/* 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): Vincent Rouvreau
* Copyright (C) 2017 Inria
* Modification(s):
* - YYYY/MM Author: Description of the modification
#include <gudhi/Simplex_tree.h>
#include <gudhi/Points_off_io.h>
#include <CGAL/Epick_d.h>
#include <CGAL/Min_sphere_of_spheres_d.h>
#include <CGAL/Min_sphere_of_points_d_traits_d.h>
#include <boost/program_options.hpp>
#include <string>
#include <vector>
#include <limits> // infinity
#include <utility> // for pair
#include <map>
// -------------------------------------------------------------------------------
// cech_complex_cgal_mini_sphere_3d is an example of each step that is required to
// build a Cech over a Simplex_tree. Please refer to cech_persistence to see
// how to do the same thing with the Cech_complex wrapper for less detailed
// steps.
// -------------------------------------------------------------------------------
// Types definition
using Simplex_handle = Simplex_tree::Simplex_handle;
using Graph_t = boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS,
boost::property<Gudhi::vertex_filtration_t, Filtration_value>,
boost::property<Gudhi::edge_filtration_t, Filtration_value> >;
using Edge_t = std::pair<Vertex_handle, Vertex_handle>;
using Kernel = CGAL::Epick_d<CGAL::Dimension_tag<3> >;
using Point = Kernel::Point_d;
using Traits = CGAL::Min_sphere_of_points_d_traits_d<Kernel, Filtration_value, 3>;
using Min_sphere = CGAL::Min_sphere_of_spheres_d<Traits>;
class Cech_blocker {
bool operator()(Simplex_handle sh) {
std::vector<Point> points;
std::clog << "Cech_blocker on [";
#endif // DEBUG_TRACES
for (auto vertex : simplex_tree_.simplex_vertex_range(sh)) {
std::clog << vertex << ", ";
#endif // DEBUG_TRACES
Min_sphere ms(points.begin(), points.end());
Filtration_value radius = ms.radius();
std::clog << "] - radius = " << radius << " - returns " << (radius > threshold_) << std::endl;
#endif // DEBUG_TRACES
simplex_tree_.assign_filtration(sh, radius);
return (radius > threshold_);
Cech_blocker(Simplex_tree& simplex_tree, Filtration_value threshold, const std::vector<Point>& point_cloud)
: simplex_tree_(simplex_tree), threshold_(threshold), point_cloud_(point_cloud) {}
Simplex_tree simplex_tree_;
Filtration_value threshold_;
std::vector<Point> point_cloud_;
template <typename InputPointRange>
Graph_t compute_proximity_graph(InputPointRange& points, Filtration_value threshold);
void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& threshold, int& dim_max);
int main(int argc, char* argv[]) {
std::string off_file_points;
Filtration_value threshold;
int dim_max;
program_options(argc, argv, off_file_points, threshold, dim_max);
// Extract the points from the file filepoints
Points_off_reader off_reader(off_file_points);
// Compute the proximity graph of the points
Graph_t prox_graph = compute_proximity_graph(off_reader.get_point_cloud(), threshold);
// Min_sphere sph1(off_reader.get_point_cloud()[0], off_reader.get_point_cloud()[1], off_reader.get_point_cloud()[2]);
// Construct the Rips complex in a Simplex Tree
// insert the proximity graph in the simplex tree
// expand the graph until dimension dim_max
st.expansion_with_blockers(dim_max, Cech_blocker(st, threshold, off_reader.get_point_cloud()));
std::clog << "The complex contains " << st.num_simplices() << " simplices \n";
std::clog << " and has dimension " << st.dimension() << " \n";
// Sort the simplices in the order of the filtration
std::clog << "********************************************************************\n";
// Display the Simplex_tree - Can not be done in the middle of 2 inserts
std::clog << "* The complex contains " << st.num_simplices() << " simplices - dimension=" << st.dimension() << "\n";
std::clog << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
for (auto f_simplex : st.filtration_simplex_range()) {
std::clog << " "
<< "[" << st.filtration(f_simplex) << "] ";
for (auto vertex : st.simplex_vertex_range(f_simplex)) {
std::clog << static_cast<int>(vertex) << " ";
std::clog << std::endl;
#endif // DEBUG_TRACES
return 0;
