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Diffstat (limited to 'src/Alpha_complex/include/gudhi/Alpha_complex.h')
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diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h new file mode 100644 index 00000000..138270ff --- /dev/null +++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h @@ -0,0 +1,346 @@ +/* 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 simplex_tree from Delaunay_triangulation +#include <gudhi/graph_simplicial_complex.h> +#include <gudhi/Simplex_tree.h> + +#include <stdio.h> +#include <stdlib.h> +#include <math.h> // isnan, fmax + +#include <boost/bimap.hpp> + +#include <CGAL/Delaunay_triangulation.h> +#include <CGAL/Epick_d.h> +#include <CGAL/algorithm.h> +#include <CGAL/assertions.h> +#include <CGAL/enum.h> + +#include <iostream> +#include <iterator> +#include <vector> +#include <string> +#include <limits> // NaN +#include <iterator> // std::iterator + +namespace Gudhi { + +namespace alphacomplex { + +#define Kinit(f) =k.f() + +/** + * \brief Alpha complex data structure. + * + * \details + * The data structure can be constructed from a CGAL Delaunay triangulation (for more informations on CGAL Delaunay + * triangulation, please refer to the corresponding chapter in page http://doc.cgal.org/latest/Triangulation/) or from + * an OFF file (cf. Delaunay_triangulation_off_reader). + * + * Please refer to \ref alpha_complex for examples. + * + */ +class Alpha_complex : public Simplex_tree<> { + private: + // From Simplex_tree + // Type required to insert into a simplex_tree (with or without subfaces). + typedef std::vector<Vertex_handle> Vector_vertex; + + // Simplex_result is the type returned from simplex_tree insert function. + typedef typename std::pair<Simplex_handle, bool> Simplex_result; + + // From CGAL + // Kernel for the Delaunay_triangulation. Dimension can be set dynamically. + typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel; + + // Delaunay_triangulation type required to create an alpha-complex. + typedef CGAL::Delaunay_triangulation<Kernel> Delaunay_triangulation; + + typedef typename Kernel::Compute_squared_radius_d Squared_Radius; + typedef typename Kernel::Side_of_bounded_sphere_d Is_Gabriel; + + // Type required to compute squared radius, or side of bounded sphere on a vector of points. + typedef std::vector<Kernel::Point_d> Vector_of_CGAL_points; + + // Vertex_iterator type from CGAL. + typedef Delaunay_triangulation::Vertex_iterator CGAL_vertex_iterator; + + // Boost bimap type to switch from CGAL vertex iterator to simplex tree vertex handle and vice versa. + typedef boost::bimap< CGAL_vertex_iterator, Vertex_handle > Bimap_vertex; + + // size_type type from CGAL. + typedef Delaunay_triangulation::size_type size_type; + + private: + /** \brief Boost bimap to switch from CGAL vertex iterator to simplex tree vertex handle and vice versa.*/ + Bimap_vertex cgal_simplextree; + /** \brief Pointer on the CGAL Delaunay triangulation.*/ + Delaunay_triangulation* triangulation; + + public: + /** \brief Alpha_complex constructor from an OFF file name. + * Uses the Delaunay_triangulation_off_reader to construct the Delaunay triangulation required to initialize + * the Alpha_complex. + * + * @param[in] off_file_name OFF file [path and] name. + */ + Alpha_complex(const std::string& off_file_name) + : triangulation(nullptr) { + Gudhi::Delaunay_triangulation_off_reader<Delaunay_triangulation> off_reader(off_file_name); + if (!off_reader.is_valid()) { + std::cerr << "Alpha_complex - Unable to read file " << off_file_name << std::endl; + exit(-1); // ----- >> + } + triangulation = off_reader.get_complex(); + init(); + } + + /** \brief Alpha_complex constructor from a Delaunay triangulation. + * + * @param[in] triangulation_ptr Pointer on a Delaunay triangulation. + */ + Alpha_complex(Delaunay_triangulation* triangulation_ptr) + : triangulation(triangulation_ptr) { + init(); + } + + /** \brief Alpha_complex constructor from a list of points. + * Uses the Delaunay_triangulation_off_reader to construct the Delaunay triangulation required to initialize + * the Alpha_complex. + * + * @param[in] dimension Dimension of points to be inserted. + * @param[in] size Number of points to be