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diff --git a/include/gudhi/Tangential_complex.h b/include/gudhi/Tangential_complex.h new file mode 100644 index 00000000..cfc82eb1 --- /dev/null +++ b/include/gudhi/Tangential_complex.h @@ -0,0 +1,2276 @@ +/* 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): Clement Jamin + * + * Copyright (C) 2016 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 TANGENTIAL_COMPLEX_H_ +#define TANGENTIAL_COMPLEX_H_ + +#include <gudhi/Tangential_complex/config.h> +#include <gudhi/Tangential_complex/Simplicial_complex.h> +#include <gudhi/Tangential_complex/utilities.h> +#include <gudhi/Kd_tree_search.h> +#include <gudhi/console_color.h> +#include <gudhi/Clock.h> +#include <gudhi/Simplex_tree.h> + +#include <CGAL/Default.h> +#include <CGAL/Dimension.h> +#include <CGAL/function_objects.h> // for CGAL::Identity +#include <CGAL/Epick_d.h> +#include <CGAL/Regular_triangulation_traits_adapter.h> +#include <CGAL/Regular_triangulation.h> +#include <CGAL/Delaunay_triangulation.h> +#include <CGAL/Combination_enumerator.h> +#include <CGAL/point_generators_d.h> + +#include <Eigen/Core> +#include <Eigen/Eigen> + +#include <boost/optional.hpp> +#include <boost/iterator/transform_iterator.hpp> +#include <boost/range/adaptor/transformed.hpp> +#include <boost/range/counting_range.hpp> +#include <boost/math/special_functions/factorials.hpp> +#include <boost/container/flat_set.hpp> + +#include <tuple> +#include <vector> +#include <set> +#include <utility> +#include <sstream> +#include <iostream> +#include <limits> +#include <algorithm> +#include <functional> +#include <iterator> +#include <cmath> // for std::sqrt +#include <string> +#include <cstddef> // for std::size_t + +#ifdef GUDHI_USE_TBB +#include <tbb/parallel_for.h> +#include <tbb/combinable.h> +#include <tbb/mutex.h> +#endif + +// #define GUDHI_TC_EXPORT_NORMALS // Only for 3D surfaces (k=2, d=3) + +namespace sps = Gudhi::spatial_searching; + +namespace Gudhi { + +namespace tangential_complex { + +using namespace internal; + +class Vertex_data { + public: + Vertex_data(std::size_t data = (std::numeric_limits<std::size_t>::max)()) + : m_data(data) { } + + operator std::size_t() { + return m_data; + } + + operator std::size_t() const { + return m_data; + } + + private: + std::size_t m_data; +}; + +/** + * \class Tangential_complex Tangential_complex.h gudhi/Tangential_complex.h + * \brief Tangential complex data structure. + * + * \ingroup tangential_complex + * + * \details + * The class Tangential_complex represents a tangential complex. + * After the computation of the complex, an optional post-processing called perturbation can + * be run to attempt to remove inconsistencies. + * + * \tparam Kernel_ requires a <a target="_blank" + * href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> class, which + * can be static if you know the ambiant dimension at compile-time, or dynamic if you don't. + * \tparam DimensionTag can be either <a target="_blank" + * href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dimension__tag.html">Dimension_tag<d></a> + * if you know the intrinsic dimension at compile-time, + * or <a target="_blank" + * href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dynamic__dimension__tag.html">CGAL::Dynamic_dimension_tag</a> + * if you don't. + * \tparam Concurrency_tag enables sequential versus parallel computation. Possible values are `CGAL::Parallel_tag` (the default) and `CGAL::Sequential_tag`. + * \tparam Triangulation_ is the type used for storing the local regular triangulations. We highly recommend to use the default value (`CGAL::Regular_triangulation`). + * + */ +template +< + typename Kernel_, // ambiant kernel + typename DimensionTag, // intrinsic dimension + typename Concurrency_tag = CGAL::Parallel_tag, + typename Triangulation_ = CGAL::Default +> +class Tangential_complex { + typedef Kernel_ K; + typedef typename K::FT FT; + typedef typename K::Point_d Point; + typedef typename K::Weighted_point_d Weighted_point; + typedef typename K::Vector_d Vector; + + typedef typename CGAL::Default::Get + < + Triangulation_, + CGAL::Regular_triangulation + < + CGAL::Epick_d<DimensionTag>, + CGAL::Triangulation_data_structure + < + typename CGAL::Epick_d<DimensionTag>::Dimension, + CGAL::Triangulation_vertex + < + CGAL::Regular_triangulation_traits_adapter< CGAL::Epick_d<DimensionTag> >, Vertex_data + >, + CGAL::Triangulation_full_cell<CGAL::Regular_triangulation_traits_adapter< CGAL::Epick_d<DimensionTag> > > + > + > + >::type Triangulation; + typedef typename Triangulation::Geom_traits Tr_traits; + typedef typename Triangulation::Weighted_point Tr_point; + typedef typename Triangulation::Bare_point Tr_bare_point; + typedef typename Triangulation::Vertex_handle Tr_vertex_handle; + typedef typename Triangulation::Full_cell_handle Tr_full_cell_handle; + typedef typename Tr_traits::Vector_d Tr_vector; + +#if defined(GUDHI_USE_TBB) + typedef tbb::mutex Mutex_for_perturb; + typedef Vector Translation_for_perturb; + typedef std::vector<Atomic_wrapper<FT> > Weights; +#else + typedef Vector Translation_for_perturb; + typedef std::vector<FT> Weights; +#endif + typedef std::vector<Translation_for_perturb> Translations_for_perturb; + + // Store a local triangulation and a handle to its center vertex + + struct Tr_and_VH { + public: + Tr_and_VH() + : m_tr(NULL) { } + + Tr_and_VH(int dim) + : m_tr(new Triangulation(dim)) { } + + ~Tr_and_VH() { + destroy_triangulation(); + } + + Triangulation & construct_triangulation(int dim) { + delete m_tr; + m_tr = new Triangulation(dim); + return tr(); + } + + void destroy_triangulation() { + delete m_tr; + m_tr = NULL; + } + + Triangulation & tr() { + return *m_tr; + } + + Triangulation const& tr() const { + return *m_tr; + } + + Tr_vertex_handle const& center_vertex() const { + return m_center_vertex; + } + + Tr_vertex_handle & center_vertex() { + return m_center_vertex; + } + + private: + Triangulation* m_tr; + Tr_vertex_handle m_center_vertex; + }; + + public: + typedef Basis<K> Tangent_space_basis; + typedef Basis<K> Orthogonal_space_basis; + typedef std::vector<Tangent_space_basis> TS_container; + typedef std::vector<Orthogonal_space_basis> OS_container; + + typedef std::vector<Point> Points; + + typedef boost::container::flat_set<std::size_t> Simplex; + typedef std::set<Simplex> Simplex_set; + + private: + typedef sps::Kd_tree_search<K, Points> Points_ds; + typedef typename Points_ds::KNS_range KNS_range; + typedef typename Points_ds::INS_range INS_range; + + typedef std::vector<Tr_and_VH> Tr_container; + typedef std::vector<Vector> Vectors; + + // An Incident_simplex is the list of the vertex indices + // except the center vertex + typedef boost::container::flat_set<std::size_t> Incident_simplex; + typedef std::vector<Incident_simplex> Star; + typedef std::vector<Star> Stars_container; + + // For transform_iterator + + static const Tr_point &vertex_handle_to_point(Tr_vertex_handle vh) { + return vh->point(); + } + + template <typename P, typename VH> + static const P &vertex_handle_to_point(VH vh) { + return vh->point(); + } + + public: + typedef internal::Simplicial_complex Simplicial_complex; + + /** \brief Constructor from a range of points. + * Points are copied into the instance, and a search data structure is initialized. + * Note the complex is not computed: `compute_tangential_complex` must be called after the creation + * of the object. + * + * @param[in] points Range of points (`Point_range::value_type` must be the same as `Kernel_::Point_d`). + * @param[in] intrinsic_dimension Intrinsic dimension of the manifold. + * @param[in] k Kernel instance. + */ + template <typename Point_range> + Tangential_complex(Point_range points, + int intrinsic_dimension, +#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM + InputIterator first_for_tse, InputIterator last_for_tse, +#endif + const K &k = K() + ) + : m_k(k), + m_intrinsic_dim(intrinsic_dimension), + m_ambient_dim(points.empty() ? 