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Diffstat (limited to 'src/Alpha_complex/include/gudhi/Alpha_complex_3d.h')
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diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h new file mode 100644 index 00000000..15acd7bd --- /dev/null +++ b/src/Alpha_complex/include/gudhi/Alpha_complex_3d.h @@ -0,0 +1,498 @@ +/* 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) 2018 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/>. + */ + +#ifndef ALPHA_COMPLEX_3D_H_ +#define ALPHA_COMPLEX_3D_H_ + +#include <boost/version.hpp> +#include <boost/variant.hpp> + +#if BOOST_VERSION >= 105400 +#include <boost/container/static_vector.hpp> +#endif + +#include <gudhi/Debug_utils.h> +#include <gudhi/Alpha_complex_3d_options.h> + +#include <CGAL/Object.h> +#include <CGAL/tuple.h> +#include <CGAL/iterator.h> +#include <CGAL/version.h> + +#include <iostream> +#include <vector> +#include <map> +#include <stdexcept> +#include <cstddef> +#include <memory> // for std::unique_ptr + +#if CGAL_VERSION_NR < 1041101000 + // Make compilation fail - required for external projects - https://gitlab.inria.fr/GUDHI/gudhi-devel/issues/10 + static_assert(false, + "Alpha_complex_3d is only available for CGAL >= 4.11"); +#endif + +namespace Gudhi { + +namespace alpha_complex { + +/** + * \class Alpha_complex_3d + * \brief Alpha complex data structure for 3d specific case. + * + * \ingroup alpha_complex + * + * \details + * The data structure is constructing a <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html">CGAL 3D Alpha + * Shapes</a> from a range of points (can be read from an OFF file, cf. Points_off_reader). + * + * \tparam AlphaComplex3dOptions can be `Gudhi::alpha_complex::Alpha_shapes_3d`, + * `Gudhi::alpha_complex::Exact_alpha_shapes_3d`, `Gudhi::alpha_complex::Weighted_alpha_shapes_3d`, + * `Gudhi::alpha_complex::Periodic_alpha_shapes_3d` or `Gudhi::alpha_complex::Weighted_periodic_alpha_shapes_3d`. + * + * Please refer to \ref alpha_complex for examples. + * + * \remark When Alpha_complex_3d is constructed with an infinite value of alpha (default value), the complex is a + * Delaunay complex. + * + */ +template<typename AlphaComplex3dOptions> +class Alpha_complex_3d { + using Alpha_shape_3 = typename AlphaComplex3dOptions::Alpha_shape_3; + using Alpha_value_type = typename Alpha_shape_3::FT; + using Dispatch = + CGAL::Dispatch_output_iterator<CGAL::cpp11::tuple<CGAL::Object, Alpha_value_type>, + CGAL::cpp11::tuple<std::back_insert_iterator<std::vector<CGAL::Object> >, + std::back_insert_iterator<std::vector<Alpha_value_type> > > >; + + using Cell_handle = typename Alpha_shape_3::Cell_handle; + using Facet = typename Alpha_shape_3::Facet; + using Edge = typename Alpha_shape_3::Edge; + using Alpha_vertex_handle = typename Alpha_shape_3::Vertex_handle; +#if BOOST_VERSION >= 105400 + using Vertex_list = boost::container::static_vector<Alpha_vertex_handle, 4>; +#else + using Vertex_list = std::vector<Alpha_vertex_handle>; +#endif + +public: + using Point_3 = typename AlphaComplex3dOptions::Point_3; + +public: + /** \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 AlphaComplex3dOptions::Point_3 + * + * @pre Available if AlphaComplex3dOptions is `Gudhi::alpha_complex::Alpha_shapes_3d` or + * `Gudhi::alpha_complex::Exact_alpha_shapes_3d`. + * + * The type InputPointRange must be a range for which std::begin and + * std::end return input iterators on a AlphaComplex3dOptions::Point_3. + */ + template<typename InputPointRange > + Alpha_complex_3d(const InputPointRange& points) { + static_assert(!AlphaComplex3dOptions::weighted, + "This constructor is not available for weighted versions of Alpha_complex_3d"); + static_assert(!AlphaComplex3dOptions::periodic, + "This constructor is not available for periodic versions of Alpha_complex_3d"); + + alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(std::begin(points), std::end(points), 0, + Alpha_shape_3::GENERAL)); + Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, Alpha_value_type>(std::back_inserter(objects_), + std::back_inserter(alpha_values_)); + + alpha_shape_3_ptr_->filtration_with_alpha_values(dispatcher); +#ifdef