inserted. + * @param[in] firstPoint Iterator on the first point to be inserted. + * @param[in] last Point Iterator on the last point to be inserted. + */ + template<typename ForwardIterator > + Alpha_complex(int dimension, size_type size, ForwardIterator firstPoint, ForwardIterator lastPoint) + : triangulation(nullptr) { + triangulation = new Delaunay_triangulation(dimension); + Delaunay_triangulation::size_type inserted = triangulation->insert<ForwardIterator>(firstPoint, lastPoint); + if (inserted != size) { + std::cerr << "Alpha_complex - insertion failed " << inserted << " != " << size<< std::endl; + exit(-1); // ----- >> + } + init(); + } + + /** \brief Alpha_complex destructor from a Delaunay triangulation. + * + * @warning Deletes the Delaunay triangulation. + */ + ~Alpha_complex() { + delete triangulation; + } + + private: + /** \brief Initialize the Alpha_complex from the Delaunay triangulation. + * + * @warning Delaunay triangulation must be already constructed with at least one vertex and dimension must be more + * than 0. + * + * Initialization can be launched once. + */ + void init() { + if (triangulation == nullptr) { + std::cerr << "Alpha_complex init - Cannot init from a NULL triangulation" << std::endl; + return; // ----- >> + } + if (triangulation->number_of_vertices() < 1) { + std::cerr << "Alpha_complex init - Cannot init from a triangulation without vertices" << std::endl; + return; // ----- >> + } + if (triangulation->maximal_dimension() < 1) { + std::cerr << "Alpha_complex init - Cannot init from a zero-dimension triangulation" << std::endl; + return; // ----- >> + } + if (num_vertices() > 0) { + std::cerr << "Alpha_complex init - Cannot init twice" << std::endl; + return; // ----- >> + } + + set_dimension(triangulation->maximal_dimension()); + + // -------------------------------------------------------------------------------------------- + // bimap to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa + // Start to insert at handle = 0 - default integer value + Vertex_handle vertex_handle = Vertex_handle(); + // Loop on triangulation vertices list + for (CGAL_vertex_iterator vit = triangulation->vertices_begin(); vit != triangulation->vertices_end(); ++vit) { + cgal_simplextree.insert(Bimap_vertex::value_type(vit, vertex_handle)); + vertex_handle++; + } + // -------------------------------------------------------------------------------------------- + + // -------------------------------------------------------------------------------------------- + // Simplex_tree construction from loop on triangulation finite full cells list + for (auto cit = triangulation->finite_full_cells_begin(); cit != triangulation->finite_full_cells_end(); ++cit) { + Vector_vertex vertexVector; +#ifdef DEBUG_TRACES + std::cout << "Simplex_tree insertion "; +#endif // DEBUG_TRACES + for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) { +#ifdef DEBUG_TRACES + std::cout << " " << cgal_simplextree.left.at(*vit); +#endif // DEBUG_TRACES + // Vector of vertex construction for simplex_tree structure + vertexVector.push_back(cgal_simplextree.left.at(*vit)); + } +#ifdef DEBUG_TRACES + std::cout << std::endl; +#endif // DEBUG_TRACES + // Insert each simplex and its subfaces in the simplex tree - filtration is NaN + Simplex_result insert_result = insert_simplex_and_subfaces(vertexVector, + std::numeric_limits<double>::quiet_NaN()); + if (!insert_result.second) { + std::cerr << "Alpha_complex::init insert_simplex_and_subfaces failed" << std::endl; + } + } + // -------------------------------------------------------------------------------------------- + + Filtration_value filtration_max = 0.0; + // -------------------------------------------------------------------------------------------- + // ### For i : d -> 0 + for (int decr_dim = dimension(); decr_dim >= 0; decr_dim--) { + // ### Foreach Sigma of dim i + for (auto f_simplex : skeleton_simplex_range(decr_dim)) { + int f_simplex_dim = dimension(f_simplex); + if (decr_dim == f_simplex_dim) { + Vector_of_CGAL_points pointVector; +#ifdef DEBUG_TRACES + std::cout << "Sigma of dim " << decr_dim << " is"; +#endif // DEBUG_TRACES + for (auto vertex : simplex_vertex_range(f_simplex)) { + pointVector.push_back((cgal_simplextree.right.at(vertex))->point()); +#ifdef