0 : k.point_dimension_d_object()(*points.begin())), + m_points(points.begin(), points.end()), + m_weights(m_points.size(), FT(0)) +#if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION) + , m_p_perturb_mutexes(NULL) +#endif + , m_points_ds(m_points) + , m_last_max_perturb(0.) + , m_are_tangent_spaces_computed(m_points.size(), false) + , m_tangent_spaces(m_points.size(), Tangent_space_basis()) +#ifdef GUDHI_TC_EXPORT_NORMALS + , m_orth_spaces(m_points.size(), Orthogonal_space_basis()) +#endif +#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM + , m_points_for_tse(first_for_tse, last_for_tse) + , m_points_ds_for_tse(m_points_for_tse) +#endif + { } + + /// Destructor + ~Tangential_complex() { +#if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION) + delete [] m_p_perturb_mutexes; +#endif + } + + /// Returns the intrinsic dimension of the manifold. + int intrinsic_dimension() const { + return m_intrinsic_dim; + } + + /// Returns the ambient dimension. + int ambient_dimension() const { + return m_ambient_dim; + } + + Points const& points() const { + return m_points; + } + + /** \brief Returns the point corresponding to the vertex given as parameter. + * + * @param[in] vertex Vertex handle of the point to retrieve. + * @return The point found. + */ + Point get_point(std::size_t vertex) const { + return m_points[vertex]; + } + + /** \brief Returns the perturbed position of the point corresponding to the vertex given as parameter. + * + * @param[in] vertex Vertex handle of the point to retrieve. + * @return The perturbed position of the point found. + */ + Point get_perturbed_point(std::size_t vertex) const { + return compute_perturbed_point(vertex); + } + + /// Returns the number of vertices. + + std::size_t number_of_vertices() const { + return m_points.size(); + } + + void set_weights(const Weights& weights) { + m_weights = weights; + } + + void set_tangent_planes(const TS_container& tangent_spaces +#ifdef GUDHI_TC_EXPORT_NORMALS + , const OS_container& orthogonal_spaces +#endif + ) { +#ifdef GUDHI_TC_EXPORT_NORMALS + GUDHI_CHECK( + m_points.size() == tangent_spaces.size() + && m_points.size() == orthogonal_spaces.size(), + std::logic_error("Wrong sizes")); +#else + GUDHI_CHECK( + m_points.size() == tangent_spaces.size(), + std::logic_error("Wrong sizes")); +#endif + m_tangent_spaces = tangent_spaces; +#ifdef GUDHI_TC_EXPORT_NORMALS + m_orth_spaces = orthogonal_spaces; +#endif + for (std::size_t i = 0; i < m_points.size(); ++i) + m_are_tangent_spaces_computed[i] = true; + } + + /// Computes the tangential complex. + void compute_tangential_complex() { +#ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS + std::cerr << red << "WARNING: GUDHI_TC_PERFORM_EXTRA_CHECKS is defined. " + << "Computation might be slower than usual.\n" << white; +#endif + +#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB) + Gudhi::Clock t; +#endif + + // We need to do that because we don't want the container to copy the + // already-computed triangulations (while resizing) since it would + // invalidate the vertex handles stored beside the triangulations + m_triangulations.resize(m_points.size()); + m_stars.resize(m_points.size()); + m_squared_star_spheres_radii_incl_margin.resize(m_points.size(), FT(-1)); +#ifdef GUDHI_TC_PERTURB_POSITION + if (m_points.empty()) + m_translations.clear(); + else + m_translations.resize(m_points.size(), + m_k.construct_vector_d_object()(m_ambient_dim)); +#if defined(GUDHI_USE_TBB) + delete [] m_p_perturb_mutexes; + m_p_perturb_mutexes = new Mutex_for_perturb[m_points.size()]; +#endif +#endif + +#ifdef GUDHI_USE_TBB + // Parallel + if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) { + tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), + Compute_tangent_triangulation(*this)); + } else { +#endif // GUDHI_USE_TBB + // Sequential + for (std::size_t i = 0; i < m_points.size(); ++i) + compute_tangent_triangulation(i); +#ifdef GUDHI_USE_TBB + } +#endif // GUDHI_USE_TBB + +#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB) + t.end(); + std::cerr << "Tangential complex computed in " << t.num_seconds() + << " seconds.\n"; +#endif + } + + /// \brief Type returned by `Tangential_complex::fix_inconsistencies_using_perturbation`. + struct Fix_inconsistencies_info { + /// `true` if all inconsistencies could be removed, `false` if the time limit has been reached before + bool success = false; + /// number of steps performed + unsigned int num_steps = 0; + /// initial number of inconsistent stars + std::size_t initial_num_inconsistent_stars = 0; + /// best number of inconsistent stars during the process + std::size_t best_num_inconsistent_stars = 0; + /// final number of inconsistent stars + std::size_t final_num_inconsistent_stars = 0; + }; + + /** \brief Attempts to fix inconsistencies by perturbing the point positions. + * + * @param[in] max_perturb Maximum length of the translations used by the perturbation. + * @param[in] time_limit Time limit in seconds. If -1, no time limit is set. + */ + Fix_inconsistencies_info fix_inconsistencies_using_perturbation(double max_perturb, double time_limit = -1.) { + Fix_inconsistencies_info info; + + if (time_limit == 0.) + return info; + + Gudhi::Clock t; + +#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES + std::tuple<std::size_t, std::size_t, std::size_t> stats_before = + number_of_inconsistent_simplices(false); + + if (std::get<1>(stats_before) == 0) { +#ifdef DEBUG_TRACES + std::cerr << "Nothing to fix.\n"; +#endif + info.success = false; + return info; + } +#endif // GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES + + m_last_max_perturb = max_perturb; + + bool done = false; + info.best_num_inconsistent_stars = m_triangulations.size(); + info.num_steps = 0; + while (!done) { +#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES + std::cerr + << "\nBefore fix step:\n" + << " * Total number of simplices in stars (incl. duplicates): " + << std::get<0>(stats_before) << "\n" + << " * Num inconsistent simplices in stars (incl. duplicates): " + << red << std::get<1>(stats_before) << white << " (" + << 100. * std::get<1>(stats_before) / std::get<0>(stats_before) << "%)\n" + << " * Number of stars containing inconsistent simplices: " + << red << std::get<2>(stats_before) << white << " (" + << 100. * std::get<2>(stats_before) / m_points.size() << "%)\n"; +#endif + +#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) + std::cerr << yellow + << "\nAttempt to fix inconsistencies using perturbations - step #" + << info.num_steps + 1 << "... " << white; +#endif + + std::size_t num_inconsistent_stars = 0; + std::vector<std::size_t> updated_points; + +#ifdef GUDHI_TC_PROFILING + Gudhi::Clock t_fix_step; +#endif + + // Parallel +#if defined(GUDHI_USE_TBB) + if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) { + tbb::combinable<std::size_t> num_inconsistencies; + tbb::combinable<std::vector<std::size_t> > tls_updated_points; + tbb::parallel_for( + tbb::blocked_range<size_t>(0, m_triangulations.size()), + Try_to_solve_inconsistencies_in_a_local_triangulation(*this, max_perturb, + num_inconsistencies, + tls_updated_points)); + num_inconsistent_stars = + num_inconsistencies.combine(std::plus<std::size_t>()); + updated_points = tls_updated_points.combine( + [](std::vector<std::size_t> const& x, + std::vector<std::size_t> const& y) { + std::vector<std::size_t> res; + res.reserve(x.size() + y.size()); + res.insert(res.end(), x.begin(), x.end()); + res.insert(res.end(), y.begin(), y.end()); + return res; + }); + } else { +#endif // GUDHI_USE_TBB + // Sequential + for (std::size_t i = 0; i < m_triangulations.size(); ++i) { + num_inconsistent_stars += + try_to_solve_inconsistencies_in_a_local_triangulation(i, max_perturb, + std::back_inserter(updated_points)); + } +#if defined(GUDHI_USE_TBB) + } +#endif // GUDHI_USE_TBB + +#ifdef GUDHI_TC_PROFILING + t_fix_step.end(); +#endif + +#if defined(GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES) || defined(DEBUG_TRACES) + std::cerr + << "\nEncountered during fix:\n" + << " * Num stars containing inconsistent simplices: " + << red << num_inconsistent_stars << white + << " (" << 100. * num_inconsistent_stars / m_points.size() << "%)\n"; +#endif + +#ifdef GUDHI_TC_PROFILING + std::cerr << yellow << "done in " << t_fix_step.num_seconds() + << " seconds.\n" << white; +#elif defined(DEBUG_TRACES) + std::cerr << yellow << "done.\n" << white; +#endif + + if (num_inconsistent_stars > 0) + refresh_tangential_complex(updated_points); + +#ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS + // Confirm that all stars were actually refreshed + std::size_t num_inc_1 = + std::get<1>(number_of_inconsistent_simplices(false)); + refresh_tangential_complex(); + std::size_t num_inc_2 = + std::get<1>(number_of_inconsistent_simplices(false)); + if (num_inc_1 != num_inc_2) + std::cerr << red << "REFRESHMENT CHECK: FAILED. (" + << num_inc_1 << " vs " << num_inc_2 << ")\n" << white; + else + std::cerr << green << "REFRESHMENT CHECK: PASSED.\n" << white; +#endif + +#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES + std::tuple<std::size_t, std::size_t, std::size_t> stats_after = + number_of_inconsistent_simplices(false); + + std::cerr + << "\nAfter fix:\n" + << " * Total number of simplices in stars (incl. duplicates): " + << std::get<0>(stats_after) << "\n" + << " * Num inconsistent simplices in stars (incl. duplicates): " + << red << std::get<1>(stats_after) << white << " (" + << 100. * std::get<1>(stats_after) / std::get<0>(stats_after) << "%)\n" + << " * Number of stars containing inconsistent simplices: " + << red << std::get<2>(stats_after) << white << " (" + << 100. * std::get<2>(stats_after) / m_points.size() << "%)\n"; + + stats_before = stats_after; +#endif + + if (info.num_steps == 0) + info.initial_num_inconsistent_stars = num_inconsistent_stars; + + if (num_inconsistent_stars < info.best_num_inconsistent_stars) + info.best_num_inconsistent_stars = num_inconsistent_stars; + + info.final_num_inconsistent_stars = num_inconsistent_stars; + + done = (num_inconsistent_stars == 0); + if (!done) { + ++info.num_steps; + if (time_limit > 0. && t.num_seconds() > time_limit) { +#ifdef DEBUG_TRACES + std::cerr << red << "Time limit reached.