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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..8919cdb9 --- /dev/null +++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h @@ -0,0 +1,432 @@ +/* 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) 2015 Inria + * + * Modification(s): + * - 2019/08 Vincent Rouvreau: Fix issue #10 for CGAL and Eigen3 + * - YYYY/MM Author: Description of the modification + */ + +#ifndef ALPHA_COMPLEX_H_ +#define ALPHA_COMPLEX_H_ + +#include <gudhi/Debug_utils.h> +// to construct Alpha_complex from a OFF file of points +#include <gudhi/Points_off_io.h> + +#include <stdlib.h> +#include <math.h> // isnan, fmax + +#include <CGAL/Delaunay_triangulation.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Spatial_sort_traits_adapter_d.h> +#include <CGAL/property_map.h> // for CGAL::Identity_property_map +#include <CGAL/NT_converter.h> +#include <CGAL/version.h> // for CGAL_VERSION_NR + +#include <Eigen/src/Core/util/Macros.h> // for EIGEN_VERSION_AT_LEAST + +#include <iostream> +#include <vector> +#include <string> +#include <limits> // NaN +#include <map> +#include <utility> // std::pair +#include <stdexcept> +#include <numeric> // for std::iota + +// Make compilation fail - required for external projects - https://github.com/GUDHI/gudhi-devel/issues/10 +#if CGAL_VERSION_NR < 1041101000 +# error Alpha_complex_3d is only available for CGAL >= 4.11 +#endif + +#if !EIGEN_VERSION_AT_LEAST(3,1,0) +# error Alpha_complex_3d is only available for Eigen3 >= 3.1.0 installed with CGAL +#endif + +namespace Gudhi { + +namespace alpha_complex { + +/** + * \class Alpha_complex Alpha_complex.h gudhi/Alpha_complex.h + * \brief Alpha complex data structure. + * + * \ingroup alpha_complex + * + * \details + * The data structure is constructing 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/) from a + * range of points or from an OFF file (cf. Points_off_reader). + * + * Please refer to \ref alpha_complex for examples. + * + * The complex is a template class requiring an Epick_d <a target="_blank" + * href="http://doc.cgal.org/latest/Kernel_d/index.html#Chapter_dD_Geometry_Kernel">dD Geometry Kernel</a> + * \cite cgal:s-gkd-15b from CGAL as template, default value is <a target="_blank" + * href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> + * < <a target="_blank" href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dynamic__dimension__tag.html"> + * CGAL::Dynamic_dimension_tag </a> > + * + * \remark When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. + * + */ +template<class Kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>> +class Alpha_complex { + public: + // Add an int in TDS to save point index in the structure + typedef CGAL::Triangulation_data_structure<typename Kernel::Dimension, + CGAL::Triangulation_vertex<Kernel, std::ptrdiff_t>, + CGAL::Triangulation_full_cell<Kernel> > TDS; + /** \brief A Delaunay triangulation of a set of points in \f$ \mathbb{R}^D\f$.*/ + typedef CGAL::Delaunay_triangulation<Kernel, TDS> Delaunay_triangulation; + + /** \brief A point in Euclidean space.*/ + typedef typename Kernel::Point_d Point_d; + /** \brief Geometric traits class that provides the geometric types and predicates needed by Delaunay + * triangulations.*/ + typedef Kernel Geom_traits; + + private: + typedef typename Kernel::Compute_squared_radius_d Squared_Radius; + typedef typename Kernel::Side_of_bounded_sphere_d Is_Gabriel; + typedef typename Kernel::Point_dimension_d Point_Dimension; + + // Type required to compute squared radius, or side of bounded sphere on a vector of points. + typedef typename std::vector<Point_d> Vector_of_CGAL_points; + + // Vertex_iterator type from CGAL. + typedef typename Delaunay_triangulation::Vertex_iterator CGAL_vertex_iterator; + + // size_type type from CGAL. + typedef typename Delaunay_triangulation::size_type size_type; + + // Map type to switch from simplex tree vertex handle to CGAL vertex iterator. + typedef typename std::map< std::size_t, CGAL_vertex_iterator > Vector_vertex_iterator; + + private: + /** \brief Vertex iterator vector to switch from simplex tree vertex handle to CGAL vertex iterator. + * Vertex handles are inserted sequentially, starting at 0.