void program_options(int argc, char* argv[], std::string& off_file_points, Filtration_value& threshold, int& dim_max) {
namespace po = boost::program_options;
po::options_description hidden("Hidden options");
hidden.add_options()("input-file", po::value<std::string>(&off_file_points),
"Name of an OFF file containing a 3d point set.\n");
po::options_description visible("Allowed options", 100);
visible.add_options()("help,h", "produce help message")(
"Maximal length of an edge for the Cech complex construction.")(
"cpx-dimension,d", po::value<int>(&dim_max)->default_value(1),
"Maximal dimension of the Cech complex we want to compute.");
po::positional_options_description pos;
pos.add("input-file", 1);
po::options_description all;
po::variables_map vm;
po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm);
if (vm.count("help") || !vm.count("input-file")) {
std::clog << std::endl;
std::clog << "Construct a Cech complex defined on a set of input points.\n \n";
std::clog << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
std::clog << visible << std::endl;
template <typename InputPointRange>
Graph_t compute_proximity_graph(InputPointRange& points, Filtration_value threshold) {
std::vector<Edge_t> edges;
std::vector<Filtration_value> edges_fil;
Kernel k;
Vertex_handle idx_u, idx_v;
idx_u = 0;
for (auto it_u = points.begin(); it_u != points.end(); ++it_u) {
idx_v = idx_u + 1;
for (auto it_v = it_u + 1; it_v != points.end(); ++it_v, ++idx_v) {
fil = k.squared_distance_d_object()(*it_u, *it_v);
// For Cech Complex, threshold is a radius (distance /2)
fil = std::sqrt(fil) / 2.;
if (fil <= threshold) {
edges.emplace_back(idx_u, idx_v);
Graph_t skel_graph(edges.begin(), edges.end(), edges_fil.begin(),
idx_u); // number of points labeled from 0 to idx_u-1
auto vertex_prop = boost::get(Gudhi::vertex_filtration_t(), skel_graph);
boost::graph_traits<Graph_t>::vertex_iterator vi, vi_end;
for (std::tie(vi, vi_end) = boost::vertices(skel_graph); vi != vi_end; ++vi) {
boost::put(vertex_prop, *vi, 0.);
return skel_graph;
OFF file reader implementation in order to read points from an OFF file.
Definition: Points_off_io.h:122
Options::Filtration_value Filtration_value
Type for the value of the filtration function.
Definition: Simplex_tree.h:86
Dictionary::iterator Simplex_handle
Handle type to a simplex contained in the simplicial complex represented by the simplex tree.
Definition: Simplex_tree.h:152
Filtration_simplex_range const & filtration_simplex_range(Indexing_tag=Indexing_tag())
Returns a range over the simplices of the simplicial complex, in the order of the filtration.
Definition: Simplex_tree.h:271
Simplex_vertex_range simplex_vertex_range(Simplex_handle sh) const
Returns a range over the vertices of a simplex.
Definition: Simplex_tree.h:282
static Filtration_value filtration(Simplex_handle sh)
Returns the filtration value of a simplex.
Definition: Simplex_tree.h:535
void expansion_with_blockers(int max_dim, Blocker block_simplex)
Expands a simplex tree containing only a graph. Simplices corresponding to cliques in the graph are a...
Definition: Simplex_tree.h:1267
Simplex_tree_siblings< Simplex_tree, Dictionary > Siblings
Set of nodes sharing a same parent in the simplex tree.
Definition: Simplex_tree.h:105
void initialize_filtration()
Initializes the filtration cache, i.e. sorts the simplices according to their order in the filtration...
Definition: Simplex_tree.h:912
Options::Vertex_handle Vertex_handle
Type for the vertex handle.
Definition: Simplex_tree.h:94
int dimension(Simplex_handle sh)
Returns the dimension of a simplex.
Definition: Simplex_tree.h:600
size_t num_simplices()
returns the number of simplices in the simplex_tree.
Definition: Simplex_tree.h:578
void insert_graph(const OneSkeletonGraph &skel_graph)
Inserts a 1-skeleton in an empty Simplex_tree.
Definition: Simplex_tree.h:1106
Global distance functions.
Graph simplicial complex methods.
Value type for a filtration function on a cell complex.
Definition: FiltrationValue.h:20
Handle type for the vertices of a cell complex.
Definition: VertexHandle.h:15