DEBUG_TRACES + std::cout << "filtration_with_alpha_values returns : " << objects_.size() << " objects" << std::endl; +#endif // DEBUG_TRACES + + } + + /** \brief Alpha_complex constructor from a list of points and associated weights. + * + * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous. + * Weights values are explained on CGAL <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0">Alpha + * shape</a> and + * <a href="https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation">Regular + * triangulation</a> documentation. + * + * @exception std::invalid_argument In debug mode, if points and weights do not have the same size. + * + * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3 + * @param[in] weights Range of weights on points. Points must be in AlphaComplex3dOptions::Point_3 + * + * @pre Available if AlphaComplex3dOptions is `Weighted_alpha_shapes_3d`. + * + * The type InputPointRange must be a range for which std::begin and + * std::end return input iterators on a AlphaComplex3dOptions::Point_3. + * The type WeightRange must be a range for which std::begin and + * std::end return an input iterator on a AlphaComplex3dOptions::Alpha_shape_3::FT. + */ + template<typename InputPointRange , typename WeightRange> + Alpha_complex_3d(const InputPointRange& points, WeightRange weights) { + static_assert(AlphaComplex3dOptions::weighted, + "This constructor is not available for non-weighted versions of Alpha_complex_3d"); + static_assert(!AlphaComplex3dOptions::periodic, + "This constructor is not available for periodic versions of Alpha_complex_3d"); + GUDHI_CHECK((weights.size() == points.size()), + std::invalid_argument("Points number in range different from weights range number")); + + using Weighted_point_3 = typename AlphaComplex3dOptions::Weighted_point_3; + std::vector<Weighted_point_3> weighted_points_3; + + std::size_t index = 0; + weighted_points_3.reserve(points.size()); + while ((index < weights.size()) && (index < points.size())) { + weighted_points_3.push_back(Weighted_point_3(points[index], weights[index])); + index++; + } + + alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(std::begin(weighted_points_3), + std::end(weighted_points_3), + 0, + Alpha_shape_3::GENERAL)); + + Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, Alpha_value_type>(std::back_inserter(objects_), + std::back_inserter(alpha_values_)); + + alpha_shape_3_ptr_->filtration_with_alpha_values(dispatcher); +#ifdef DEBUG_TRACES + std::cout << "filtration_with_alpha_values returns : " << objects_.size() << " objects" << std::endl; +#endif // DEBUG_TRACES + } + + /** \brief Alpha_complex constructor from a list of points and an iso-cuboid coordinates. + * + * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous. + * + * Refer to the <a href="https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html">CGAL’s 3D Periodic + * Triangulations User Manual </a> for more details. + * The periodicity is defined by an iso-oriented cuboid with diagonal opposite vertices (x_min, y_min, z_min) and + * (x_max, y_max, z_max). + * + * @exception std::invalid_argument In debug mode, if the size of the cuboid in every directions is not the same. + * + * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3 + * @param[in] x_min Iso-oriented cuboid x_min. + * @param[in] y_min Iso-oriented cuboid y_min. + * @param[in] z_min Iso-oriented cuboid z_min. + * @param[in] x_max Iso-oriented cuboid x_max. + * @param[in] y_max Iso-oriented cuboid y_max. + * @param[in] z_max Iso-oriented cuboid z_max. + * + * @pre Available if AlphaComplex3dOptions is `Periodic_alpha_shapes_3d`. + * + * The type InputPointRange must be a range for which std::begin and + * std::end return input iterators on a AlphaComplex3dOptions::Point_3. + * The type of x_min, y_min, z_min, x_max, y_max and z_max is AlphaComplex3dOptions::Alpha_shape_3::FT. + */ + template<typename InputPointRange> + Alpha_complex_3d(const InputPointRange& points, + Alpha_value_type x_min, Alpha_value_type y_min, Alpha_value_type z_min, + Alpha_value_type x_max, Alpha_value_type y_max, Alpha_value_type z_max) { + static_assert(!AlphaComplex3dOptions::weighted, + "This constructor is not available