*/ + Vector_vertex_iterator vertex_handle_to_iterator_; + /** \brief Pointer on the CGAL Delaunay triangulation.*/ + Delaunay_triangulation* triangulation_; + /** \brief Kernel for triangulation_ functions access.*/ + Kernel kernel_; + + public: + /** \brief Alpha_complex constructor from an OFF file name. + * + * Uses the Points_off_reader to construct the Delaunay triangulation required to initialize + * the Alpha_complex. + * + * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous. + * + * @param[in] off_file_name OFF file [path and] name. + */ + Alpha_complex(const std::string& off_file_name) + : triangulation_(nullptr) { + Gudhi::Points_off_reader<Point_d> off_reader(off_file_name); + if (!off_reader.is_valid()) { + std::cerr << "Alpha_complex - Unable to read file " << off_file_name << "\n"; + exit(-1); // ----- >> + } + + init_from_range(off_reader.get_point_cloud()); + } + + /** \brief Alpha_complex constructor from a list of points. + * + * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous. + * + * @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d + * + * The type InputPointRange must be a range for which std::begin and + * std::end return input iterators on a Kernel::Point_d. + */ + template<typename InputPointRange > + Alpha_complex(const InputPointRange& points) + : triangulation_(nullptr) { + init_from_range(points); + } + + /** \brief Alpha_complex destructor deletes the Delaunay triangulation. + */ + ~Alpha_complex() { + delete triangulation_; + } + + // Forbid copy/move constructor/assignment operator + Alpha_complex(const Alpha_complex& other) = delete; + Alpha_complex& operator= (const Alpha_complex& other) = delete; + Alpha_complex (Alpha_complex&& other) = delete; + Alpha_complex& operator= (Alpha_complex&& other) = delete; + + /** \brief get_point returns the point corresponding to the vertex given as parameter. + * + * @param[in] vertex Vertex handle of the point to retrieve. + * @return The point found. + * @exception std::out_of_range In case vertex is not found (cf. std::vector::at). + */ + const Point_d& get_point(std::size_t vertex) const { + return vertex_handle_to_iterator_.at(vertex)->point(); + } + + /** \brief number_of_vertices returns the number of vertices (same as the number of points). + * + * @return The number of vertices. + */ + std::size_t number_of_vertices() const { + return vertex_handle_to_iterator_.size(); + } + + private: + template<typename InputPointRange > + void init_from_range(const InputPointRange& points) { + auto first = std::begin(points); + auto last = std::end(points); + + if (first != last) { + // point_dimension function initialization + Point_Dimension point_dimension = kernel_.point_dimension_d_object(); + + // Delaunay triangulation is point dimension. + triangulation_ = new Delaunay_triangulation(point_dimension(*first)); + + std::vector<Point_d> point_cloud(first, last); + + // Creates a vector {0, 1, ..., N-1} + std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0), + boost::counting_iterator<std::ptrdiff_t>(point_cloud.size())); + + typedef boost::iterator_property_map<typename std::vector<Point_d>::iterator, + CGAL::Identity_property_map<std::ptrdiff_t>> Point_property_map; + typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_property_map> Search_traits_d; + + CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud))); + + typename Delaunay_triangulation::Full_cell_handle hint; + for (auto index : indices) { + typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint); + // Save index value as data to retrieve it after insertion + pos->data() = index; + hint = pos->full_cell(); + } + // -------------------------------------------------------------------------------------------- + // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa + // Loop on triangulation vertices list + for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) { + if (!triangulation_->is_infinite(*vit)) { +#ifdef DEBUG_TRACES + std::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl; +#endif // DEBUG_TRACES + vertex_handle_to_iterator_.emplace(vit->data(), vit); + } + } + // -------------------------------------------------------------------------------------------- + } + } + + public: + /** \brief Inserts all Delaunay triangulation into the simplicial complex. + * It also computes the filtration values accordingly to the \ref createcomplexalgorithm + * + * \tparam SimplicialComplexForAlpha must meet `SimplicialComplexForAlpha` concept. + * + * @param[in] complex SimplicialComplexForAlpha to be created. + * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$, and there is very + * little point using anything else since it does not save time. + * + * @return true if creation succeeds, false otherwise. + * + * @pre Delaunay triangulation must be already constructed with dimension strictly greater than 0. + * @pre The simplicial complex must be empty (no vertices) + * + * Initialization can be launched once. + */ + template <typename SimplicialComplexForAlpha, + typename Filtration_value = typename SimplicialComplexForAlpha::Filtration_value> + bool create_complex(SimplicialComplexForAlpha& complex, + Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity()) { + // From SimplicialComplexForAlpha type required to insert into a simplicial complex (with or without subfaces). + typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle; + typedef typename SimplicialComplexForAlpha::Simplex_handle Simplex_handle; + typedef std::vector<Vertex_handle> Vector_vertex; + + if (triangulation_ == nullptr) { + std::cerr << "Alpha_complex cannot create_complex from a NULL triangulation\n"; + return false; // ----- >> + } + if (triangulation_->maximal_dimension() < 1) { + std::cerr << "Alpha_complex cannot create_complex from a zero-dimension triangulation\n"; + return false; // ----- >> + } + if (complex.num_vertices() > 0) { + std::cerr << "Alpha_complex create_complex - complex is not empty\n"; + return false; // ----- >> + } + + // -------------------------------------------------------------------------------------------- + // Simplex_tree construction from loop on triangulation finite full cells list + if (triangulation_->number_of_vertices() > 0) { + 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) { + if (*vit != nullptr) { +#ifdef DEBUG_TRACES + std::cout << " " << (*vit)->data(); +#endif // DEBUG_TRACES + // Vector of vertex construction for simplex_tree structure + vertexVector.push_back((*vit)->data()); + } + } +#ifdef DEBUG_TRACES + std::cout << std::endl; +#endif // DEBUG_TRACES + // Insert each simplex and its subfaces in the simplex tree - filtration is NaN + complex.insert_simplex_and_subfaces(vertexVector, std::numeric_limits<double>::quiet_NaN()); + } + } + // -------------------------------------------------------------------------------------------- + + // -------------------------------------------------------------------------------------------- + // Will be re-used many times + Vector_of_CGAL_points pointVector; + // ### For i : d -> 0 + for (int decr_dim = triangulation_->maximal_dimension(); decr_dim >= 0; decr_dim--) { + // ### Foreach Sigma of dim i + for (Simplex_handle f_simplex : complex.skeleton_simplex_range(decr_dim)) { + int f_simplex_dim = complex.dimension(f_simplex); + if (decr_dim == f_simplex_dim) { + pointVector.clear(); +#ifdef DEBUG_TRACES + std::cout << "Sigma of dim " << decr_dim << " is"; +#endif // DEBUG_TRACES + for (auto vertex : complex.simplex_vertex_range(f_simplex)) { + pointVector.push_back(get_point(vertex)); +#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 (std::isnan(complex.