diff options
Diffstat (limited to 'src/Alpha_complex/include/gudhi/Alpha_complex.h')
| -rw-r--r-- | src/Alpha_complex/include/gudhi/Alpha_complex.h | 438 |
1 files changed, 269 insertions, 169 deletions
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h index 8919cdb9..a7372f19 100644 --- a/src/Alpha_complex/include/gudhi/Alpha_complex.h +++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h @@ -12,22 +12,30 @@ #ifndef ALPHA_COMPLEX_H_ #define ALPHA_COMPLEX_H_ +#include <gudhi/Alpha_complex/Alpha_kernel_d.h> #include <gudhi/Debug_utils.h> // to construct Alpha_complex from a OFF file of points #include <gudhi/Points_off_io.h> -#include <stdlib.h> -#include <math.h> // isnan, fmax +#include <cmath> // isnan, fmax +#include <memory> // for std::unique_ptr +#include <cstddef> // for std::size_t #include <CGAL/Delaunay_triangulation.h> -#include <CGAL/Epick_d.h> +#include <CGAL/Regular_triangulation.h> // aka. Weighted Delaunay triangulation +#include <CGAL/Epeck_d.h> // For EXACT or SAFE version +#include <CGAL/Epick_d.h> // For FAST version #include <CGAL/Spatial_sort_traits_adapter_d.h> #include <CGAL/property_map.h> // for CGAL::Identity_property_map -#include <CGAL/NT_converter.h> #include <CGAL/version.h> // for CGAL_VERSION_NR +#include <CGAL/NT_converter.h> #include <Eigen/src/Core/util/Macros.h> // for EIGEN_VERSION_AT_LEAST +#include <boost/range/size.hpp> +#include <boost/range/combine.hpp> +#include <boost/range/adaptor/transformed.hpp> + #include <iostream> #include <vector> #include <string> @@ -36,20 +44,24 @@ #include <utility> // std::pair #include <stdexcept> #include <numeric> // for std::iota +#include <algorithm> // for std::sort // Make compilation fail - required for external projects - https://github.com/GUDHI/gudhi-devel/issues/10 #if CGAL_VERSION_NR < 1041101000 -# error Alpha_complex_3d is only available for CGAL >= 4.11 +# error Alpha_complex is only available for CGAL >= 4.11 #endif #if !EIGEN_VERSION_AT_LEAST(3,1,0) -# error Alpha_complex_3d is only available for Eigen3 >= 3.1.0 installed with CGAL +# error Alpha_complex is only available for Eigen3 >= 3.1.0 installed with CGAL #endif namespace Gudhi { namespace alpha_complex { +template<typename D> struct Is_Epeck_D { static const bool value = false; }; +template<typename D> struct Is_Epeck_D<CGAL::Epeck_d<D>> { static const bool value = true; }; + /** * \class Alpha_complex Alpha_complex.h gudhi/Alpha_complex.h * \brief Alpha complex data structure. @@ -57,63 +69,91 @@ namespace alpha_complex { * \ingroup alpha_complex * * \details - * The data structure is constructing a CGAL Delaunay triangulation (for more informations on CGAL Delaunay + * The data structure is constructing a CGAL Delaunay triangulation (for more information on CGAL Delaunay * triangulation, please refer to the corresponding chapter in page http://doc.cgal.org/latest/Triangulation/) from a * range of points or from an OFF file (cf. Points_off_reader). * * Please refer to \ref alpha_complex for examples. * - * The complex is a template class requiring an Epick_d <a target="_blank" + * The complex is a template class requiring an <a target="_blank" + * href="https://doc.cgal.org/latest/Kernel_d/structCGAL_1_1Epeck__d.html">CGAL::Epeck_d</a>, + * or an <a target="_blank" + * href="https://doc.cgal.org/latest/Kernel_d/structCGAL_1_1Epick__d.html">CGAL::Epick_d</a> <a target="_blank" * href="http://doc.cgal.org/latest/Kernel_d/index.html#Chapter_dD_Geometry_Kernel">dD Geometry Kernel</a> - * \cite cgal:s-gkd-15b from CGAL as template, default value is <a target="_blank" - * href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> + * \cite cgal:s-gkd-19b from CGAL as template, default value is <a target="_blank" + * href="https://doc.cgal.org/latest/Kernel_d/structCGAL_1_1Epeck__d.html">CGAL::Epeck_d</a> * < <a target="_blank" href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dynamic__dimension__tag.html"> * CGAL::Dynamic_dimension_tag </a> > * - * \remark When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. - * + * \remark + * - When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex. + * - Using the default `CGAL::Epeck_d` makes the construction safe. If you pass exact=true to create_complex, the + * filtration values are