for weighted versions of Alpha_complex_3d"); + static_assert(AlphaComplex3dOptions::periodic, + "This constructor is not available for non-periodic versions of Alpha_complex_3d"); + // Checking if the cuboid is the same in x,y and z direction. If not, CGAL will not process it. + GUDHI_CHECK((x_max - x_min == y_max - y_min) && + (x_max - x_min == z_max - z_min) && + (z_max - z_min == y_max - y_min), + std::invalid_argument("The size of the cuboid in every directions is not the same.")); + + using Periodic_delaunay_triangulation_3 = typename AlphaComplex3dOptions::Periodic_delaunay_triangulation_3; + using Iso_cuboid_3 = typename AlphaComplex3dOptions::Iso_cuboid_3; + // Define the periodic cube + Periodic_delaunay_triangulation_3 pdt(Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max)); + // Heuristic for inserting large point sets (if pts is reasonably large) + pdt.insert(std::begin(points), std::end(points), true); + // As pdt won't be modified anymore switch to 1-sheeted cover if possible + if (!pdt.is_triangulation_in_1_sheet()) { + throw std::invalid_argument("Unable to construct a triangulation within a single periodic domain."); + } + pdt.convert_to_1_sheeted_covering(); + + // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode + // Maybe need to set it to GENERAL mode + alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(pdt, 0, + Alpha_shape_3::GENERAL)); + + Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, Alpha_value_type>(std::back_inserter(objects_), + std::back_inserter(alpha_values_)); + + alpha_shape_3_ptr_->filtration_with_alpha_values(dispatcher); +#ifdef DEBUG_TRACES + std::cout << "filtration_with_alpha_values returns : " << objects_.size() << " objects" << std::endl; +#endif // DEBUG_TRACES + + } + + /** \brief Alpha_complex constructor from a list of points, associated weights and an iso-cuboid coordinates. + * + * Duplicate points are inserted once in the Alpha_complex. This is the reason why the vertices may be not contiguous. + * + * Weights values are explained on CGAL <a href="https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0">Alpha + * shape</a> and + * <a href="https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation">Regular + * triangulation</a> documentation. + * + * Refer to the <a href="https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html">CGAL’s 3D Periodic + * Triangulations User Manual</a> for more details. + * The periodicity is defined by an iso-oriented cuboid with diagonal opposite vertices (x_min, y_min, z_min) and + * (x_max, y_max, z_max). + * + * @exception std::invalid_argument In debug mode, if points and weights do not have the same size. + * @exception std::invalid_argument In debug mode, if the size of the cuboid in every directions is not the same. + * @exception std::invalid_argument In debug mode, if a weight is negative, zero, or greater than 1/64*cuboid length + * squared. + * + * @param[in] points Range of points to triangulate. Points must be in AlphaComplex3dOptions::Point_3 + * @param[in] weights Range of weights on points. Points must be in AlphaComplex3dOptions::Point_3 + * @param[in] x_min Iso-oriented cuboid x_min. + * @param[in] y_min Iso-oriented cuboid y_min. + * @param[in] z_min Iso-oriented cuboid z_min. + * @param[in] x_max Iso-oriented cuboid x_max. + * @param[in] y_max Iso-oriented cuboid y_max. + * @param[in] z_max Iso-oriented cuboid z_max. + * + * @pre Available if AlphaComplex3dOptions is `Weighted_periodic_alpha_shapes_3d`. + * + * The type InputPointRange must be a range for which std::begin and + * std::end return input iterators on a AlphaComplex3dOptions::Point_3. + * The type WeightRange must be a range for which std::begin and + * std::end return an input iterator on a AlphaComplex3dOptions::Alpha_shape_3::FT. + * The type of x_min, y_min, z_min, x_max, y_max and z_max is AlphaComplex3dOptions::Alpha_shape_3::FT. + */ + template<typename InputPointRange , typename WeightRange> + Alpha_complex_3d(const InputPointRange& points, WeightRange weights, + Alpha_value_type x_min, Alpha_value_type y_min, Alpha_value_type z_min, + Alpha_value_type x_max, Alpha_value_type y_max, Alpha_value_type