMPLEX_H_
 
#include <gudhi/IO/output_debug_traces_to_html.h>  // for DEBUG_TRACES
#include <gudhi/IO/Mesh_medit.h>
 
#include <Eigen/Dense>
 
#include <cstdlib>  // for std::size_t
#include <map>
#include <set>
#include <string>
#include <utility>    // for std::make_pair
#include <algorithm>  // for std::min
 
namespace Gudhi {
 
namespace coxeter_triangulation {
 
struct Configuration {
  Configuration(bool t_edges, bool t_triangles, bool t_tetrahedra, std::size_t r_edges, std::size_t r_triangles,
                std::size_t r_tetrahedra)
      : toggle_edges(t_edges),
        toggle_triangles(t_triangles),
        toggle_tetrahedra(t_tetrahedra),
        ref_edges(r_edges),
        ref_triangles(r_triangles),
        ref_tetrahedra(r_tetrahedra) {}
 
  Configuration() {}
 
  bool toggle_edges = true, toggle_triangles = true, toggle_tetrahedra = true;
  std::size_t ref_edges = 1, ref_triangles = 1, ref_tetrahedra = 1;
};
 
template <class Hasse_cell, class Simplex_cell_map>
void populate_mesh(Mesh_medit& output, Simplex_cell_map& sc_map, Configuration configuration, std::size_t amb_d,
                   std::map<Hasse_cell*, std::size_t> vi_map) {
  using Mesh_element_vertices = Mesh_medit::Mesh_elements::value_type::first_type;
  std::map<Hasse_cell*, std::size_t> ci_map;
  std::size_t index = vi_map.size() + 1;  // current size of output.vertex_points
  if (sc_map.size() >= 3)
    for (const auto& sc_pair : sc_map[2]) {
      Eigen::VectorXd barycenter = Eigen::VectorXd::Zero(amb_d);
      std::set<std::size_t> vertex_indices;
      Hasse_cell* cell = sc_pair.second;
      for (const auto& ei_pair : cell->get_boundary())
        for (const auto& vi_pair : ei_pair.first->get_boundary()) vertex_indices.emplace(vi_map[vi_pair.first]);
      for (const std::size_t& v : vertex_indices) barycenter += output.vertex_points[v - 1];
      ci_map.emplace(cell, index++);
      output.vertex_points.emplace_back((1. / vertex_indices.size()) * barycenter);
#ifdef DEBUG_TRACES
      std::string vlist = " (" + std::to_string(index - 1) + ")";
      for (const std::size_t& v : vertex_indices) vlist += " " + std::to_string(v);
      cell_vlist_map.emplace(to_string(cell), vlist);
#endif
    }
 
  if (configuration.toggle_edges && sc_map.size() >= 2)
    for (const auto& sc_pair : sc_map[1]) {
      Hasse_cell* edge_cell = sc_pair.second;
      Mesh_element_vertices edge;
      for (const auto& vi_pair : edge_cell->get_boundary()) edge.push_back(vi_map[vi_pair.first]);
      output.edges.emplace_back(edge, configuration.ref_edges);
#ifdef DEBUG_TRACES
      std::string vlist;
      for (const std::size_t& v : edge) vlist += " " + std::to_string(v);
      cell_vlist_map.emplace(to_string(edge_cell), vlist);
#endif
    }
 
  if (configuration.toggle_triangles && sc_map.size() >= 3)
    for (const auto& sc_pair : sc_map[2]) {
      for (const auto& ei_pair : sc_pair.second->get_boundary()) {
        Mesh_element_vertices triangle(1, ci_map[sc_pair.second]);
        for (const auto& vi_pair : ei_pair.first->get_boundary()) triangle.push_back(vi_map[vi_pair.first]);
        output.triangles.emplace_back(triangle, configuration.ref_triangles);
      }
    }
 
  if (configuration.toggle_tetrahedra && sc_map.size() >= 4)
    for (const auto& sc_pair : sc_map[3]) {
      Eigen::VectorXd barycenter = Eigen::VectorXd::Zero(amb_d);
      std::set<std::size_t> vertex_indices;
      Hasse_cell* cell = sc_pair.second;
      for (const auto& ci_pair : cell->get_boundary())
        for (const auto& ei_pair : ci_pair.first->get_boundary())
          for (const auto& vi_pair : ei_pair.first->get_boundary()) vertex_indices.emplace(vi_map[vi_pair.first]);
      for (const std::size_t& v : vertex_indices) barycenter += output.vertex_points[v - 1];
      output.vertex_points.emplace_back((1. / vertex_indices.size()) * barycenter);
#ifdef DEBUG_TRACES
      std::string vlist = " (" + std::to_string(index) + ")";
      for (const std::size_t& v : vertex_indices) vlist += " " + std::to_string(v);
      cell_vlist_map.emplace(to_string(cell), vlist);
#endif
 
      for (const auto& ci_pair : cell->get_boundary())
        for (const auto& ei_pair : ci_pair.first->get_boundary()) {
          Mesh_element_vertices tetrahedron = {index, ci_map[sc_pair.second]};
          for (const auto& vi_pair : ei_pair.first->get_boundary()) tetrahedron.push_back(vi_map[vi_pair.first]);
          output.tetrahedra.emplace_back(tetrahedron, configuration.ref_tetrahedra);
        }
      index++;
    }
}
 
template <class Cell_complex>
Mesh_medit build_mesh_from_cell_complex(const Cell_complex& cell_complex,
                                        Configuration i_configuration = Configuration(),
                                        Configuration b_configuration = Configuration()) {
  using Hasse_cell = typename Cell_complex::Hasse_cell;
  Mesh_medit output;
  std::map<Hasse_cell*, std::size_t> vi_map;  // one for vertices, other for 2d-cells
  std::size_t index = 1;                      // current size of output.vertex_points
 
  if (cell_complex.cell_point_map().empty()) return output;
  std::size_t amb_d = std::min((int)cell_complex.cell_point_map().begin()->second.size(), 3);
 
  for (const auto& cp_pair : cell_complex.cell_point_map()) {
#ifdef DEBUG_TRACES
    std::string vlist;
    vlist += " " + std::to_string(index);
    cell_vlist_map.emplace(to_string(cp_pair.first), vlist);
#endif
    vi_map.emplace(cp_pair.first, index++);
    output.vertex_points.push_back(cp_pair.second);
    output.vertex_points.back().conservativeResize(amb_d);
  }
 
  populate_mesh(output, cell_complex.interior_simplex_cell_maps(), i_configuration, amb_d, vi_map);
#ifdef DEBUG_TRACES
  for (const auto& sc_map : cell_complex.interior_simplex_cell_maps())
    for (const auto& sc_pair : sc_map) {
      std::string simplex = "I" + to_string(sc_pair.first);
      std::string cell = to_string(sc_pair.second);
      std::string vlist = cell_vlist_map.at(cell).substr(1);
      simplex_vlist_map.emplace(simplex, vlist);
    }
#endif
  populate_mesh(output, cell_complex.boundary_simplex_cell_maps(), b_configuration, amb_d, vi_map);
#ifdef DEBUG_TRACES
  for (const auto& sc_map : cell_complex.boundary_simplex_cell_maps())
    for (const auto& sc_pair : sc_map) {
      std::string simplex = "B" + to_string(sc_pair.first);
      std::string cell = to_string(sc_pair.second);
      std::string vlist = cell_vlist_map.at(cell).substr(1);
      simplex_vlist_map.emplace(simplex, vlist);
    }
#endif
  return output;
}
 
}  // namespace coxeter_triangulation
 
}  // namespace Gudhi
 
#endif