the exact ones converted to the filtration value type of the simplicial complex. This can be + * very slow. If you pass exact=false (the default), the filtration values are only guaranteed to have a small + * multiplicative error compared to the exact value, see <code><a class="el" target="_blank" + * href="https://doc.cgal.org/latest/Number_types/classCGAL_1_1Lazy__exact__nt.html"> + * CGAL::Lazy_exact_nt<NT>::set_relative_precision_of_to_double</a></code> for details. A drawback, when computing + * persistence, is that an empty exact interval [10^12,10^12] may become a non-empty approximate interval + * [10^12,10^12+10^6]. Using `CGAL::Epick_d` makes the computations slightly faster, and the combinatorics are still + * exact, but the computation of filtration values can exceptionally be arbitrarily bad. In all cases, we still + * guarantee that the output is a valid filtration (faces have a filtration value no larger than their cofaces). + * - For performances reasons, it is advised to use `Alpha_complex` with \ref cgal ≥ 5.0.0. */ -template<class Kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>> +template<class Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>, bool Weighted = false> class Alpha_complex { + private: + // Vertex_handle internal type (required by triangulation_ and vertices_). + using Internal_vertex_handle = std::ptrdiff_t; + public: + /** \brief Geometric traits class that provides the geometric types and predicates needed by the triangulations.*/ + using Geom_traits = std::conditional_t<Weighted, CGAL::Regular_triangulation_traits_adapter<Kernel>, Kernel>; + // Add an int in TDS to save point index in the structure - typedef CGAL::Triangulation_data_structure<typename Kernel::Dimension, - CGAL::Triangulation_vertex<Kernel, std::ptrdiff_t>, - CGAL::Triangulation_full_cell<Kernel> > TDS; - /** \brief A Delaunay triangulation of a set of points in \f$ \mathbb{R}^D\f$.*/ - typedef CGAL::Delaunay_triangulation<Kernel, TDS> Delaunay_triangulation; - - /** \brief A point in Euclidean space.*/ - typedef typename Kernel::Point_d Point_d; - /** \brief Geometric traits class that provides the geometric types and predicates needed by Delaunay - * triangulations.*/ - typedef Kernel Geom_traits; + using TDS = CGAL::Triangulation_data_structure<typename Geom_traits::Dimension, + CGAL::Triangulation_vertex<Geom_traits, Internal_vertex_handle>, + CGAL::Triangulation_full_cell<Geom_traits> >; - private: - typedef typename Kernel::Compute_squared_radius_d Squared_Radius; - typedef typename Kernel::Side_of_bounded_sphere_d Is_Gabriel; - typedef typename Kernel::Point_dimension_d Point_Dimension; + /** \brief A (Weighted or not) Delaunay triangulation of a set of points in \f$ \mathbb{R}^D\f$.*/ + using Triangulation = std::conditional_t<Weighted, CGAL::Regular_triangulation<Kernel, TDS>, + CGAL::Delaunay_triangulation<Kernel, TDS>>; - // Type required to compute squared radius, or side of bounded sphere on a vector of points. - typedef typename std::vector<Point_d> Vector_of_CGAL_points; + /** \brief CGAL kernel container for computations in function of the weighted or not characteristics.*/ + using A_kernel_d = Alpha_kernel_d<Kernel, Weighted>; - // Vertex_iterator type from CGAL. - typedef typename Delaunay_triangulation::Vertex_iterator CGAL_vertex_iterator; + // Numeric type of coordinates in the kernel + using FT = typename A_kernel_d::FT; - // size_type type from CGAL. - typedef typename Delaunay_triangulation::size_type size_type; + /** \brief Sphere is a std::pair<Kernel::Point_d, Kernel::FT> (aka. circurmcenter and squared radius). + * If Weighted, Sphere is a Kernel::Weighted_point_d (aka. circurmcenter and the weight value is the squared radius). + */ + using Sphere = typename A_kernel_d::Sphere; - // Map type to switch from simplex tree vertex handle to CGAL vertex iterator. - typedef typename std::map< std::size_t, CGAL_vertex_iterator > Vector_vertex_iterator; + /** \brief A point, or a weighted point in Euclidean space.*/ + using Point_d = typename Geom_traits::Point_d; + + private: + // Vertex_iterator type from CGAL. + using CGAL_vertex_iterator = typename Triangulation::Vertex_iterator; + + // Structure to switch from simplex tree vertex handle to CGAL vertex iterator. + using Vector_vertex_iterator = std::vector< CGAL_vertex_iterator >; private: /** \brief Vertex iterator vector to switch from simplex tree vertex handle to CGAL vertex iterator. * Vertex handles are inserted sequentially, starting at 0.