\n" << white; +#endif + info.success = false; + return info; + } + } + } + +#ifdef DEBUG_TRACES + std::cerr << green << "Fixed!\n" << white; +#endif + info.success = true; + return info; + } + + /// \brief Type returned by `Tangential_complex::number_of_inconsistent_simplices`. + struct Num_inconsistencies { + /// Total number of simplices in stars (including duplicates that appear in several stars) + std::size_t num_simplices = 0; + /// Number of inconsistent simplices + std::size_t num_inconsistent_simplices = 0; + /// Number of stars containing at least one inconsistent simplex + std::size_t num_inconsistent_stars = 0; + }; + + /// Returns the number of inconsistencies + /// @param[in] verbose If true, outputs a message into `std::cerr`. + + Num_inconsistencies + number_of_inconsistent_simplices( +#ifdef DEBUG_TRACES + bool verbose = true +#else + bool verbose = false +#endif + ) const { + Num_inconsistencies stats; + + // For each triangulation + for (std::size_t idx = 0; idx < m_points.size(); ++idx) { + bool is_star_inconsistent = false; + + // For each cell + Star::const_iterator it_inc_simplex = m_stars[idx].begin(); + Star::const_iterator it_inc_simplex_end = m_stars[idx].end(); + for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) { + // Don't check infinite cells + if (is_infinite(*it_inc_simplex)) + continue; + + Simplex c = *it_inc_simplex; + c.insert(idx); // Add the missing index + + if (!is_simplex_consistent(c)) { + ++stats.num_inconsistent_simplices; + is_star_inconsistent = true; + } + + ++stats.num_simplices; + } + stats.num_inconsistent_stars += is_star_inconsistent; + } + + if (verbose) { + std::cerr + << "\n==========================================================\n" + << "Inconsistencies:\n" + << " * Total number of simplices in stars (incl. duplicates): " + << stats.num_simplices << "\n" + << " * Number of inconsistent simplices in stars (incl. duplicates): " + << stats.num_inconsistent_simplices << " (" + << 100. * stats.num_inconsistent_simplices / stats.num_simplices << "%)\n" + << " * Number of stars containing inconsistent simplices: " + << stats.num_inconsistent_stars << " (" + << 100. * stats.num_inconsistent_stars / m_points.size() << "%)\n" + << "==========================================================\n"; + } + + return stats; + } + + /** \brief Exports the complex into a Simplex_tree. + * + * \tparam Simplex_tree_ must be a `Simplex_tree`. + * + * @param[out] tree The result, where each `Vertex_handle` is the index of the + * corresponding point in the range provided to the constructor (it can also be + * retrieved through the `Tangential_complex::get_point` function. + * @param[in] export_inconsistent_simplices Also export inconsistent simplices or not? + * @return The maximal dimension of the simplices. + */ + template <typename Simplex_tree_> + int create_complex(Simplex_tree_ &tree + , bool export_inconsistent_simplices = true + /// \cond ADVANCED_PARAMETERS + , bool export_infinite_simplices = false + , Simplex_set *p_inconsistent_simplices = NULL + /// \endcond + ) const { +#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) + std::cerr << yellow + << "\nExporting the TC as a Simplex_tree... " << white; +#endif +#ifdef GUDHI_TC_PROFILING + Gudhi::Clock t; +#endif + + int max_dim = -1; + + // For each triangulation + for (std::size_t idx = 0; idx < m_points.size(); ++idx) { + // For each cell of the star + Star::const_iterator it_inc_simplex = m_stars[idx].begin(); + Star::const_iterator it_inc_simplex_end = m_stars[idx].end(); + for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) { + Simplex c = *it_inc_simplex; + + // Don't export infinite cells + if (!export_infinite_simplices && is_infinite(c)) + continue; + + if (!export_inconsistent_simplices && !is_simplex_consistent(c)) + continue; + + if (static_cast<int> (c.size()) > max_dim) + max_dim = static_cast<int> (c.size()); + // Add the missing center vertex + c.insert(idx); + + // Try to insert the simplex + bool inserted = tree.insert_simplex_and_subfaces(c).second; + + // Inconsistent? + if (p_inconsistent_simplices && inserted && !is_simplex_consistent(c)) { + p_inconsistent_simplices->insert(c); + } + } + } + +#ifdef GUDHI_TC_PROFILING + t.end(); + std::cerr << yellow << "done in " << t.num_seconds() + << " seconds.\n" << white; +#elif defined(DEBUG_TRACES) + std::cerr << yellow << "done.\n" << white; +#endif + + return max_dim; + } + + // First clears the complex then exports the TC into it + // Returns the max dimension of the simplices + // check_lower_and_higher_dim_simplices : 0 (false), 1 (true), 2 (auto) + // If the check is enabled, the function: + // - won't insert the simplex if it is already in a higher dim simplex + // - will erase any lower-dim simplices that are faces of the new simplex + // "auto" (= 2) will enable the check as a soon as it encounters a + // simplex whose dimension is different from the previous ones. + // N.B.: The check is quite expensive. + + int create_complex(Simplicial_complex &complex, + bool export_inconsistent_simplices = true, + bool export_infinite_simplices = false, + int check_lower_and_higher_dim_simplices = 2, + Simplex_set *p_inconsistent_simplices = NULL) const { +#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) + std::cerr << yellow + << "\nExporting the TC as a Simplicial_complex... " << white; +#endif +#ifdef GUDHI_TC_PROFILING + Gudhi::Clock t; +#endif + + int max_dim = -1; + complex.clear(); + + // For each triangulation + for (std::size_t idx = 0; idx < m_points.size(); ++idx) { + // For each cell of the star + Star::const_iterator it_inc_simplex = m_stars[idx].begin(); + Star::const_iterator it_inc_simplex_end = m_stars[idx].end(); + for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) { + Simplex c = *it_inc_simplex; + + // Don't export infinite cells + if (!export_infinite_simplices && is_infinite(c)) + continue; + + if (!export_inconsistent_simplices && !is_simplex_consistent(c)) + continue; + + // Unusual simplex dim? + if (check_lower_and_higher_dim_simplices == 2 + && max_dim != -1 + && static_cast<int> (c.size()) != max_dim) { + // Let's activate the check + std::cerr << red << + "Info: check_lower_and_higher_dim_simplices ACTIVATED. " + "Export might be take some time...\n" << white; + check_lower_and_higher_dim_simplices = 1; + } + + if (static_cast<int> (c.size()) > max_dim) + max_dim = static_cast<int> (c.size()); + // Add the missing center vertex + c.insert(idx); + + // Try to insert the simplex + bool added = + complex.add_simplex(c, check_lower_and_higher_dim_simplices == 1); + + // Inconsistent? + if (p_inconsistent_simplices && added && !is_simplex_consistent(c)) { + p_inconsistent_simplices->insert(c); + } + } + } + +#ifdef GUDHI_TC_PROFILING + t.end(); + std::cerr << yellow << "done in " << t.num_seconds() + << " seconds.\n" << white; +#elif defined(DEBUG_TRACES) + std::cerr << yellow << "done.\n" << white; +#endif + + return max_dim; + } + + template<typename ProjectionFunctor = CGAL::Identity<Point> > + std::ostream &export_to_off( + const Simplicial_complex &complex, std::ostream & os, + Simplex_set const *p_simpl_to_color_in_red = NULL, + Simplex_set const *p_simpl_to_color_in_green = NULL, + Simplex_set const *p_simpl_to_color_in_blue = NULL, + ProjectionFunctor const& point_projection = ProjectionFunctor()) + const { + return export_to_off( + os, false, p_simpl_to_color_in_red, p_simpl_to_color_in_green, + p_simpl_to_color_in_blue, &complex, point_projection); + } + + template<typename ProjectionFunctor = CGAL::Identity<Point> > + std::ostream &export_to_off( + std::ostream & os, bool color_inconsistencies = false, + Simplex_set const *p_simpl_to_color_in_red = NULL, + Simplex_set const *p_simpl_to_color_in_green = NULL, + Simplex_set const *p_simpl_to_color_in_blue = NULL, + const Simplicial_complex *p_complex = NULL, + ProjectionFunctor const& point_projection = ProjectionFunctor()) const { + if (m_points.empty()) + return os; + + if (m_ambient_dim < 2) { + std::cerr << "Error: export_to_off => ambient dimension should be >= 2.\n"; + os << "Error: export_to_off => ambient dimension should be >= 2.\n"; + return os; + } + if (m_ambient_dim > 3) { + std::cerr << "Warning: export_to_off => ambient dimension should be " + "<= 3. Only the first 3 coordinates will be exported.\n"; + } + + if (m_intrinsic_dim < 1 || m_intrinsic_dim > 3) { + std::cerr << "Error: export_to_off => intrinsic dimension should be " + "between 1 and 3.\n"; + os << "Error: export_to_off => intrinsic dimension should be " + "between 1 and 3.