DEBUG_TRACES + std::cout << " " << vertex; +#endif // DEBUG_TRACES + } +#ifdef DEBUG_TRACES + std::cout << std::endl; +#endif // DEBUG_TRACES + // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma) + if (isnan(filtration(f_simplex))) { + Filtration_value alpha_complex_filtration = 0.0; + // No need to compute squared_radius on a single point - alpha is 0.0 + if (f_simplex_dim > 0) { + // squared_radius function initialization + Kernel k; + Squared_Radius squared_radius Kinit(compute_squared_radius_d_object); + + alpha_complex_filtration = squared_radius(pointVector.begin(), pointVector.end()); + } + assign_filtration(f_simplex, alpha_complex_filtration); + filtration_max = fmax(filtration_max, alpha_complex_filtration); +#ifdef DEBUG_TRACES + std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << filtration(f_simplex) << std::endl; +#endif // DEBUG_TRACES + } + propagate_alpha_filtration(f_simplex, decr_dim); + } + } + } + // -------------------------------------------------------------------------------------------- + +#ifdef DEBUG_TRACES + std::cout << "filtration_max=" << filtration_max << std::endl; +#endif // DEBUG_TRACES + set_filtration(filtration_max); + } + + template<typename Simplex_handle> + void propagate_alpha_filtration(Simplex_handle f_simplex, int decr_dim) { + // ### Foreach Tau face of Sigma + for (auto f_boundary : boundary_simplex_range(f_simplex)) { +#ifdef DEBUG_TRACES + std::cout << " | --------------------------------------------------" << std::endl; + std::cout << " | Tau "; + for (auto vertex : simplex_vertex_range(f_boundary)) { + std::cout << vertex << " "; + } + std::cout << "is a face of Sigma" << std::endl; + std::cout << " | isnan(filtration(Tau)=" << isnan(filtration(f_boundary)) << std::endl; +#endif // DEBUG_TRACES + // ### If filt(Tau) is not NaN + if (!isnan(filtration(f_boundary))) { + // ### filt(Tau) = fmin(filt(Tau), filt(Sigma)) + Filtration_value alpha_complex_filtration = fmin(filtration(f_boundary), filtration(f_simplex)); + assign_filtration(f_boundary, alpha_complex_filtration); + // No need to check for filtration_max, alpha_complex_filtration is a min of an existing filtration value +#ifdef DEBUG_TRACES + std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << filtration(f_boundary) << std::endl; +#endif // DEBUG_TRACES + // ### Else + } else { + // No need to compute is_gabriel for dimension <= 2 + // i.e. : Sigma = (3,1) => Tau = 1 + if (decr_dim > 1) { + // insert the Tau points in a vector for is_gabriel function + Vector_of_CGAL_points pointVector; + Vertex_handle vertexForGabriel = Vertex_handle(); + for (auto vertex : simplex_vertex_range(f_boundary)) { + pointVector.push_back((cgal_simplextree.right.at(vertex))->point()); + } + // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function + for (auto vertex : simplex_vertex_range(f_simplex)) { + if (std::find(pointVector.begin(), pointVector.end(), (cgal_simplextree.right.at(vertex))->point()) + == pointVector.end()) { + // vertex is not found in Tau + vertexForGabriel = vertex; + // No need to continue loop + break; + } + } + // is_gabriel function initialization + Kernel k; + Is_Gabriel is_gabriel Kinit(side_of_bounded_sphere_d_object); +#ifdef DEBUG_TRACES + bool is_gab = is_gabriel(pointVector.begin(), pointVector.end(), (cgal_simplextree.right.at(vertexForGabriel))->point()) + != CGAL::ON_BOUNDED_SIDE; + std::cout << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << vertexForGabriel << std::endl; +#endif // DEBUG_TRACES + // ### If Tau is not Gabriel of Sigma + if ((is_gabriel(pointVector.begin(), pointVector.end(), (cgal_simplextree.right.at(vertexForGabriel))->point()) + == CGAL::ON_BOUNDED_SIDE)) { + // ### filt(Tau) = filt(Sigma) + Filtration_value alpha_complex_filtration = filtration(f_simplex); + assign_filtration(f_boundary, alpha_complex_filtration); + // No need to check for filtration_max, alpha_complex_filtration is an existing filtration value +#ifdef DEBUG_TRACES + std::cout << " | filt(Tau) = filt(Sigma) = " << filtration(f_boundary) << std::endl; +#endif // DEBUG_TRACES + } + } + } + } + } +}; + +} // namespace alphacomplex + +} // namespace Gudhi + +#endif // SRC_ALPHA_COMPLEX_INCLUDE_GUDHI_ALPHA_COMPLEX_H_ |