*/ Vector_vertex_iterator vertex_handle_to_iterator_; /** \brief Pointer on the CGAL Delaunay triangulation.*/ - Delaunay_triangulation* triangulation_; + std::unique_ptr<Triangulation> triangulation_; /** \brief Kernel for triangulation_ functions access.*/ - Kernel kernel_; + A_kernel_d kernel_; + /** \brief Vertices to be inserted first by the create_complex method to avoid quadratic complexity. + * It isn't just [0, n) if some points have multiplicity (only one copy appears in the complex). + */ + std::vector<Internal_vertex_handle> vertices_; + + /** \brief Cache for geometric constructions: circumcenter and squared radius of a simplex.*/ + std::vector<Sphere> cache_, old_cache_; public: /** \brief Alpha_complex constructor from an OFF file name. @@ -125,8 +165,7 @@ class Alpha_complex { * * @param[in] off_file_name OFF file [path and] name. */ - Alpha_complex(const std::string& off_file_name) - : triangulation_(nullptr) { + Alpha_complex(const std::string& off_file_name) { Gudhi::Points_off_reader<Point_d> off_reader(off_file_name); if (!off_reader.is_valid()) { std::cerr << "Alpha_complex - Unable to read file " << off_file_name << "\n"; @@ -138,23 +177,40 @@ class Alpha_complex { /** \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. + * The vertices may be not contiguous as some points may be discarded in the triangulation (duplicate points, + * weighted hidden point, ...). * - * @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d + * @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d or Kernel::Weighted_point_d. * - * The type InputPointRange must be a range for which std::begin and - * std::end return input iterators on a Kernel::Point_d. + * The type InputPointRange must be a range for which std::begin and std::end return input iterators on a + * Kernel::Point_d or Kernel::Weighted_point_d. */ template<typename InputPointRange > - Alpha_complex(const InputPointRange& points) - : triangulation_(nullptr) { + Alpha_complex(const InputPointRange& points) { init_from_range(points); } - /** \brief Alpha_complex destructor deletes the Delaunay triangulation. + /** \brief Alpha_complex constructor from a list of points and weights. + * + * The vertices may be not contiguous as some points may be discarded in the triangulation (duplicate points, + * weighted hidden point, ...). + * + * @param[in] points Range of points to triangulate. Points must be in Kernel::Point_d. + * + * @param[in] weights Range of points weights. Weights must be in Kernel::FT. + * + * The type InputPointRange must be a range for which std::begin and std::end return input iterators on a + * Kernel::Point_d. */ - ~Alpha_complex() { - delete triangulation_; + template <typename InputPointRange, typename WeightRange> + Alpha_complex(const InputPointRange& points, WeightRange weights) { + static_assert(Weighted, "This constructor is not available for non-weighted versions of Alpha_complex"); + // FIXME: this test is only valid if we have a forward range + GUDHI_CHECK(boost::size(weights) == boost::size(points), + std::invalid_argument("Points number in range different from weights range number")); + auto weighted_points = boost::range::combine(points, weights) + | boost::adaptors::transformed([](auto const&t){return Point_d(boost::get<0>(t), boost::get<1>(t));}); + init_from_range(weighted_points); } // Forbid copy/move constructor/assignment operator @@ -163,6 +219,15 @@ class Alpha_complex { Alpha_complex (Alpha_complex&& other) = delete; Alpha_complex& operator= (Alpha_complex&& other) = delete; + /** \brief Returns the number of finite vertices in the triangulation. + */ + std::size_t num_vertices() const { + if (triangulation_ == nullptr) + return 0; + else + return triangulation_->number_of_vertices(); + } + /** \brief get_point returns the point corresponding to the vertex given as parameter. * * @param[in] vertex Vertex handle of the point to retrieve. @@ -173,71 +238,128 @@ class Alpha_complex { return vertex_handle_to_iterator_.at(vertex)->point(); } - /** \brief