\n"; + return os; + } + + std::stringstream output; + std::size_t num_simplices, num_vertices; + export_vertices_to_off(output, num_vertices, false, point_projection); + if (p_complex) { + export_simplices_to_off( + *p_complex, output, num_simplices, p_simpl_to_color_in_red, + p_simpl_to_color_in_green, p_simpl_to_color_in_blue); + } else { + export_simplices_to_off( + output, num_simplices, color_inconsistencies, p_simpl_to_color_in_red, + p_simpl_to_color_in_green, p_simpl_to_color_in_blue); + } + +#ifdef GUDHI_TC_EXPORT_NORMALS + os << "N"; +#endif + + os << "OFF \n" + << num_vertices << " " + << num_simplices << " " + << "0 \n" + << output.str(); + + return os; + } + + private: + void refresh_tangential_complex() { +#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) + std::cerr << yellow << "\nRefreshing TC... " << white; +#endif + +#ifdef GUDHI_TC_PROFILING + Gudhi::Clock t; +#endif +#ifdef GUDHI_USE_TBB + // Parallel + if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) { + tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), + Compute_tangent_triangulation(*this)); + } else { +#endif // GUDHI_USE_TBB + // Sequential + for (std::size_t i = 0; i < m_points.size(); ++i) + compute_tangent_triangulation(i); +#ifdef GUDHI_USE_TBB + } +#endif // GUDHI_USE_TBB + +#ifdef GUDHI_TC_PROFILING + t.end(); + std::cerr << yellow << "done in " << t.num_seconds() + << " seconds.\n" << white; +#elif defined(DEBUG_TRACES) + std::cerr << yellow << "done.\n" << white; +#endif + } + + // If the list of perturbed points is provided, it is much faster + template <typename Point_indices_range> + void refresh_tangential_complex( + Point_indices_range const& perturbed_points_indices) { +#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) + std::cerr << yellow << "\nRefreshing TC... " << white; +#endif + +#ifdef GUDHI_TC_PROFILING + Gudhi::Clock t; +#endif + + // ANN tree containing only the perturbed points + Points_ds updated_pts_ds(m_points, perturbed_points_indices); + +#ifdef GUDHI_USE_TBB + // Parallel + if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) { + tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), + Refresh_tangent_triangulation(*this, updated_pts_ds)); + } else { +#endif // GUDHI_USE_TBB + // Sequential + for (std::size_t i = 0; i < m_points.size(); ++i) + refresh_tangent_triangulation(i, updated_pts_ds); +#ifdef GUDHI_USE_TBB + } +#endif // GUDHI_USE_TBB + +#ifdef GUDHI_TC_PROFILING + t.end(); + std::cerr << yellow << "done in " << t.num_seconds() + << " seconds.\n" << white; +#elif defined(DEBUG_TRACES) + std::cerr << yellow << "done.\n" << white; +#endif + } + + void export_inconsistent_stars_to_OFF_files(std::string const& filename_base) const { + // For each triangulation + for (std::size_t idx = 0; idx < m_points.size(); ++idx) { + // We build a SC along the way in case it's inconsistent + Simplicial_complex sc; + // For each cell + bool is_inconsistent = false; + Star::const_iterator it_inc_simplex = m_stars[idx].begin(); + Star::const_iterator it_inc_simplex_end = m_stars[idx].end(); + for (; it_inc_simplex != it_inc_simplex_end; + ++it_inc_simplex) { + // Skip infinite cells + if (is_infinite(*it_inc_simplex)) + continue; + + Simplex c = *it_inc_simplex; + c.insert(idx); // Add the missing index + + sc.add_simplex(c); + + // If we do not already know this star is inconsistent, test it + if (!is_inconsistent && !is_simplex_consistent(c)) + is_inconsistent = true; + } + + if (is_inconsistent) { + // Export star to OFF file + std::stringstream output_filename; + output_filename << filename_base << "_" << idx << ".off"; + std::ofstream off_stream(output_filename.str().c_str()); + export_to_off(sc, off_stream); + } + } + } + + class Compare_distance_to_ref_point { + public: + Compare_distance_to_ref_point(Point const& ref, K const& k) + : m_ref(ref), m_k(k) { } + + bool operator()(Point const& p1, Point const& p2) { + typename K::Squared_distance_d sqdist = + m_k.squared_distance_d_object(); + return sqdist(p1, m_ref) < sqdist(p2, m_ref); + } + + private: + Point const& m_ref; + K const& m_k; + }; + +#ifdef GUDHI_USE_TBB + // Functor for compute_tangential_complex function + class Compute_tangent_triangulation { + Tangential_complex & m_tc; + + public: + // Constructor + Compute_tangent_triangulation(Tangential_complex &tc) + : m_tc(tc) { } + + // Constructor + Compute_tangent_triangulation(const Compute_tangent_triangulation &ctt) + : m_tc(ctt.m_tc) { } + + // operator() + void operator()(const tbb::blocked_range<size_t>& r) const { + for (size_t i = r.begin(); i != r.end(); ++i) + m_tc.compute_tangent_triangulation(i); + } + }; + + // Functor for refresh_tangential_complex function + class Refresh_tangent_triangulation { + Tangential_complex & m_tc; + Points_ds const& m_updated_pts_ds; + + public: + // Constructor + Refresh_tangent_triangulation(Tangential_complex &tc, Points_ds const& updated_pts_ds) + : m_tc(tc), m_updated_pts_ds(updated_pts_ds) { } + + // Constructor + Refresh_tangent_triangulation(const Refresh_tangent_triangulation &ctt) + : m_tc(ctt.m_tc), m_updated_pts_ds(ctt.m_updated_pts_ds) { } + + // operator() + void operator()(const tbb::blocked_range<size_t>& r) const { + for (size_t i = r.begin(); i != r.end(); ++i) + m_tc.refresh_tangent_triangulation(i, m_updated_pts_ds); + } + }; +#endif // GUDHI_USE_TBB + + bool is_infinite(Simplex const& s) const { + return *s.rbegin() == (std::numeric_limits<std::size_t>::max)(); + } + + // Output: "triangulation" is a Regular Triangulation containing at least the + // star of "center_pt" + // Returns the handle of the center vertex + Tr_vertex_handle compute_star(std::size_t i, const Point ¢er_pt, const Tangent_space_basis &tsb, + Triangulation &triangulation, bool verbose = false) { + int tangent_space_dim = tsb.dimension(); + const Tr_traits &local_tr_traits = triangulation.geom_traits(); + Tr_vertex_handle center_vertex; + + // Kernel functor & objects + typename K::Squared_distance_d k_sqdist = m_k.squared_distance_d_object(); + + // Triangulation's traits functor & objects + typename Tr_traits::Compute_weight_d point_weight = local_tr_traits.compute_weight_d_object(); + typename Tr_traits::Power_center_d power_center = local_tr_traits.power_center_d_object(); + + //*************************************************** + // Build a minimal triangulation in the tangent space + // (we only need the star of p) + //*************************************************** + + // Insert p + Tr_point proj_wp; + if (i == tsb.origin()) { + // Insert {(0, 0, 0...), m_weights[i]} + proj_wp = local_tr_traits.construct_weighted_point_d_object()(local_tr_traits.construct_point_d_object()(tangent_space_dim, CGAL::ORIGIN), + m_weights[i]); + } else { + const Weighted_point& wp = compute_perturbed_weighted_point(i); + proj_wp = project_point_and_compute_weight(wp, tsb, local_tr_traits); + } + + center_vertex = triangulation.insert(proj_wp); + center_vertex->data() = i; + if (verbose) + std::cerr << "* Inserted point #" << i << "\n"; + +#ifdef GUDHI_TC_VERY_VERBOSE + std::size_t num_attempts_to_insert_points = 1; + std::size_t num_inserted_points = 1; +#endif + // const int NUM_NEIGHBORS = 150; + // KNS_range ins_range = m_points_ds.query_k_nearest_neighbors(center_pt, NUM_NEIGHBORS); + INS_range ins_range = m_points_ds.query_incremental_nearest_neighbors(center_pt); + + // While building the local triangulation, we keep the radius + // of the sphere "star sphere" centered at "center_vertex" + // and which contains all the + // circumspheres of the star of "center_vertex" + boost::optional<FT> squared_star_sphere_radius_plus_margin; + + // Insert points until we find a point which is outside "star sphere" + for (auto nn_it = ins_range.begin(); + nn_it != ins_range.end(); + ++nn_it) { + std::size_t neighbor_point_idx = nn_it->first; + + // ith point = p, which is already inserted + if (neighbor_point_idx != i) { + // No need to lock the Mutex_for_perturb here since this will not be + // called while other threads are perturbing the positions + Point neighbor_pt; + FT neighbor_weight; + compute_perturbed_weighted_point(neighbor_point_idx, neighbor_pt, neighbor_weight); + + if (squared_star_sphere_radius_plus_margin && + k_sqdist(center_pt, neighbor_pt) > *squared_star_sphere_radius_plus_margin) + break; + + Tr_point proj_pt = project_point_and_compute_weight(neighbor_pt, neighbor_weight, tsb, + local_tr_traits); + +#ifdef GUDHI_TC_VERY_VERBOSE + ++num_attempts_to_insert_points; +#endif + + + Tr_vertex_handle vh = triangulation.insert_if_in_star(proj_pt, center_vertex); + // Tr_vertex_handle vh = triangulation.insert(proj_pt); + if (vh != Tr_vertex_handle() && vh->data() == (std::numeric_limits<std::size_t>::max)()) { +#ifdef GUDHI_TC_VERY_VERBOSE + ++num_inserted_points; +#endif + if (verbose) + std::cerr << "* Inserted point #" << neighbor_point_idx << "\n"; + + vh->data() = neighbor_point_idx; + + // Let's recompute squared_star_sphere_radius_plus_margin + if (triangulation.current_dimension() >= tangent_space_dim) { + squared_star_sphere_radius_plus_margin = boost::none; + // Get the incident cells and look for the biggest circumsphere + std::vector<Tr_full_cell_handle> incident_cells; + triangulation.incident_full_cells( + center_vertex, + std::back_inserter(incident_cells)); + for (typename std::vector<Tr_full_cell_handle>::iterator cit = + incident_cells.begin(); cit != incident_cells.end(); ++cit) { + Tr_full_cell_handle cell = *cit; + if (triangulation.is_infinite(cell)) { + squared_star_sphere_radius_plus_margin = boost::none; + break; + } else { + // Note that this uses the perturbed point since it uses + // the points of the local triangulation + Tr_point c = power_center(boost::make_transform_iterator(cell->vertices_begin(), + vertex_handle_to_point<Tr_point, + Tr_vertex_handle>), + boost::make_transform_iterator(cell->vertices_end(), + vertex_handle_to_point<Tr_point, + Tr_vertex_handle>)); + + FT sq_power_sphere_diam = 4 * point_weight(c); + + if (!squared_star_sphere_radius_plus_margin || + sq_power_sphere_diam > *squared_star_sphere_radius_plus_margin) { + squared_star_sphere_radius_plus_margin = sq_power_sphere_diam; + } + } + } + + // Let's add the margin, now + // The value depends on whether we perturb weight or position + if (squared_star_sphere_radius_plus_margin) { + // "2*m_last_max_perturb" because both points can be perturbed + squared_star_sphere_radius_plus_margin = CGAL::square(std::sqrt(*squared_star_sphere_radius_plus_margin) + + 2 * m_last_max_perturb); + + // Save it in `m_squared_star_spheres_radii_incl_margin` + m_squared_star_spheres_radii_incl_margin[i] = + *squared_star_sphere_radius_plus_margin; + } else { + m_squared_star_spheres_radii_incl_margin[i] = FT(-1); + } + } + } + } + } + + return center_vertex; + } + + void refresh_tangent_triangulation(std::size_t i, Points_ds const& updated_pts_ds, bool verbose = false) { + if (verbose) + std::cerr << "** Refreshing tangent tri #" << i << " **\n"; + + if (m_squared_star_spheres_radii_incl_margin[i] == FT(-1)) + return compute_tangent_triangulation(i, verbose); + + Point center_point = compute_perturbed_point(i); + // Among updated point, what is the closer from our center point? + std::size_t closest_pt_index = + updated_pts_ds.query_k_nearest_neighbors(center_point, 1, false).begin()->first; + + typename K::Construct_weighted_point_d k_constr_wp = + m_k.construct_weighted_point_d_object(); + typename K::Power_distance_d k_power_dist = m_k.power_distance_d_object(); + + // Construct a weighted point equivalent to the star sphere + Weighted_point star_sphere = k_constr_wp(compute_perturbed_point(i), + m_squared_star_spheres_radii_incl_margin[i]); + Weighted_point closest_updated_point = + compute_perturbed_weighted_point(closest_pt_index); + + // Is the "closest point" inside our star sphere? + if (k_power_dist(star_sphere, closest_updated_point) <= FT(0)) + compute_tangent_triangulation(i, verbose); + } + + void compute_tangent_triangulation(std::size_t i, bool verbose = false) { + if (verbose) + std::cerr << "** Computing tangent tri #" << i << " **\n"; + // std::cerr << "***********************************************\n"; + + // No need to lock the mutex here since this will not be called while + // other threads are perturbing the positions + const Point center_pt = compute_perturbed_point(i); + Tangent_space_basis &tsb = m_tangent_spaces[i]; + + // Estimate the tangent space + if (!m_are_tangent_spaces_computed[i]) { +#ifdef GUDHI_TC_EXPORT_NORMALS + tsb = compute_tangent_space(center_pt, i, true /*normalize*/, &m_orth_spaces[i]); +#else + tsb = compute_tangent_space(center_pt, i); +#endif + } + +#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) + Gudhi::Clock t; +#endif + int tangent_space_dim = tangent_basis_dim(i); + Triangulation &local_tr = + m_triangulations[i].construct_triangulation(tangent_space_dim); + + m_triangulations[i].center_vertex() = + compute_star(i, center_pt, tsb, local_tr, verbose); + +#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) + t.end(); + std::cerr << " - triangulation construction: " << t.num_seconds() << " s.\n"; + t.reset(); +#endif + +#ifdef GUDHI_TC_VERY_VERBOSE + std::cerr << "Inserted " << num_inserted_points << " points / " + << num_attempts_to_insert_points << " attemps to compute the star\n"; +#endif + + update_star(i); + +#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) + t.end(); + std::cerr << " - update_star: " << t.num_seconds() << " s.\n"; +#endif + } + + // Updates m_stars[i] directly from m_triangulations[i] + + void update_star(std::size_t i) { + Star &star = m_stars[i]; + star.clear(); + Triangulation &local_tr = m_triangulations[i].tr(); + Tr_vertex_handle center_vertex = m_triangulations[i].center_vertex(); + int cur_dim_plus_1 = local_tr.current_dimension() + 1; + + std::vector<Tr_full_cell_handle> incident_cells; + local_tr.incident_full_cells( + center_vertex, std::back_inserter(incident_cells)); + + typename std::vector<Tr_full_cell_handle>::const_iterator it_c = incident_cells.begin(); + typename std::vector<Tr_full_cell_handle>::const_iterator it_c_end = incident_cells.end(); + // For each cell + for (; it_c != it_c_end; ++it_c) { + // Will contain all indices except center_vertex + Incident_simplex incident_simplex; + for (int j = 0; j < cur_dim_plus_1; ++j) { + std::size_t index = (*it_c)->vertex(j)->data(); + if (index != i) + incident_simplex.insert(index); + } + GUDHI_CHECK(incident_simplex.size() == cur_dim_plus_1 - 1, + std::logic_error("update_star: wrong size of incident simplex")); + star.push_back(incident_simplex); + } + } + + // Estimates tangent subspaces using PCA + + Tangent_space_basis compute_tangent_space(const Point &p + , const std::size_t i + , bool normalize_basis = true + , Orthogonal_space_basis *p_orth_space_basis = NULL + ) { + unsigned int num_pts_for_pca = (std::min)(static_cast<unsigned int> (std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)), + static_cast<unsigned int> (m_points.size())); + + // Kernel functors + typename K::Construct_vector_d constr_vec = + m_k.construct_vector_d_object(); + typename K::Compute_coordinate_d coord = + m_k.compute_coordinate_d_object(); + +#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM + KNS_range kns_range = m_points_ds_for_tse.query_k_nearest_neighbors( + p, num_pts_for_pca, false); + const Points &points_for_pca = m_points_for_tse; +#else + KNS_range kns_range = m_points_ds.query_k_nearest_neighbors(p, num_pts_for_pca, false); + const Points &points_for_pca = m_points; +#endif + + // One row = one point + Eigen::MatrixXd mat_points(num_pts_for_pca, m_ambient_dim); + auto nn_it = kns_range.begin(); + for (unsigned int j = 0; + j < num_pts_for_pca && nn_it != kns_range.end(); + ++j, ++nn_it) { + for (int i = 0; i < m_ambient_dim; ++i) { + mat_points(j, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i)); + } + } + Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean(); + Eigen::MatrixXd cov = centered.adjoint() * centered; + Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov); + + Tangent_space_basis tsb(i); // p = compute_perturbed_point(i) here + + // The eigenvectors are sorted in increasing order of their corresponding + // eigenvalues + for (int j = m_ambient_dim - 1; + j >= m_ambient_dim - m_intrinsic_dim; + --j) { + if (normalize_basis) { + Vector v = constr_vec(m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim); + tsb.push_back(normalize_vector(v, m_k)); + } else { + tsb.push_back(constr_vec( + m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim)); + } + } + + if (p_orth_space_basis) { + p_orth_space_basis->set_origin(i); + for (int j = m_ambient_dim - m_intrinsic_dim - 1; + j >= 0; + --j) { + if (normalize_basis) { + Vector v = constr_vec(m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim); + p_orth_space_basis->push_back(normalize_vector(v, m_k)); + } else { + p_orth_space_basis->push_back(constr_vec( + m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim)); + } + } + } + + m_are_tangent_spaces_computed[i] = true; + + return tsb; + } + + // Compute the space tangent to a simplex (p1, p2, ... pn) + // TODO(CJ): Improve this? + // Basically, it takes all the neighbor points to p1, p2... pn and runs PCA + // on it. Note that most points are duplicated. + + Tangent_space_basis compute_tangent_space(const Simplex &s, bool normalize_basis = true) { + unsigned int num_pts_for_pca = (std::min)(static_cast<unsigned int> (std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)), + static_cast<unsigned int> (m_points.size())); + + // Kernel functors + typename K::Construct_vector_d constr_vec = + m_k.construct_vector_d_object(); + typename K::Compute_coordinate_d coord = + m_k.compute_coordinate_d_object(); + typename K::Squared_length_d sqlen = + m_k.squared_length_d_object(); + typename K::Scaled_vector_d scaled_vec = + m_k.scaled_vector_d_object(); + typename K::Scalar_product_d scalar_pdct = + m_k.scalar_product_d_object(); + typename K::Difference_of_vectors_d diff_vec = + m_k.difference_of_vectors_d_object(); + + // One row = one point + Eigen::MatrixXd mat_points(s.size() * num_pts_for_pca, m_ambient_dim); + unsigned int current_row = 0; + + for (Simplex::const_iterator it_index = s.begin(); + it_index != s.end(); ++it_index) { + const Point &p = m_points[*it_index]; + +#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM + KNS_range kns_range = m_points_ds_for_tse.query_k_nearest_neighbors( + p, num_pts_for_pca, false); + const Points &points_for_pca = m_points_for_tse; +#else + KNS_range kns_range = m_points_ds.query_k_nearest_neighbors(p, num_pts_for_pca, false); + const Points &points_for_pca = m_points; +#endif + + auto nn_it = kns_range.begin(); + for (; + current_row < num_pts_for_pca && nn_it != kns_range.end(); + ++current_row, ++nn_it) { + for (int i = 0; i < m_ambient_dim; ++i) { + mat_points(current_row, i) = + CGAL::to_double(coord(points_for_pca[nn_it->first], i)); + } + } + } + Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean(); + Eigen::MatrixXd cov = centered.adjoint() * centered; + Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov); + + Tangent_space_basis tsb; + + // The eigenvectors are sorted in increasing order of their corresponding + // eigenvalues + for (int j = m_ambient_dim - 1; + j >= m_ambient_dim - m_intrinsic_dim; + --j) { + if (normalize_basis) { + Vector v = constr_vec(m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim); + tsb.push_back(normalize_vector(v, m_k)); + } else { + tsb.push_back(constr_vec( + m_ambient_dim, + eig.eigenvectors().col(j).data(), + eig.eigenvectors().col(j).data() + m_ambient_dim)); + } + } + + return tsb; + } + + // Returns the dimension of the ith local triangulation + + int tangent_basis_dim(std::size_t i) const { + return m_tangent_spaces[i].dimension(); + } + + Point compute_perturbed_point(std::size_t pt_idx) const { +#ifdef GUDHI_TC_PERTURB_POSITION + return m_k.translated_point_d_object()( + m_points[pt_idx], m_translations[pt_idx]); +#else + return m_points[pt_idx]; +#endif + } + + void compute_perturbed_weighted_point(std::size_t pt_idx, Point &p, FT &w) const { +#ifdef GUDHI_TC_PERTURB_POSITION + p = m_k.translated_point_d_object()( + m_points[pt_idx], m_translations[pt_idx]); +#else + p = m_points[pt_idx]; +#endif + w = m_weights[pt_idx]; + } + + Weighted_point compute_perturbed_weighted_point(std::size_t pt_idx) const { + typename K::Construct_weighted_point_d k_constr_wp = + m_k.construct_weighted_point_d_object(); + + Weighted_point wp = k_constr_wp( +#ifdef GUDHI_TC_PERTURB_POSITION + m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]), +#else + m_points[pt_idx], +#endif + m_weights[pt_idx]); + + return wp; + } + + Point unproject_point(const Tr_point &p, + const Tangent_space_basis &tsb, + const Tr_traits &tr_traits) const { + typename K::Translated_point_d k_transl = + m_k.translated_point_d_object(); + typename K::Scaled_vector_d k_scaled_vec = + m_k.scaled_vector_d_object(); + typename Tr_traits::Compute_coordinate_d coord = + tr_traits.compute_coordinate_d_object(); + + Point global_point = compute_perturbed_point(tsb.origin()); + for (int i = 0; i < m_intrinsic_dim; ++i) + global_point = k_transl(global_point, + k_scaled_vec(tsb[i], coord(p, i))); + + return global_point; + } + + // Project the point in the tangent space + // Resulting point coords are expressed in tsb's space + Tr_bare_point project_point(const Point &p, + const Tangent_space_basis &tsb, + const Tr_traits &tr_traits) const { + typename K::Scalar_product_d scalar_pdct = + m_k.scalar_product_d_object(); + typename K::Difference_of_points_d diff_points = + m_k.difference_of_points_d_object(); + + Vector v = diff_points(p, compute_perturbed_point(tsb.origin())); + + std::vector<FT> coords; + // Ambiant-space coords of the projected point + coords.reserve(tsb.dimension()); + for (std::size_t i = 0; i < m_intrinsic_dim; ++i) { + // Local coords are given by the scalar product with the vectors of tsb + FT coord = scalar_pdct(v, tsb[i]); + coords.push_back(coord); + } + + return tr_traits.construct_point_d_object()( + static_cast<int> (coords.size()), coords.begin(), coords.end()); + } + + // Project the point in the tangent space + // The weight will be the squared distance between p and the projection of p + // Resulting point coords are expressed in tsb's space + + Tr_point project_point_and_compute_weight(const Weighted_point &wp, + const Tangent_space_basis &tsb, + const Tr_traits &tr_traits) const { + typename K::Point_drop_weight_d k_drop_w = + m_k.point_drop_weight_d_object(); + typename K::Compute_weight_d k_point_weight = + m_k.compute_weight_d_object(); + return project_point_and_compute_weight( + k_drop_w(wp), k_point_weight(wp), tsb, tr_traits); + } + + // Same as above, with slightly different parameters + Tr_point project_point_and_compute_weight(const Point &p, const FT w, + const Tangent_space_basis &tsb, + const Tr_traits &tr_traits) const { + const int point_dim = m_k.point_dimension_d_object()(p); + + typename K::Construct_point_d constr_pt = + m_k.construct_point_d_object(); + typename K::Scalar_product_d scalar_pdct = + m_k.scalar_product_d_object(); + typename K::Difference_of_points_d diff_points = + m_k.difference_of_points_d_object(); + typename K::Compute_coordinate_d coord = + m_k.compute_coordinate_d_object(); + typename K::Construct_cartesian_const_iterator_d ccci = + m_k.construct_cartesian_const_iterator_d_object(); + + Point origin = compute_perturbed_point(tsb.origin()); + Vector v = diff_points(p, origin); + + // Same dimension? Then the weight is 0 + bool same_dim = (point_dim == tsb.dimension()); + + std::vector<FT> coords; + // Ambiant-space coords of the projected point + std::vector<FT> p_proj(ccci(origin), ccci(origin, 0)); + coords.reserve(tsb.dimension()); + for (int i = 0; i < tsb.dimension(); ++i) { + // Local coords are given by the scalar product with the vectors of tsb + FT c = scalar_pdct(v, tsb[i]); + coords.push_back(c); + + // p_proj += c * tsb[i] + if (!same_dim) { + for (int j = 0; j < point_dim; ++j) + p_proj[j] += c * coord(tsb[i], j); + } + } + + // Same dimension? Then the weight is 0 + FT sq_dist_to_proj_pt = 0; + if (!same_dim) { + Point projected_pt = constr_pt(point_dim, p_proj.begin(), p_proj.end()); + sq_dist_to_proj_pt = m_k.squared_distance_d_object()(p, projected_pt); + } + + return tr_traits.construct_weighted_point_d_object() + (tr_traits.construct_point_d_object()(static_cast<int> (coords.size()), coords.begin(), coords.end()), + w - sq_dist_to_proj_pt); + } + + // Project all the points in the tangent space + + template <typename Indexed_point_range> + std::vector<Tr_point> project_points_and_compute_weights( + const Indexed_point_range &point_indices, + const Tangent_space_basis &tsb, + const Tr_traits &tr_traits) const { + std::vector<Tr_point> ret; + for (typename Indexed_point_range::const_iterator + it = point_indices.begin(), it_end = point_indices.end(); + it != it_end; ++it) { + ret.push_back(project_point_and_compute_weight( + compute_perturbed_weighted_point(*it), tsb, tr_traits)); + } + return ret; + } + + // A simplex here is a local tri's full cell handle + + bool is_simplex_consistent(Tr_full_cell_handle fch, int cur_dim) const { + Simplex c; + for (int i = 0; i < cur_dim + 1; ++i) { + std::size_t data = fch->vertex(i)->data(); + c.insert(data); + } + return is_simplex_consistent(c); + } + + // A simplex here is a list of point indices + // TODO(CJ): improve it like the other "is_simplex_consistent" below + + bool is_simplex_consistent(Simplex const& simplex) const { + // Check if the simplex is in the stars of all its vertices + Simplex::const_iterator it_point_idx = simplex.begin(); + // For each point p of the simplex, we parse the incidents cells of p + // and we check if "simplex" is among them + for (; it_point_idx != simplex.end(); ++it_point_idx) { + std::size_t point_idx = *it_point_idx; + // Don't check infinite simplices + if (point_idx == (std::numeric_limits<std::size_t>::max)()) + continue; + + Star const& star = m_stars[point_idx]; + + // What we're looking for is "simplex" \ point_idx + Incident_simplex is_to_find = simplex; + is_to_find.erase(point_idx); + + // For each cell + if (std::find(star.begin(), star.end(), is_to_find) == star.end()) + return false; + } + + return true; + } + + // A simplex here is a list of point indices + // "s" contains all the points of the simplex except "center_point" + // This function returns the points whose star doesn't contain the simplex + // N.B.: the function assumes that the simplex is contained in + // star(center_point) + + template <typename OutputIterator> // value_type = std::size_t + bool is_simplex_consistent( + std::size_t center_point, + Incident_simplex const& s, // without "center_point" + OutputIterator points_whose_star_does_not_contain_s, + bool check_also_in_non_maximal_faces = false) const { + Simplex full_simplex = s; + full_simplex.insert(center_point); + + // Check if the simplex is in the stars of all its vertices + Incident_simplex::const_iterator it_point_idx = s.begin(); + // For each point p of the simplex, we parse the incidents cells of p + // and we check if "simplex" is among them + for (; it_point_idx != s.end(); ++it_point_idx) { + std::size_t point_idx = *it_point_idx; + // Don't check infinite simplices + if (point_idx == (std::numeric_limits<std::size_t>::max)()) + continue; + + Star const& star = m_stars[point_idx]; + + // What we're looking for is full_simplex \ point_idx + Incident_simplex is_to_find = full_simplex; + is_to_find.erase(point_idx); + + if (check_also_in_non_maximal_faces) { + // For each simplex "is" of the star, check if ic_to_simplex is + // included in "is" + bool found = false; + for (Star::const_iterator is = star.begin(), is_end = star.end(); + !found && is != is_end; ++is) { + if (std::includes(is->begin(), is->end(), + is_to_find.begin(), is_to_find.end())) + found = true; + } + + if (!found) + *points_whose_star_does_not_contain_s++ = point_idx; + } else { + // Does the star contain is_to_find? + if (std::find(star.begin(), star.end(), is_to_find) == star.end()) + *points_whose_star_does_not_contain_s++ = point_idx; + } + } + + return true; + } + + // A simplex here is a list of point indices + // It looks for s in star(p). + // "s" contains all the points of the simplex except p. + bool is_simplex_in_star(std::size_t p, + Incident_simplex const& s, + bool check_also_in_non_maximal_faces = true) const { + Star const& star = m_stars[p]; + + if (check_also_in_non_maximal_faces) { + // For each simplex "is" of the star, check if ic_to_simplex is + // included in "is" + bool found = false; + for (Star::const_iterator is = star.begin(), is_end = star.end(); + !found && is != is_end; ++is) { + if (std::includes(is->begin(), is->end(), s.begin(), s.end())) + found = true; + } + + return found; + } else { + return !(std::find(star.begin(), star.end(), s) == star.end()); + } + } + +#ifdef GUDHI_USE_TBB + // Functor for try_to_solve_inconsistencies_in_a_local_triangulation function + class Try_to_solve_inconsistencies_in_a_local_triangulation { + Tangential_complex & m_tc; + double m_max_perturb; + tbb::combinable<std::size_t> &m_num_inconsistencies; + tbb::combinable<std::vector<std::size_t> > &m_updated_points; + + public: + // Constructor + Try_to_solve_inconsistencies_in_a_local_triangulation(Tangential_complex &tc, + double max_perturb, + tbb::combinable<std::size_t> &num_inconsistencies, + tbb::combinable<std::vector<std::size_t> > &updated_points) + : m_tc(tc), + m_max_perturb(max_perturb), + m_num_inconsistencies(num_inconsistencies), + m_updated_points(updated_points) { } + + // Constructor + Try_to_solve_inconsistencies_in_a_local_triangulation(const Try_to_solve_inconsistencies_in_a_local_triangulation& + tsilt) + : m_tc(tsilt.m_tc), + m_max_perturb(tsilt.m_max_perturb), + m_num_inconsistencies(tsilt.m_num_inconsistencies), + m_updated_points(tsilt.m_updated_points) { } + + // operator() + void operator()(const tbb::blocked_range<size_t>& r) const { + for (size_t i = r.begin(); i != r.end(); ++i) { + m_num_inconsistencies.local() += + m_tc.try_to_solve_inconsistencies_in_a_local_triangulation(i, m_max_perturb, + std::back_inserter(m_updated_points.local())); + } + } + }; +#endif // GUDHI_USE_TBB + + void perturb(std::size_t point_idx, double max_perturb) { + const Tr_traits &local_tr_traits = + m_triangulations[point_idx].tr().geom_traits(); + typename Tr_traits::Compute_coordinate_d coord = + local_tr_traits.compute_coordinate_d_object(); + typename K::Translated_point_d k_transl = + m_k.translated_point_d_object(); + typename K::Construct_vector_d k_constr_vec = + m_k.construct_vector_d_object(); + typename K::Scaled_vector_d k_scaled_vec = + m_k.scaled_vector_d_object(); + + CGAL::Random_points_in_ball_d<Tr_bare_point> + tr_point_in_ball_generator(m_intrinsic_dim, + m_random_generator.get_double(0., max_perturb)); + + Tr_point local_random_transl = + local_tr_traits.construct_weighted_point_d_object()(*tr_point_in_ball_generator++, 0); + Translation_for_perturb global_transl = k_constr_vec(m_ambient_dim); + const Tangent_space_basis &tsb = m_tangent_spaces[point_idx]; + for (int i = 0; i < m_intrinsic_dim; ++i) { + global_transl = k_transl(global_transl, + k_scaled_vec(tsb[i], coord(local_random_transl, i))); + } + // Parallel +#if defined(GUDHI_USE_TBB) + m_p_perturb_mutexes[point_idx].lock(); + m_translations[point_idx] = global_transl; + m_p_perturb_mutexes[point_idx].unlock(); + // Sequential +#else + m_translations[point_idx] = global_transl; +#endif + } + + // Return true if inconsistencies were found + template <typename OutputIt> + bool try_to_solve_inconsistencies_in_a_local_triangulation(std::size_t tr_index, + double max_perturb, + OutputIt perturbed_pts_indices = CGAL::Emptyset_iterator()) { + bool is_inconsistent = false; + + Star const& star = m_stars[tr_index]; + Tr_vertex_handle center_vh = m_triangulations[tr_index].center_vertex(); + + // For each incident simplex + Star::const_iterator it_inc_simplex = star.begin(); + Star::const_iterator it_inc_simplex_end = star.end(); + for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) { + const Incident_simplex &incident_simplex = *it_inc_simplex; + + // Don't check infinite cells + if (is_infinite(incident_simplex)) + continue; + + Simplex c = incident_simplex; + c.insert(tr_index); // Add the missing index + + // Perturb the center point + if (!is_simplex_consistent(c)) { + is_inconsistent = true; + + std::size_t idx = tr_index; + + perturb(tr_index, max_perturb); + *perturbed_pts_indices++ = idx; + + // We will try the other cells next time + break; + } + } + + return is_inconsistent; + } + + + // 1st line: number of points + // Then one point per line + std::ostream &export_point_set(std::ostream & os, + bool use_perturbed_points = false, + const char *coord_separator = " ") const { + if (use_perturbed_points) { + std::vector<Point> perturbed_points; + perturbed_points.reserve(m_points.size()); + for (std::size_t i = 0; i < m_points.size(); ++i) + perturbed_points.push_back(compute_perturbed_point(i)); + + return export_point_set( + m_k, perturbed_points, os, coord_separator); + } else { + return export_point_set( + m_k, m_points, os, coord_separator); + } + } + + template<typename ProjectionFunctor = CGAL::Identity<Point> > + std::ostream &export_vertices_to_off( + std::ostream & os, std::size_t &num_vertices, + bool use_perturbed_points = false, + ProjectionFunctor const& point_projection = ProjectionFunctor()) const { + if (m_points.empty()) { + num_vertices = 0; + return os; + } + + // If m_intrinsic_dim = 1, we output each point two times + // to be able to export each segment as a flat triangle with 3 different + // indices (otherwise, Meshlab detects degenerated simplices) + const int N = (m_intrinsic_dim == 1 ? 2 : 1); + + // Kernel functors + typename K::Compute_coordinate_d coord = + m_k.compute_coordinate_d_object(); + +#ifdef GUDHI_TC_EXPORT_ALL_COORDS_IN_OFF + int num_coords = m_ambient_dim; +#else + int num_coords = (std::min)(m_ambient_dim, 3); +#endif + +#ifdef GUDHI_TC_EXPORT_NORMALS + OS_container::const_iterator it_os = m_orth_spaces.begin(); +#endif + typename Points::const_iterator it_p = m_points.begin(); + typename Points::const_iterator it_p_end = m_points.end(); + // For each point p + for (std::size_t i = 0; it_p != it_p_end; ++it_p, ++i) { + Point p = point_projection( + use_perturbed_points ? compute_perturbed_point(i) : *it_p); + for (int ii = 0; ii < N; ++ii) { + int j = 0; + for (; j < num_coords; ++j) + os << CGAL::to_double(coord(p, j)) << " "; + if (j == 2) + os << "0"; + +#ifdef GUDHI_TC_EXPORT_NORMALS + for (j = 0; j < num_coords; ++j) + os << " " << CGAL::to_double(coord(*it_os->begin(), j)); +#endif + os << "\n"; + } +#ifdef GUDHI_TC_EXPORT_NORMALS + ++it_os; +#endif + } + + num_vertices = N * m_points.size(); + return os; + } + + std::ostream &export_simplices_to_off(std::ostream & os, std::size_t &num_OFF_simplices, + bool color_inconsistencies = false, + Simplex_set const *p_simpl_to_color_in_red = NULL, + Simplex_set const *p_simpl_to_color_in_green = NULL, + Simplex_set const *p_simpl_to_color_in_blue = NULL) + const { + // If m_intrinsic_dim = 1, each point is output two times + // (see export_vertices_to_off) + num_OFF_simplices = 0; + std::size_t num_maximal_simplices = 0; + std::size_t num_inconsistent_maximal_simplices = 0; + std::size_t num_inconsistent_stars = 0; + typename Tr_container::const_iterator it_tr = m_triangulations.begin(); + typename Tr_container::const_iterator it_tr_end = m_triangulations.end(); + // For each triangulation + for (std::size_t idx = 0; it_tr != it_tr_end; ++it_tr, ++idx) { + bool is_star_inconsistent = false; + + Triangulation const& tr = it_tr->tr(); + Tr_vertex_handle center_vh = it_tr->center_vertex(); + + if (tr.current_dimension() < m_intrinsic_dim) + continue; + + // Color for this star + std::stringstream color; + // color << rand()%256 << " " << 100+rand()%156 << " " << 100+rand()%156; + color << 128 << " " << 128 << " " << 128; + + // Gather the triangles here, with an int telling its color + typedef