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
|
/* 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) 2015 INRIA Saclay (France)
*
* 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/>.
*/
#ifndef SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
#define SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
// to construct a Delaunay_triangulation from a OFF file
#include <gudhi/Alpha_shapes/Delaunay_triangulation_off_io.h>
// to construct a simplex_tree from Delaunay_triangulation
#include <gudhi/graph_simplicial_complex.h>
#include <gudhi/Simplex_tree.h>
#include <stdio.h>
#include <stdlib.h>
#include <CGAL/Delaunay_triangulation.h>
#include <CGAL/Epick_d.h>
#include <CGAL/algorithm.h>
#include <CGAL/assertions.h>
#include <iostream>
#include <iterator>
#include <vector>
#include <string>
namespace Gudhi {
namespace alphashapes {
/** \defgroup alpha_shapes Alpha shapes in dimension N
*
<DT>Implementations:</DT>
Alpha shapes in dimension N are a subset of Delaunay Triangulation in dimension N.
* \author Vincent Rouvreau
* \version 1.0
* \date 2015
* \copyright GNU General Public License v3.
* @{
*/
/**
* \brief Alpha shapes data structure.
*
* \details Every simplex \f$[v_0, \cdots ,v_d]\f$ admits a canonical orientation
* induced by the order relation on vertices \f$ v_0 < \cdots < v_d \f$.
*
* Details may be found in \cite boissonnatmariasimplextreealgorithmica.
*
* \implements FilteredComplex
*
*/
class Alpha_shapes {
private:
// From Simplex_tree
/** \brief Type required to insert into a simplex_tree (with or without subfaces).*/
typedef std::vector<Vertex_handle> typeVectorVertex;
// From CGAL
/** \brief Kernel for the Delaunay_triangulation.
* Dimension can be set dynamically.
*/
typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel;
/** \brief Delaunay_triangulation type required to create an alpha-shape.
*/
typedef CGAL::Delaunay_triangulation<Kernel> Delaunay_triangulation;
private:
/** \brief Upper bound on the simplex tree of the simplicial complex.*/
Gudhi::Simplex_tree<> _st;
public:
Alpha_shapes(std::string off_file_name, int dimension) {
Delaunay_triangulation dt(dimension);
Gudhi::alphashapes::Delaunay_triangulation_off_reader<Delaunay_triangulation>
off_reader(off_file_name, dt, true, true);
if (!off_reader.is_valid()) {
std::cerr << "Unable to read file " << off_file_name << std::endl;
exit(-1); // ----- >>
}
#ifdef DEBUG_TRACES
std::cout << "number of vertices=" << dt.number_of_vertices() << std::endl;
std::cout << "number of full cells=" << dt.number_of_full_cells() << std::endl;
std::cout << "number of finite full cells=" << dt.number_of_finite_full_cells() << std::endl;
#endif // DEBUG_TRACES
init<Delaunay_triangulation>(dt);
}
template<typename T>
Alpha_shapes(T triangulation) {
init<T>(triangulation);
}
~Alpha_shapes() { }
private:
template<typename T>
void init(T triangulation) {
_st.set_dimension(triangulation.maximal_dimension());
_st.set_filtration(0.0);
// triangulation points list
for (auto vit = triangulation.finite_vertices_begin();
vit != triangulation.finite_vertices_end(); ++vit) {
typeVectorVertex vertexVector;
Vertex_handle vertexHdl = std::distance(triangulation.finite_vertices_begin(), vit);
vertexVector.push_back(vertexHdl);
// Insert each point in the simplex tree
_st.insert_simplex(vertexVector, 0.0);
#ifdef DEBUG_TRACES
std::cout << "P" << vertexHdl << ":";
for (auto Coord = vit->point().cartesian_begin(); Coord != vit->point().cartesian_end(); ++Coord) {
std::cout << *Coord << " ";
}
std::cout << std::endl;
#endif // DEBUG_TRACES
}
// triangulation finite full cells list
for (auto cit = triangulation.finite_full_cells_begin();
cit != triangulation.finite_full_cells_end(); ++cit) {
typeVectorVertex vertexVector;
for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
// Vertex handle is distance - 1
Vertex_handle vertexHdl = std::distance(triangulation.vertices_begin(), *vit) - 1;
vertexVector.push_back(vertexHdl);
}
// Insert each point in the simplex tree
_st.insert_simplex_and_subfaces(vertexVector, 0.0);
#ifdef DEBUG_TRACES
std::cout << "C" << std::distance(triangulation.finite_full_cells_begin(), cit) << ":";
for (auto value : vertexVector) {
std::cout << value << ' ';
}
std::cout << std::endl;
#endif // DEBUG_TRACES
}
}
public:
/** \brief Returns the number of vertices in the complex. */
size_t num_vertices() {
return _st.num_vertices();
}
/** \brief Returns the number of simplices in the complex.
*
* Does not count the empty simplex. */
unsigned num_simplices() const {
return _st.num_simplices();
}
/** \brief Returns an upper bound on the dimension of the simplicial complex. */
int dimension() {
return _st.dimension();
}
/** \brief Returns an upper bound of the filtration values of the simplices. */
Filtration_value filtration() {
return _st.filtration();
}
friend std::ostream& operator<<(std::ostream& os, const Alpha_shapes& alpha_shape) {
// TODO: Program terminated with signal SIGABRT, Aborted - Maybe because of copy constructor
Gudhi::Simplex_tree<> st = alpha_shape._st;
os << st << std::endl;
return os;
}
};
} // namespace alphashapes
} // namespace Gudhi
#endif // SRC_ALPHA_SHAPES_INCLUDE_GUDHI_ALPHA_SHAPES_H_
|