number_of_vertices returns the number of vertices (same as the number of points). - * - * @return The number of vertices. - */ - std::size_t number_of_vertices() const { - return vertex_handle_to_iterator_.size(); - } - private: template<typename InputPointRange > void init_from_range(const InputPointRange& points) { + #if CGAL_VERSION_NR < 1050000000 + if (Is_Epeck_D<Kernel>::value) + std::cerr << "It is strongly advised to use a CGAL version >= 5.0 with Epeck_d Kernel for performance reasons." + << std::endl; + #endif + +#if CGAL_VERSION_NR < 1050101000 + // Make compilation fail if weighted and CGAL < 5.1 + static_assert(!Weighted, "Weighted Alpha_complex is only available for CGAL >= 5.1"); +#endif + auto first = std::begin(points); auto last = std::end(points); if (first != last) { - // point_dimension function initialization - Point_Dimension point_dimension = kernel_.point_dimension_d_object(); - - // Delaunay triangulation is point dimension. - triangulation_ = new Delaunay_triangulation(point_dimension(*first)); + // Delaunay triangulation init with point dimension. + triangulation_ = std::make_unique<Triangulation>(kernel_.get_dimension(*first)); std::vector<Point_d> point_cloud(first, last); // Creates a vector {0, 1, ..., N-1} - std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0), - boost::counting_iterator<std::ptrdiff_t>(point_cloud.size())); + std::vector<Internal_vertex_handle> indices(boost::counting_iterator<Internal_vertex_handle>(0), + boost::counting_iterator<Internal_vertex_handle>(point_cloud.size())); - typedef boost::iterator_property_map<typename std::vector<Point_d>::iterator, - CGAL::Identity_property_map<std::ptrdiff_t>> Point_property_map; - typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_property_map> Search_traits_d; + using Point_property_map = boost::iterator_property_map<typename std::vector<Point_d>::iterator, + CGAL::Identity_property_map<Internal_vertex_handle>>; + using Search_traits_d = CGAL::Spatial_sort_traits_adapter_d<Geom_traits, Point_property_map>; CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud))); - typename Delaunay_triangulation::Full_cell_handle hint; + typename Triangulation::Full_cell_handle hint; for (auto index : indices) { - typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint); - // Save index value as data to retrieve it after insertion - pos->data() = index; - hint = pos->full_cell(); + typename Triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint); + if (pos != nullptr) { + // Save index value as data to retrieve it after insertion + pos->data() = index; + hint = pos->full_cell(); + } } // -------------------------------------------------------------------------------------------- - // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa + // structure to retrieve CGAL points from vertex handle - one vertex handle per point. + // Needs to be constructed before as vertex handles arrives in no particular order. + vertex_handle_to_iterator_.resize(point_cloud.size()); + // List of sorted unique vertices in the triangulation. We take advantage of the existing loop to construct it + // Vertices list avoids quadratic complexity with the Simplex_tree. We should not fill it up with Toplex_map e.g. + vertices_.reserve(triangulation_->number_of_vertices()); // Loop on triangulation vertices list for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) { if (!triangulation_->is_infinite(*vit)) { #ifdef DEBUG_TRACES - std::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl; + std::clog << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl; #endif // DEBUG_TRACES - vertex_handle_to_iterator_.emplace(vit->data(), vit); + vertex_handle_to_iterator_[vit->data()] = vit; + vertices_.push_back(vit->data()); } } + std::sort(vertices_.begin(), vertices_.end()); // -------------------------------------------------------------------------------------------- } } + /** \brief get_point_ returns the point corresponding to the vertex given as parameter. + * Only for internal use for faster access. + * + * @param[in] vertex Vertex handle of the point to retrieve. + * @return The point found. + */ + const Point_d& get_point_(std::size_t vertex) const { + return vertex_handle_to_iterator_[vertex]->point(); + } + + /// Return