std::vector<std::pair<Simplex, int> > Star_using_triangles; + Star_using_triangles star_using_triangles; + + // For each cell of the star + Star::const_iterator it_inc_simplex = m_stars[idx].begin(); + Star::const_iterator it_inc_simplex_end = m_stars[idx].end(); + for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) { + Simplex c = *it_inc_simplex; + c.insert(idx); + std::size_t num_vertices = c.size(); + ++num_maximal_simplices; + + int color_simplex = -1; // -1=no color, 0=yellow, 1=red, 2=green, 3=blue + if (color_inconsistencies && !is_simplex_consistent(c)) { + ++num_inconsistent_maximal_simplices; + color_simplex = 0; + is_star_inconsistent = true; + } else { + if (p_simpl_to_color_in_red && + std::find( + p_simpl_to_color_in_red->begin(), + p_simpl_to_color_in_red->end(), + c) != p_simpl_to_color_in_red->end()) { + color_simplex = 1; + } else if (p_simpl_to_color_in_green && + std::find( + p_simpl_to_color_in_green->begin(), + p_simpl_to_color_in_green->end(), + c) != p_simpl_to_color_in_green->end()) { + color_simplex = 2; + } else if (p_simpl_to_color_in_blue && + std::find( + p_simpl_to_color_in_blue->begin(), + p_simpl_to_color_in_blue->end(), + c) != p_simpl_to_color_in_blue->end()) { + color_simplex = 3; + } + } + + // If m_intrinsic_dim = 1, each point is output two times, + // so we need to multiply each index by 2 + // And if only 2 vertices, add a third one (each vertex is duplicated in + // the file when m_intrinsic dim = 2) + if (m_intrinsic_dim == 1) { + Simplex tmp_c; + Simplex::iterator it = c.begin(); + for (; it != c.end(); ++it) + tmp_c.insert(*it * 2); + if (num_vertices == 2) + tmp_c.insert(*tmp_c.rbegin() + 1); + + c = tmp_c; + } + + if (num_vertices <= 3) { + star_using_triangles.push_back(std::make_pair(c, color_simplex)); + } else { + // num_vertices >= 4: decompose the simplex in triangles + std::vector<bool> booleans(num_vertices, false); + std::fill(booleans.begin() + num_vertices - 3, booleans.end(), true); + do { + Simplex triangle; + Simplex::iterator it = c.begin(); + for (int i = 0; it != c.end(); ++i, ++it) { + if (booleans[i]) + triangle.insert(*it); + } + star_using_triangles.push_back( + std::make_pair(triangle, color_simplex)); + } while (std::next_permutation(booleans.begin(), booleans.end())); + } + } + + // For each cell + Star_using_triangles::const_iterator it_simplex = + star_using_triangles.begin(); + Star_using_triangles::const_iterator it_simplex_end = + star_using_triangles.end(); + for (; it_simplex != it_simplex_end; ++it_simplex) { + const Simplex &c = it_simplex->first; + + // Don't export infinite cells + if (is_infinite(c)) + continue; + + int color_simplex = it_simplex->second; + + std::stringstream sstr_c; + + Simplex::const_iterator it_point_idx = c.begin(); + for (; it_point_idx != c.end(); ++it_point_idx) { + sstr_c << *it_point_idx << " "; + } + + os << 3 << " " << sstr_c.str(); + if (color_inconsistencies || p_simpl_to_color_in_red + || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) { + switch (color_simplex) { + case 0: os << " 255 255 0"; + break; + case 1: os << " 255 0 0"; + break; + case 2: os << " 0 255 0"; + break; + case 3: os << " 0 0 255"; + break; + default: os << " " << color.str(); + break; + } + } + ++num_OFF_simplices; + os << "\n"; + } + if (is_star_inconsistent) + ++num_inconsistent_stars; + } + +#ifdef DEBUG_TRACES + std::cerr + << "\n==========================================================\n" + << "Export from list of stars to OFF:\n" + << " * Number of vertices: " << m_points.size() << "\n" + << " * Total number of maximal simplices: " << num_maximal_simplices + << "\n"; + if (color_inconsistencies) { + std::cerr + << " * Number of inconsistent stars: " + << num_inconsistent_stars << " (" + << (m_points.size() > 0 ? + 100. * num_inconsistent_stars / m_points.size() : 0.) << "%)\n" + << " * Number of inconsistent maximal simplices: " + << num_inconsistent_maximal_simplices << " (" + << (num_maximal_simplices > 0 ? + 100. * num_inconsistent_maximal_simplices / num_maximal_simplices + : 0.) << "%)\n"; + } + std::cerr << "==========================================================\n"; +#endif + + return os; + } + + public: + std::ostream &export_simplices_to_off( + const Simplicial_complex &complex, + std::ostream & os, std::size_t &num_OFF_simplices, + Simplex_set const *p_simpl_to_color_in_red = NULL, + Simplex_set const *p_simpl_to_color_in_green = NULL, + Simplex_set const *p_simpl_to_color_in_blue = NULL) + const { + typedef Simplicial_complex::Simplex Simplex; + typedef Simplicial_complex::Simplex_set Simplex_set; + + // If m_intrinsic_dim = 1, each point is output two times + // (see export_vertices_to_off) + num_OFF_simplices = 0; + std::size_t num_maximal_simplices = 0; + + typename Simplex_set::const_iterator it_s = + complex.simplex_range().begin(); + typename Simplex_set::const_iterator it_s_end = + complex.simplex_range().end(); + // For each simplex + for (; it_s != it_s_end; ++it_s) { + Simplex c = *it_s; + ++num_maximal_simplices; + + int color_simplex = -1; // -1=no color, 0=yellow, 1=red, 2=green, 3=blue + if (p_simpl_to_color_in_red && + std::find( + p_simpl_to_color_in_red->begin(), + p_simpl_to_color_in_red->end(), + c) != p_simpl_to_color_in_red->end()) { + color_simplex = 1; + } else if (p_simpl_to_color_in_green && + std::find(p_simpl_to_color_in_green->begin(), + p_simpl_to_color_in_green->end(), + c) != p_simpl_to_color_in_green->end()) { + color_simplex = 2; + } else if (p_simpl_to_color_in_blue && + std::find(p_simpl_to_color_in_blue->begin(), + p_simpl_to_color_in_blue->end(), + c) != p_simpl_to_color_in_blue->end()) { + color_simplex = 3; + } + + // Gather the triangles here + typedef std::vector<Simplex> Triangles; + Triangles triangles; + + int num_vertices = static_cast<int>(c.size()); + // Do not export smaller dimension simplices + if (num_vertices < m_intrinsic_dim + 1) + continue; + + // If m_intrinsic_dim = 1, each point is output two times, + // so we need to multiply each index by 2 + // And if only 2 vertices, add a third one (each vertex is duplicated in + // the file when m_intrinsic dim = 2) + if (m_intrinsic_dim == 1) { + Simplex tmp_c; + Simplex::iterator it = c.begin(); + for (; it != c.end(); ++it) + tmp_c.insert(*it * 2); + if (num_vertices == 2) + tmp_c.insert(*tmp_c.rbegin() + 1); + + c = tmp_c; + } + + if (num_vertices <= 3) { + triangles.push_back(c); + } else { + // num_vertices >= 4: decompose the simplex in triangles + std::vector<bool> booleans(num_vertices, false); + std::fill(booleans.begin() + num_vertices - 3, booleans.end(), true); + do { + Simplex triangle; + Simplex::iterator it = c.begin(); + for (int i = 0; it != c.end(); ++i, ++it) { + if (booleans[i]) + triangle.insert(*it); + } + triangles.push_back(triangle); + } while (std::next_permutation(booleans.begin(), booleans.end())); + } + + // For each cell + Triangles::const_iterator it_tri = triangles.begin(); + Triangles::const_iterator it_tri_end = triangles.end(); + for (; it_tri != it_tri_end; ++it_tri) { + // Don't export infinite cells + if (is_infinite(*it_tri)) + continue; + + os << 3 << " "; + Simplex::const_iterator it_point_idx = it_tri->begin(); + for (; it_point_idx != it_tri->end(); ++it_point_idx) { + os << *it_point_idx << " "; + } + + if (p_simpl_to_color_in_red || p_simpl_to_color_in_green + || p_simpl_to_color_in_blue) { + switch (color_simplex) { + case 0: os << " 255 255 0"; + break; + case 1: os << " 255 0 0"; + break; + case 2: os << " 0 255 0"; + break; + case 3: os << " 0 0 255"; + break; + default: os << " 128 128 128"; + break; + } + } + + ++num_OFF_simplices; + os << "\n"; + } + } + +#ifdef DEBUG_TRACES + std::cerr + << "\n==========================================================\n" + << "Export from complex to OFF:\n" + << " * Number of vertices: " << m_points.size() << "\n" + << " * Total number of maximal simplices: " << num_maximal_simplices + << "\n" + << "==========================================================\n"; +#endif + + return os; + } + + private: + const K m_k; + const int m_intrinsic_dim; + const int m_ambient_dim; + + Points m_points; + Weights m_weights; +#ifdef GUDHI_TC_PERTURB_POSITION + Translations_for_perturb m_translations; +#if defined(GUDHI_USE_TBB) + Mutex_for_perturb *m_p_perturb_mutexes; +#endif +#endif + + Points_ds m_points_ds; + double m_last_max_perturb; + std::vector<bool> m_are_tangent_spaces_computed; + TS_container m_tangent_spaces; +#ifdef GUDHI_TC_EXPORT_NORMALS + OS_container m_orth_spaces; +#endif + Tr_container m_triangulations; // Contains the triangulations + // and their center vertex + Stars_container m_stars; + std::vector<FT> m_squared_star_spheres_radii_incl_margin; + +#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM + Points m_points_for_tse; + Points_ds m_points_ds_for_tse; +#endif + + mutable CGAL::Random m_random_generator; +}; // /class Tangential_complex + +} // end namespace tangential_complex +} // end namespace Gudhi + +#endif // TANGENTIAL_COMPLEX_H_ |