cech_complex_example_from_points.cpp

Bitmap_cubical_complex

#include <gudhi/Cech_complex.h>
#include <gudhi/Simplex_tree.h>
 
#include <CGAL/Epeck_d.h>  // For EXACT or SAFE version
 
#include <iostream>
#include <string>
#include <vector>
 
int main() {
  // Type definitions
  using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
  using Filtration_value = Simplex_tree::Filtration_value;
  using Kernel = CGAL::Epeck_d<CGAL::Dimension_tag<2>>;
  using Point = typename Kernel::Point_d;
  using Point_cloud = std::vector<Point>;
  using Cech_complex = Gudhi::cech_complex::Cech_complex<Kernel, Simplex_tree>;
 
  Point_cloud points;
  points.emplace_back(1., 0.);                    // 0
  points.emplace_back(0., 1.);                    // 1
  points.emplace_back(2., 1.);                    // 2
  points.emplace_back(3., 2.);                    // 3
  points.emplace_back(0., 3.);                    // 4
  points.emplace_back(3. + std::sqrt(3.), 3.);    // 5
  points.emplace_back(1., 4.);                    // 6
  points.emplace_back(3., 4.);                    // 7
  points.emplace_back(2., 4. + std::sqrt(3.));    // 8
  points.emplace_back(0., 4.);                    // 9
  points.emplace_back(-0.5, 2.);                  // 10
 
  // ----------------------------------------------------------------------------
  // Init of a Cech complex from points
  // ----------------------------------------------------------------------------
  Filtration_value max_radius = 1.;
  Cech_complex cech_complex_from_points(points, max_radius);
 
  Simplex_tree stree;
  cech_complex_from_points.create_complex(stree, 2);
  // ----------------------------------------------------------------------------
  // Display information about the one skeleton Cech complex
  // ----------------------------------------------------------------------------
  std::clog << "Cech complex is of dimension " << stree.dimension() << " - " << stree.num_simplices() << " simplices - "
            << stree.num_vertices() << " vertices." << std::endl;
 
  std::clog << "Iterator on Cech complex simplices in the filtration order, with [filtration value]:" << std::endl;
  for (auto f_simplex : stree.filtration_simplex_range()) {
    std::clog << "   ( ";
    for (auto vertex : stree.simplex_vertex_range(f_simplex)) {
      std::clog << vertex << " ";
    }
    std::clog << ") -> "
              << "[" << stree.filtration(f_simplex) << "] ";
    std::clog << std::endl;
  }
  return 0;
}