Surface_mesh_topology/path_homotopy_double_torus.cpp

#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
#include <CGAL/Linear_cell_complex_constructors.h>
#include <CGAL/Curves_on_surface_topology.h>
#include <CGAL/Path_on_surface.h>
#include <CGAL/draw_face_graph_with_paths.h>

typedef CGAL::Linear_cell_complex_for_combinatorial_map<2,3> LCC_3_cmap;
using namespace CGAL::Surface_mesh_topology;

void create_path_1(Path_on_surface<LCC_3_cmap>& p)
{
  p.push_back_by_index(14); // Its starting dart
  for (int i=0; i<7; ++i)
  { p.extend_positive_turn(2); } // Extend the path
}

void create_path_2(Path_on_surface<LCC_3_cmap>& p)
{ p.push_back_by_index({202, 206, 335, 317, 322, 69, 62, 414}); }

void create_path_3(Path_on_surface<LCC_3_cmap>& p)
{
  p.push_back_by_index(470); // Its starting dart
  for (int i=0; i<13; ++i)
  { p.extend_positive_turn(2); } // Extend the path
}

int main(int argc, char** argv)
{
  bool draw=(argc>1?std::string(argv[1])=="-draw":false);
  LCC_3_cmap lcc;
  if (!CGAL::load_off(lcc, "data/double-torus.off"))
  {
    std::cout<<"ERROR reading file data/double-torus.off"<<std::endl;
    exit(EXIT_FAILURE);
  }

  Curves_on_surface_topology<LCC_3_cmap> cst(lcc);
  Path_on_surface<LCC_3_cmap> p1(lcc), p2(lcc), p3(lcc);
  create_path_1(p1);
  create_path_2(p2);
  create_path_3(p3);

  bool res1=cst.is_contractible(p1);
  std::cout<<"Path p1 (pink) "<<(res1?"IS":"IS NOT")
           <<" contractible."<<std::endl;

  bool res2=cst.are_freely_homotopic(p1, p2);
  std::cout<<"Path p1 (pink) "<<(res2?"IS":"IS NOT")
           <<" homotopic with path p2 (green)."<<std::endl;

  bool res3=cst.are_freely_homotopic(p1, p3);
  std::cout<<"Path p1 (pink) "<<(res3?"IS":"IS NOT")
           <<" homotopic with path p3 (orange)."<<std::endl;

  if (draw)
  { CGAL::draw(lcc, {p1, p2, p3}); }

  return EXIT_SUCCESS;
}