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 + Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object(); + CGAL::NT_converter<typename Geom_traits::FT, Filtration_value> cv; + + alpha_complex_filtration = cv(squared_radius(pointVector.begin(), pointVector.end())); + } + complex.assign_filtration(f_simplex, alpha_complex_filtration); +#ifdef DEBUG_TRACES + std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl; +#endif // DEBUG_TRACES + } + // No need to propagate further, unweighted points all have value 0 + if (decr_dim > 1) + propagate_alpha_filtration(complex, f_simplex); + } + } + } + // -------------------------------------------------------------------------------------------- + + // -------------------------------------------------------------------------------------------- + // As Alpha value is an approximation, we have to make filtration non decreasing while increasing the dimension + complex.make_filtration_non_decreasing(); + // Remove all simplices that have a filtration value greater than max_alpha_square + complex.prune_above_filtration(max_alpha_square); + // -------------------------------------------------------------------------------------------- + return true; + } + + private: + template <typename SimplicialComplexForAlpha, typename Simplex_handle> + void propagate_alpha_filtration(SimplicialComplexForAlpha& complex, Simplex_handle f_simplex) { + // From SimplicialComplexForAlpha type required to assign filtration values. + typedef typename SimplicialComplexForAlpha::Filtration_value Filtration_value; +#ifdef DEBUG_TRACES + typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle; +#endif // DEBUG_TRACES + + // ### Foreach Tau face of Sigma + for (auto f_boundary : complex.boundary_simplex_range(f_simplex)) { +#ifdef DEBUG_TRACES + std::cout << " | --------------------------------------------------\n"; + std::cout << " | Tau "; + for (auto vertex : complex.simplex_vertex_range(f_boundary)) { + std::cout << vertex << " "; + } + std::cout << "is a face of Sigma\n"; + std::cout << " | isnan(complex.filtration(Tau)=" << std::isnan(complex.filtration(f_boundary)) << std::endl; +#endif // DEBUG_TRACES + // ### If filt(Tau) is not NaN + if (!std::isnan(complex.filtration(f_boundary))) { + // ### filt(Tau) = fmin(filt(Tau), filt(Sigma)) + Filtration_value alpha_complex_filtration = fmin(complex.filtration(f_boundary), + complex.filtration(f_simplex)); + complex.assign_filtration(f_boundary, alpha_complex_filtration); +#ifdef DEBUG_TRACES + std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl; +#endif // DEBUG_TRACES + // ### Else + } else { + // insert the Tau points in a vector for is_gabriel function + Vector_of_CGAL_points pointVector; +#ifdef DEBUG_TRACES + Vertex_handle vertexForGabriel = Vertex_handle(); +#endif // DEBUG_TRACES + for (auto vertex : complex.simplex_vertex_range(f_boundary)) { + pointVector.push_back(get_point(vertex)); + } + // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function + Point_d point_for_gabriel; + for (auto vertex : complex.simplex_vertex_range(f_simplex)) { + point_for_gabriel = get_point(vertex); + if (std::find(pointVector.begin(), pointVector.end(), point_for_gabriel) == pointVector.end()) { +#ifdef DEBUG_TRACES + // vertex is not found in Tau + vertexForGabriel = vertex; +#endif // DEBUG_TRACES + // No need to continue loop + break; + } + } + // is_gabriel function initialization + Is_Gabriel is_gabriel = kernel_.side_of_bounded_sphere_d_object(); + bool is_gab = is_gabriel(pointVector.begin(), pointVector.end(), point_for_gabriel) + != CGAL::ON_BOUNDED_SIDE; +#ifdef DEBUG_TRACES + std::cout << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << vertexForGabriel << std::endl; +#endif // DEBUG_TRACES + // ### If Tau is not Gabriel of Sigma + if (false == is_gab) { + // ### filt(Tau) = filt(Sigma) + Filtration_value alpha_complex_filtration = complex.filtration(f_simplex); + complex.assign_filtration(f_boundary, alpha_complex_filtration); +#ifdef DEBUG_TRACES + std::cout << " | filt(Tau) = filt(Sigma) = " << complex.filtration(f_boundary) << std::endl; +#endif // DEBUG_TRACES + } + } + } + } +}; + +} // namespace alpha_complex + +namespace alphacomplex = alpha_complex; + +} // namespace Gudhi + +#endif // ALPHA_COMPLEX_H_ |