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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
Gudhi::coxeter_triangulation::Cell_complex
A class that constructs the cell complex from the output provided by the class Gudhi::coxeter_triangu...
Definition Cell_complex.h:38
Gudhi::coxeter_triangulation::Cell_complex::cell_point_map
const Cell_point_map & cell_point_map() const
Returns a map from the vertex cells in the cell complex of type Gudhi::Hasse_cell to their Cartesian ...
Definition Cell_complex.h:315
Gudhi::coxeter_triangulation::Cell_complex::interior_simplex_cell_maps
const Simplex_cell_maps & interior_simplex_cell_maps() const
Returns a vector of maps from the cells of various dimensions in the interior of the cell complex of ...
Definition Cell_complex.h:273
Gudhi::coxeter_triangulation::Cell_complex::boundary_simplex_cell_maps
const Simplex_cell_maps & boundary_simplex_cell_maps() const
Returns a vector of maps from the cells of various dimensions on the boundary of the cell complex of ...
Definition Cell_complex.h:280
Gudhi::coxeter_triangulation::Cell_complex::Hasse_cell
Gudhi::Hasse_diagram::Hasse_diagram_cell< int, double, bool > Hasse_cell
Type of a cell in the cell complex. Always is Gudhi::Hasse_cell from the Hasse diagram module....
Definition Cell_complex.h:49
Gudhi::coxeter_triangulation::build_mesh_from_cell_complex
Mesh_medit build_mesh_from_cell_complex(const Cell_complex &cell_complex, Configuration i_configuration=Configuration(), Configuration b_configuration=Configuration())
Builds a Gudhi::coxeter_triangulation::Mesh_medit from a Gudhi::coxeter_triangulation::Cell_complex.
Definition build_mesh_from_cell_complex.h:122
Gudhi
Gudhi namespace.
Definition SimplicialComplexForAlpha.h:14
Gudhi::coxeter_triangulation::Mesh_medit
Structure to store a mesh that can be output in Medit .mesh file format using the output_meshes_to_me...
Definition Mesh_medit.h:29
Gudhi::coxeter_triangulation::Mesh_medit::vertex_points
Vertex_points vertex_points
Range of vertices of type Eigen::VectorXd to output.
Definition Mesh_medit.h:43