a reference to the circumcenter and circumradius, writing them in the cache if necessary. + template<class SimplicialComplexForAlpha> + auto& get_cache(SimplicialComplexForAlpha& cplx, typename SimplicialComplexForAlpha::Simplex_handle s) { + auto k = cplx.key(s); + if(k==cplx.null_key()){ + k = cache_.size(); + cplx.assign_key(s, k); + // Using a transform_range is slower, currently. + thread_local std::vector<Point_d> v; + v.clear(); + for (auto vertex : cplx.simplex_vertex_range(s)) + v.push_back(get_point_(vertex)); + cache_.emplace_back(kernel_.get_sphere(v.cbegin(), v.cend())); + } + return cache_[k]; + } + + /// Return the circumradius, either from the old cache or computed, without writing to the cache. + template<class SimplicialComplexForAlpha> + auto radius(SimplicialComplexForAlpha& cplx, typename SimplicialComplexForAlpha::Simplex_handle s) { + auto k = cplx.key(s); + if(k!=cplx.null_key()) + return kernel_.get_squared_radius(old_cache_[k]); + // Using a transform_range is slower, currently. + thread_local std::vector<Point_d> v; + v.clear(); + for (auto vertex : cplx.simplex_vertex_range(s)) + v.push_back(get_point_(vertex)); + return kernel_.get_squared_radius(v.cbegin(), v.cend()); + } + public: /** \brief Inserts all Delaunay triangulation into the simplicial complex. - * It also computes the filtration values accordingly to the \ref createcomplexalgorithm + * It also computes the filtration values accordingly to the \ref createcomplexalgorithm if default_filtration_value + * is not set. * * \tparam SimplicialComplexForAlpha must meet `SimplicialComplexForAlpha` concept. * * @param[in] complex SimplicialComplexForAlpha to be created. * @param[in] max_alpha_square maximum for alpha square value. Default value is +\f$\infty\f$, and there is very - * little point using anything else since it does not save time. - * + * little point using anything else since it does not save time. Useless if `default_filtration_value` is set to + * `true`. + * @param[in] exact Exact filtration values computation. Not exact if `Kernel` is not <a target="_blank" + * href="https://doc.cgal.org/latest/Kernel_d/structCGAL_1_1Epeck__d.html">CGAL::Epeck_d</a>. + * @param[in] default_filtration_value Set this value to `true` if filtration values are not needed to be computed + * (will be set to `NaN`). + * Default value is `false` (which means compute the filtration values). + * * @return true if creation succeeds, false otherwise. * * @pre Delaunay triangulation must be already constructed with dimension strictly greater than 0. @@ -248,11 +370,13 @@ class Alpha_complex { template <typename SimplicialComplexForAlpha, typename Filtration_value = typename SimplicialComplexForAlpha::Filtration_value> bool create_complex(SimplicialComplexForAlpha& complex, - Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity()) { + Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity(), + bool exact = false, + bool default_filtration_value = false) { // From SimplicialComplexForAlpha type required to insert into a simplicial complex (with or without subfaces). - typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle; - typedef typename SimplicialComplexForAlpha::Simplex_handle Simplex_handle; - typedef std::vector<Vertex_handle> Vector_vertex; + using Vertex_handle = typename SimplicialComplexForAlpha::Vertex_handle; + using Simplex_handle = typename SimplicialComplexForAlpha::Simplex_handle; + using Vector_vertex = std::vector<Vertex_handle>; if (triangulation_ == nullptr) { std::cerr << "Alpha_complex cannot create_complex from a NULL triangulation\n"; @@ -269,25 +393,34 @@ class Alpha_complex { // -------------------------------------------------------------------------------------------- // Simplex_tree construction from loop on triangulation finite full cells list - if (triangulation_->number_of_vertices() > 0) { + if (num_vertices() > 0) { + std::vector<Vertex_handle> one_vertex(1); + for (auto vertex : vertices_) { +#ifdef DEBUG_TRACES + std::clog << "SimplicialComplex insertion " << vertex << std::endl; +#endif // DEBUG_TRACES + one_vertex[0] = vertex; + complex.insert_simplex_and_subfaces(one_vertex, std::numeric_limits<double>::quiet_NaN()); + } + for (auto cit = triangulation_->finite_full_cells_begin(); cit != triangulation_->finite_full_cells_end(); ++cit) { Vector_vertex vertexVector; #ifdef DEBUG_TRACES - std::cout << "Simplex_tree insertion "; + std::clog << "SimplicialComplex insertion "; #endif // DEBUG_TRACES for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) { if (*vit != nullptr) { #ifdef DEBUG_TRACES - std::cout << " " << (*vit)->data(); + std::clog << " " << (*vit)->data(); #endif // DEBUG_TRACES // Vector of vertex construction for simplex_tree structure vertexVector.push_back((*vit)->data()); } } #ifdef DEBUG_TRACES - std::cout << std::endl; + std::clog << std::endl; #endif // DEBUG_TRACES // Insert each simplex and its subfaces in the simplex tree - filtration is NaN complex.insert_simplex_and_subfaces(vertexVector, std::numeric_limits<double>::quiet_NaN()); @@ -295,58 +428,50 @@ class Alpha_complex { } // -------------------------------------------------------------------------------------------- - // -------------------------------------------------------------------------------------------- - // Will be re-used many times - Vector_of_CGAL_points pointVector; - // ### For i : d -> 0 - for (int decr_dim = triangulation_->maximal_dimension(); decr_dim >= 0; decr_dim--) { - // ### Foreach Sigma of dim i - for (Simplex_handle f_simplex : complex.skeleton_simplex_range(decr_dim)) { - int f_simplex_dim = complex.dimension(f_simplex); - if (decr_dim == f_simplex_dim) { - pointVector.clear(); -#ifdef DEBUG_TRACES - std::cout << "Sigma of dim " << decr_dim << " is"; -#endif // DEBUG_TRACES - for (auto vertex : complex.simplex_vertex_range(f_simplex)) { - pointVector.push_back(get_point(vertex)); -#ifdef DEBUG_TRACES - std::cout << " " << vertex; -#endif // DEBUG_TRACES - } + if (!default_filtration_value) { + CGAL::NT_converter<FT, Filtration_value> cgal_converter; + // -------------------------------------------------------------------------------------------- + // ### For i : d -> 0 + for (int decr_dim = triangulation_->maximal_dimension(); decr_dim >= 0; decr_dim--) { + // ### Foreach Sigma of dim i + for (Simplex_handle f_simplex : complex.skeleton_simplex_range(decr_dim)) { + int f_simplex_dim = complex.dimension(f_simplex); + if (decr_dim == f_simplex_dim) { + // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma) + if (std::isnan(complex.filtration(f_simplex))) { + Filtration_value alpha_complex_filtration = 0.0; + // No need to compute squared_radius on a non-weighted single point - alpha is 0.0 + if (Weighted || f_simplex_dim > 0) { + auto const& sqrad = radius(complex, f_simplex); +#if CGAL_VERSION_NR >= 1050000000 + if(exact) CGAL::exact(sqrad); +#endif + alpha_complex_filtration = cgal_converter(sqrad); + } + complex.assign_filtration(f_simplex, alpha_complex_filtration); #ifdef DEBUG_TRACES - std::cout << std::endl; + std::clog << "filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl; #endif // DEBUG_TRACES - // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma) - if (std::isnan(complex.filtration(f_simplex))) { - Filtration_value alpha_complex_filtration = 0.0; - // No need to compute squared_radius on a single point - alpha is 0.0 - if (f_simplex_dim > 0) { - // squared_radius function initialization - Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object(); - CGAL::NT_converter<typename Geom_traits::FT, Filtration_value> cv; - - alpha_complex_filtration = cv(squared_radius(pointVector.begin(), pointVector.end())); } - complex.assign_filtration(f_simplex, alpha_complex_filtration); -#ifdef DEBUG_TRACES - std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl; -#endif // DEBUG_TRACES + // No need to propagate further, unweighted points all have value 0 + if (decr_dim > !Weighted) + propagate_alpha_filtration(complex, f_simplex); } - // No need to propagate further, unweighted points all have value 0 - if (decr_dim > 1) - propagate_alpha_filtration(complex, f_simplex); } + old_cache_ = std::move(cache_); + cache_.clear(); } + // -------------------------------------------------------------------------------------------- + + // -------------------------------------------------------------------------------------------- + if (!exact) + // As Alpha value is an approximation, we have to make filtration non decreasing while