106 using Internal_vertex_handle = std::ptrdiff_t;
110 using Geom_traits = std::conditional_t<Weighted, CGAL::Regular_triangulation_traits_adapter<Kernel>, Kernel>;
113 using TDS = CGAL::Triangulation_data_structure<
typename Geom_traits::Dimension,
114 CGAL::Triangulation_vertex<Geom_traits, Internal_vertex_handle>,
115 CGAL::Triangulation_full_cell<Geom_traits> >;
118 using Triangulation = std::conditional_t<Weighted, CGAL::Regular_triangulation<Kernel, TDS>,
119 CGAL::Delaunay_triangulation<Kernel, TDS>>;
125 using FT =
typename A_kernel_d::FT;
130 using Sphere =
typename A_kernel_d::Sphere;
133 using Point_d =
typename Geom_traits::Point_d;
137 using CGAL_vertex_iterator =
typename Triangulation::Vertex_iterator;
140 using Vector_vertex_iterator = std::vector< CGAL_vertex_iterator >;
145 Vector_vertex_iterator vertex_handle_to_iterator_;
147 std::unique_ptr<Triangulation> triangulation_;
153 std::vector<Internal_vertex_handle> vertices_;
156 std::vector<Sphere> cache_, old_cache_;
171 std::cerr <<
"Alpha_complex - Unable to read file " << off_file_name <<
"\n";
188 template<
typename InputPo
intRange >
190 init_from_range(points);
205 template <
typename InputPo
intRange,
typename WeightRange>
207 static_assert(Weighted,
"This constructor is not available for non-weighted versions of Alpha_complex");
209 GUDHI_CHECK(boost::size(weights) == boost::size(points),
210 std::invalid_argument(
"Points number in range different from weights range number"));
211 auto weighted_points = boost::range::combine(points, weights)
212 | boost::adaptors::transformed([](
auto const&t){
return Point_d(boost::get<0>(t), boost::get<1>(t));});
213 init_from_range(weighted_points);
225 if (triangulation_ ==
nullptr)
228 return triangulation_->number_of_vertices();
238 auto it = vertex_handle_to_iterator_.at(vertex);
239 if (it ==
nullptr)
throw std::out_of_range(
"This vertex is missing, maybe hidden by a duplicate or another heavier point.");
244 template<
typename InputPo
intRange >
245 void init_from_range(
const InputPointRange& points) {
246 #if CGAL_VERSION_NR < 1050000000
247 if (Is_Epeck_D<Kernel>::value)
248 std::cerr <<
"It is strongly advised to use a CGAL version >= 5.0 with Epeck_d Kernel for performance reasons."
252#if CGAL_VERSION_NR < 1050101000
254 static_assert(!Weighted,
"Weighted Alpha_complex is only available for CGAL >= 5.1");
257 auto first = std::begin(points);
258 auto last = std::end(points);
262 triangulation_ = std::make_unique<Triangulation>(kernel_.get_dimension(*first));
264 std::vector<Point_d> point_cloud(first, last);
267 std::vector<Internal_vertex_handle> indices(boost::counting_iterator<Internal_vertex_handle>(0),
268 boost::counting_iterator<Internal_vertex_handle>(point_cloud.size()));
270 using Point_property_map = boost::iterator_property_map<typename std::vector<Point_d>::iterator,
271 CGAL::Identity_property_map<Internal_vertex_handle>>;
272 using Search_traits_d = CGAL::Spatial_sort_traits_adapter_d<Geom_traits, Point_property_map>;
274 CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud)));
276 typename Triangulation::Full_cell_handle hint;
277 for (
auto index : indices) {
278 typename Triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint);
279 if (pos !=
nullptr) {
282 hint = pos->full_cell();
288 vertex_handle_to_iterator_.resize(point_cloud.size());
291 vertices_.reserve(triangulation_->number_of_vertices());
293 for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
294 if (!triangulation_->is_infinite(*vit)) {
296 std::clog <<
"Vertex insertion - " << vit->data() <<
" -> " << vit->point() << std::endl;
298 vertex_handle_to_iterator_[vit->data()] = vit;
299 vertices_.push_back(vit->data());
302 std::sort(vertices_.begin(), vertices_.end());
313 const Point_d& get_point_(std::size_t vertex)
const {