z_max) { + static_assert(AlphaComplex3dOptions::weighted, + "This constructor is not available for non-weighted versions of Alpha_complex_3d"); + static_assert(AlphaComplex3dOptions::periodic, + "This constructor is not available for non-periodic versions of Alpha_complex_3d"); + GUDHI_CHECK((weights.size() == points.size()), + std::invalid_argument("Points number in range different from weights range number")); + // Checking if the cuboid is the same in x,y and z direction. If not, CGAL will not process it. + GUDHI_CHECK((x_max - x_min == y_max - y_min) && + (x_max - x_min == z_max - z_min) && + (z_max - z_min == y_max - y_min), + std::invalid_argument("The size of the cuboid in every directions is not the same.")); + + using Weighted_point_3 = typename AlphaComplex3dOptions::Weighted_point_3; + std::vector<Weighted_point_3> weighted_points_3; + + std::size_t index = 0; + weighted_points_3.reserve(points.size()); + +#ifdef GUDHI_DEBUG + // Defined in GUDHI_DEBUG to avoid unused variable warning for GUDHI_CHECK + double maximal_possible_weight = 0.015625 * (x_max - x_min) * (x_max - x_min); +#endif + + while ((index < weights.size()) && (index < points.size())) { + GUDHI_CHECK((weights[index] < maximal_possible_weight) && (weights[index] >= 0), + std::invalid_argument("Invalid weight at line" + std::to_string(index + 1) + + ". Must be positive and less than maximal possible weight = 1/64*cuboid length " + "squared, which is not an acceptable input.")); + weighted_points_3.push_back(Weighted_point_3(points[index], weights[index])); + index++; + } + + using Periodic_delaunay_triangulation_3 = typename AlphaComplex3dOptions::Periodic_delaunay_triangulation_3; + using Iso_cuboid_3 = typename AlphaComplex3dOptions::Iso_cuboid_3; + // Define the periodic cube + Periodic_delaunay_triangulation_3 pdt(Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max)); + // Heuristic for inserting large point sets (if pts is reasonably large) + pdt.insert(std::begin(weighted_points_3), std::end(weighted_points_3), true); + // As pdt won't be modified anymore switch to 1-sheeted cover if possible + if (!pdt.is_triangulation_in_1_sheet()) { + throw std::invalid_argument("Unable to construct a triangulation within a single periodic domain."); + } + pdt.convert_to_1_sheeted_covering(); + + // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode + // Maybe need to set it to GENERAL mode + alpha_shape_3_ptr_ = std::unique_ptr<Alpha_shape_3>(new Alpha_shape_3(pdt, 0, + Alpha_shape_3::GENERAL)); + + Dispatch dispatcher = CGAL::dispatch_output<CGAL::Object, Alpha_value_type>(std::back_inserter(objects_), + std::back_inserter(alpha_values_)); + + alpha_shape_3_ptr_->filtration_with_alpha_values(dispatcher); +#ifdef DEBUG_TRACES + std::cout << "filtration_with_alpha_values returns : " << objects_.size() << " objects" << std::endl; +#endif // DEBUG_TRACES + } + + + template <typename SimplicialComplexForAlpha3d> + bool create_complex(SimplicialComplexForAlpha3d& complex) { + using Filtration_value = typename SimplicialComplexForAlpha3d::Filtration_value; + return create_complex(complex, std::numeric_limits<Filtration_value>::infinity()); + } + + /** \brief Inserts all Delaunay triangulation into the simplicial complex. + * It also computes the filtration values accordingly to the \ref createcomplexalgorithm + * + * \tparam SimplicialComplexForAlpha3d must meet `SimplicialComplexForAlpha3d` concept. + * + * @param[in] complex SimplicialComplexForAlpha3d to be created. + * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$. + * + * @return true if creation succeeds, false otherwise. + * + * @pre The simplicial complex must be empty (no vertices) + * + * Initialization can be launched once. + */ + template <typename SimplicialComplexForAlpha3d> + bool create_complex(SimplicialComplexForAlpha3d& complex, + typename SimplicialComplexForAlpha3d::Filtration_value max_alpha_square) { + if (complex.num_vertices() > 0) { + std::cerr << "Alpha_complex_3d create_complex - complex is not empty\n"; + return false; // ----- >> + } + + using Filtration_value = typename SimplicialComplexForAlpha3d::Filtration_value; + using Complex_vertex_handle = typename