summaryrefslogtreecommitdiff
path: root/example/Simplex_tree/cech_complex_cgal_mini_sphere_3d.cpp
blob: 08ed74bbfe698ee2efa5318b6df2d3aadbdb9b7c (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
/*    This file is part of the Gudhi Library. The Gudhi library
 *    (Geometric Understanding in Higher Dimensions) is a generic C++
 *    library for computational topology.
 *
 *    Author(s):       Vincent Rouvreau
 *
 *    Copyright (C) 2017 Inria
 *
 *    This program is free software: you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation, either version 3 of the License, or
 *    (at your option) any later version.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#include <gudhi/graph_simplicial_complex.h>
#include <gudhi/distance_functions.h>
#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_tree = Gudhi::Simplex_tree<>;
using Vertex_handle = Simplex_tree::Vertex_handle;
using Simplex_handle = Simplex_tree::Simplex_handle;
using Filtration_value = Simplex_tree::Filtration_value;
using Siblings = Simplex_tree::Siblings;
using Graph_t = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS,
                                      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>;

using Points_off_reader = Gudhi::Points_off_reader<Point>;

class Cech_blocker {
 public:
  bool operator()(Simplex_handle sh) {
    std::vector<Point> points;
#if DEBUG_TRACES
    std::cout << "Cech_blocker on [";
#endif  // DEBUG_TRACES
    for (auto vertex : simplex_tree_.simplex_vertex_range(sh)) {
      points.push_back(point_cloud_[vertex]);
#if DEBUG_TRACES
      std::cout << vertex << ", ";
#endif  // DEBUG_TRACES
    }
    Min_sphere ms(points.begin(), points.end());
    Filtration_value radius = ms.radius();
#if DEBUG_TRACES
    std::cout << "] - 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) {}

 private:
  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
  Simplex_tree st;
  // insert the proximity graph in the simplex tree
  st.insert_graph(prox_graph);
  // expand the graph until dimension dim_max
  st.expansion_with_blockers(dim_max, Cech_blocker(st, threshold, off_reader.get_point_cloud()));

  std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
  std::cout << "   and has dimension " << st.dimension() << " \n";

  // Sort the simplices in the order of the filtration
  st.initialize_filtration();

#if DEBUG_TRACES
  std::cout << "********************************************************************\n";
  // Display the Simplex_tree - Can not be done in the middle of 2 inserts
  std::cout << "* The complex contains " << st.num_simplices() << " simplices - dimension=" << st.dimension() << "\n";
  std::cout << "* Iterator on Simplices in the filtration, with [filtration value]:\n";
  for (auto f_simplex : st.filtration_simplex_range()) {
    std::cout << "   "
              << "[" << st.filtration(f_simplex) << "] ";
    for (auto vertex : st.simplex_vertex_range(f_simplex)) {
      std::cout << static_cast<int>(vertex) << " ";
    }
    std::cout << 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")(
      "max-edge-length,r",
      po::value<Filtration_value>(&threshold)->default_value(std::numeric_limits<Filtration_value>::infinity()),
      "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;
  all.add(visible).add(hidden);

  po::variables_map vm;
  po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm);
  po::notify(vm);

  if (vm.count("help") || !vm.count("input-file")) {
    std::cout << std::endl;
    std::cout << "Construct a Cech complex defined on a set of input points.\n \n";

    std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
    std::cout << visible << std::endl;
    std::abort();
  }
}

/** Output the proximity graph of the points.
 *
 * If points contains n elements, the proximity graph is the graph
 * with n vertices, and an edge [u,v] iff the distance function between
 * points u and v is smaller than threshold.
 *
 * The type PointCloud furnishes .begin() and .end() methods, that return
 * iterators with value_type Point.
 */
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;
  Filtration_value fil;
  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);
        edges_fil.push_back(fil);
      }
    }
    ++idx_u;
  }

  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;
}