increasing the dimension + // Only in not exact version, cf. https://github.com/GUDHI/gudhi-devel/issues/57 + 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); + // -------------------------------------------------------------------------------------------- } - // -------------------------------------------------------------------------------------------- - - // -------------------------------------------------------------------------------------------- - // 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; } @@ -354,21 +479,19 @@ class Alpha_complex { template <typename SimplicialComplexForAlpha, typename Simplex_handle> void propagate_alpha_filtration(SimplicialComplexForAlpha& complex, Simplex_handle f_simplex) { // From SimplicialComplexForAlpha type required to assign filtration values. - typedef typename SimplicialComplexForAlpha::Filtration_value Filtration_value; -#ifdef DEBUG_TRACES - typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle; -#endif // DEBUG_TRACES + using Filtration_value = typename SimplicialComplexForAlpha::Filtration_value; // ### Foreach Tau face of Sigma - for (auto f_boundary : complex.boundary_simplex_range(f_simplex)) { + for (auto face_opposite_vertex : complex.boundary_opposite_vertex_simplex_range(f_simplex)) { + auto f_boundary = face_opposite_vertex.first; #ifdef DEBUG_TRACES - std::cout << " | --------------------------------------------------\n"; - std::cout << " | Tau "; + std::clog << " | --------------------------------------------------\n"; + std::clog << " | Tau "; for (auto vertex : complex.simplex_vertex_range(f_boundary)) { - std::cout << vertex << " "; + std::clog << vertex << " "; } - std::cout << "is a face of Sigma\n"; - std::cout << " | isnan(complex.filtration(Tau)=" << std::isnan(complex.filtration(f_boundary)) << std::endl; + std::clog << "is a face of Sigma\n"; + std::clog << " | isnan(complex.filtration(Tau)=" << std::isnan(complex.filtration(f_boundary)) << std::endl; #endif // DEBUG_TRACES // ### If filt(Tau) is not NaN if (!std::isnan(complex.filtration(f_boundary))) { @@ -377,37 +500,14 @@ class Alpha_complex { complex.filtration(f_simplex)); complex.assign_filtration(f_boundary, alpha_complex_filtration); #ifdef DEBUG_TRACES - std::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl; + std::clog << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl; #endif // DEBUG_TRACES // ### Else } else { - // insert the Tau points in a vector for is_gabriel function - Vector_of_CGAL_points pointVector; -#ifdef DEBUG_TRACES - Vertex_handle vertexForGabriel = Vertex_handle(); -#endif // DEBUG_TRACES - for (auto vertex : complex.simplex_vertex_range(f_boundary)) { - pointVector.push_back(get_point(vertex)); - } - // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function - Point_d point_for_gabriel; - for (auto vertex : complex.simplex_vertex_range(f_simplex)) { - point_for_gabriel = get_point(vertex); - if (std::find(pointVector.begin(), pointVector.end(), point_for_gabriel) == pointVector.end()) { -#ifdef DEBUG_TRACES - // vertex is not found in Tau - vertexForGabriel = vertex; -#endif // DEBUG_TRACES - // No need to continue loop - break; - } - } - // is_gabriel function initialization - Is_Gabriel is_gabriel = kernel_.side_of_bounded_sphere_d_object(); - bool is_gab = is_gabriel(pointVector.begin(), pointVector.end(), point_for_gabriel) - != CGAL::ON_BOUNDED_SIDE; + auto const& cache=get_cache(complex, f_boundary); + bool is_gab = kernel_.is_gabriel(cache, get_point_(face_opposite_vertex.second)); #ifdef DEBUG_TRACES - std::cout << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << vertexForGabriel << std::endl; + std::clog << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << face_opposite_vertex.second << std::endl; #endif // DEBUG_TRACES // ### If Tau is not Gabriel of Sigma if (false == is_gab) { @@ -415,7 +515,7 @@ class Alpha_complex { Filtration_value alpha_complex_filtration = complex.filtration(f_simplex); complex.assign_filtration(f_boundary, alpha_complex_filtration); #ifdef DEBUG_TRACES - std::cout << " | filt(Tau) = filt(Sigma) = " << complex.filtration(f_boundary) << std::endl; + std::clog << " | filt(Tau) = filt(Sigma) = " << complex.filtration(f_boundary) << std::endl; #endif // DEBUG_TRACES } } |