SimplicialComplexForAlpha3d::Vertex_handle; + using Alpha_shape_simplex_tree_map = std::map<Alpha_vertex_handle, + Complex_vertex_handle>; + using Simplex_tree_vector_vertex = std::vector<Complex_vertex_handle>; + +#ifdef DEBUG_TRACES + std::size_t count_vertices = 0; + std::size_t count_edges = 0; + std::size_t count_facets = 0; + std::size_t count_cells = 0; +#endif // DEBUG_TRACES + + Alpha_shape_simplex_tree_map map_cgal_simplex_tree; + auto the_alpha_value_iterator = alpha_values_.begin(); + for (auto object_iterator : objects_) { + Vertex_list vertex_list; + + // Retrieve Alpha shape vertex list from object + if (const Cell_handle *cell = CGAL::object_cast<Cell_handle>(&object_iterator)) { + for (auto i = 0; i < 4; i++) { +#ifdef DEBUG_TRACES + std::cout << "from cell[" << i << "]=" << (*cell)->vertex(i)->point() << std::endl; +#endif // DEBUG_TRACES + vertex_list.push_back((*cell)->vertex(i)); + } +#ifdef DEBUG_TRACES + count_cells++; +#endif // DEBUG_TRACES + } else if (const Facet *facet = CGAL::object_cast<Facet>(&object_iterator)) { + for (auto i = 0; i < 4; i++) { + if ((*facet).second != i) { +#ifdef DEBUG_TRACES + std::cout << "from facet=[" << i << "]" << (*facet).first->vertex(i)->point() << std::endl; +#endif // DEBUG_TRACES + vertex_list.push_back((*facet).first->vertex(i)); + } + } +#ifdef DEBUG_TRACES + count_facets++; +#endif // DEBUG_TRACES + } else if (const Edge *edge = CGAL::object_cast<Edge>(&object_iterator)) { + for (auto i : {(*edge).second, (*edge).third}) { +#ifdef DEBUG_TRACES + std::cout << "from edge[" << i << "]=" << (*edge).first->vertex(i)->point() << std::endl; +#endif // DEBUG_TRACES + vertex_list.push_back((*edge).first->vertex(i)); + } +#ifdef DEBUG_TRACES + count_edges++; +#endif // DEBUG_TRACES + } else if (const Alpha_vertex_handle *vertex = CGAL::object_cast<Alpha_vertex_handle>(&object_iterator)) { +#ifdef DEBUG_TRACES + count_vertices++; + std::cout << "from vertex=" << (*vertex)->point() << std::endl; +#endif // DEBUG_TRACES + vertex_list.push_back((*vertex)); + } + // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex + Simplex_tree_vector_vertex the_simplex; + for (auto the_alpha_shape_vertex : vertex_list) { + auto the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex); + if (the_map_iterator == map_cgal_simplex_tree.end()) { + // alpha shape not found + Complex_vertex_handle vertex = map_cgal_simplex_tree.size(); +#ifdef DEBUG_TRACES + std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl; +#endif // DEBUG_TRACES + the_simplex.push_back(vertex); + map_cgal_simplex_tree.emplace(the_alpha_shape_vertex, vertex); + } else { + // alpha shape found + Complex_vertex_handle vertex = the_map_iterator->second; +#ifdef DEBUG_TRACES + std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl; +#endif // DEBUG_TRACES + the_simplex.push_back(vertex); + } + } + // Construction of the simplex_tree + //Alpha_value_type filtr; + Filtration_value filtr = + AlphaComplex3dOptions::template value_from_iterator<Filtration_value, + typename std::vector<Alpha_value_type>::iterator> + (the_alpha_value_iterator); +#ifdef DEBUG_TRACES + std::cout << "filtration = " << filtr << std::endl; +#endif // DEBUG_TRACES + complex.insert_simplex(the_simplex, static_cast<Filtration_value>(filtr)); + GUDHI_CHECK(the_alpha_value_iterator != alpha_values_.end(), "CGAL provided more simplices than values"); + ++the_alpha_value_iterator; + } + +#ifdef DEBUG_TRACES + std::cout << "vertices \t" << count_vertices << std::endl; + std::cout << "edges \t\t" << count_edges << std::endl; + std::cout << "facets \t\t" << count_facets << std::endl; + std::cout << "cells \t\t" << count_cells << std::endl; +#endif // DEBUG_TRACES + // -------------------------------------------------------------------------------------------- + // 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: + // Needs to store alpha_shape_3_ptr_ as objects_ and alpha_shape_3_ptr_ are freed with alpha_shape_3_ptr_ + std::unique_ptr<Alpha_shape_3> alpha_shape_3_ptr_; + std::vector<CGAL::Object> objects_; + std::vector<Alpha_value_type> alpha_values_; + +}; + +} // namespace alpha_complex + +} // namespace Gudhi + +#endif // ALPHA_COMPLEX_3D_H_ |