314 return vertex_handle_to_iterator_[vertex]->point();
318 template<
class SimplicialComplexForAlpha>
320 auto k = cplx.key(s);
321 if(k==cplx.null_key()){
323 cplx.assign_key(s, k);
325 thread_local std::vector<Point_d> v;
327 for (
auto vertex : cplx.simplex_vertex_range(s))
328 v.push_back(get_point_(vertex));
329 cache_.emplace_back(kernel_.get_sphere(v.cbegin(), v.cend()));
335 template<
class SimplicialComplexForAlpha>
337 auto k = cplx.key(s);
338 if(k!=cplx.null_key())
339 return kernel_.get_squared_radius(old_cache_[k]);
341 thread_local std::vector<Point_d> v;
343 for (
auto vertex : cplx.simplex_vertex_range(s))
344 v.push_back(get_point_(vertex));
345 return kernel_.get_squared_radius(v.cbegin(), v.cend());
372 template <
typename SimplicialComplexForAlpha,
375 Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity(),
377 bool default_filtration_value =
false) {
379 static_assert(std::numeric_limits<Filtration_value>::has_quiet_NaN);
386 using Vector_vertex = std::vector<Vertex_handle>;
388 if (triangulation_ ==
nullptr) {
389 std::cerr <<
"Alpha_complex cannot create_complex from a NULL triangulation\n";
392 if (triangulation_->maximal_dimension() < 1) {
393 std::cerr <<
"Alpha_complex cannot create_complex from a zero-dimension triangulation\n";
397 std::cerr <<
"Alpha_complex create_complex - complex is not empty\n";
404 std::vector<Vertex_handle> one_vertex(1);
405 for (
auto vertex : vertices_) {
407 std::clog <<
"SimplicialComplex insertion " << vertex << std::endl;
409 one_vertex[0] = vertex;
413 for (
auto cit = triangulation_->finite_full_cells_begin();
414 cit != triangulation_->finite_full_cells_end();
416 Vector_vertex vertexVector;
418 std::clog <<
"SimplicialComplex insertion ";
420 for (
auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
421 if (*vit !=
nullptr) {
423 std::clog <<
" " << (*vit)->data();
426 vertexVector.push_back((*vit)->data());
430 std::clog << std::endl;
438 if (!default_filtration_value) {
439 CGAL::NT_converter<FT, Filtration_value> cgal_converter;
442 for (
int decr_dim = triangulation_->maximal_dimension(); decr_dim >= 0; decr_dim--) {
445 int f_simplex_dim = complex.
dimension(f_simplex);
446 if (decr_dim == f_simplex_dim) {
448 if (isnan(complex.filtration(f_simplex))) {
451 if (Weighted || f_simplex_dim > 0) {
452 auto const& sqrad = radius(complex, f_simplex);
453#if CGAL_VERSION_NR >= 1050000000
454 if(exact) CGAL::exact(sqrad);
456 alpha_complex_filtration = cgal_converter(sqrad);
460 std::clog <<
"filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl;
464 if (decr_dim > !Weighted)
465 propagate_alpha_filtration(complex, f_simplex);
468 old_cache_ = std::move(cache_);
486 template <
typename SimplicialComplexForAlpha,
typename Simplex_handle>
494 for (
auto face_opposite_vertex : complex.boundary_opposite_vertex_simplex_range(f_simplex)) {
495 auto f_boundary = face_opposite_vertex.first;
497 std::clog <<
" | --------------------------------------------------\n";
498 std::clog <<
" | Tau ";
499 for (
auto vertex : complex.simplex_vertex_range(f_boundary)) {
500 std::clog << vertex <<
" ";
502 std::clog <<
"is a face of Sigma\n";
503 std::clog <<
" | isnan(complex.filtration(Tau)=" << isnan(complex.filtration(f_boundary)) << std::endl;
506 if (!isnan(complex.filtration(f_boundary))) {
508 Filtration_value alpha_complex_filtration = fmin(complex.filtration(f_boundary),
509 complex.filtration(f_simplex));
512 std::clog <<
" | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl;
516 auto const& cache=get_cache(complex, f_boundary);
517 bool is_gab = kernel_.is_gabriel(cache, get_point_(face_opposite_vertex.second));
519 std::clog <<
" | Tau is_gabriel(Sigma)=" << is_gab <<
" - vertexForGabriel=" << face_opposite_vertex.second << std::endl;
522 if (
false == is_gab) {
527 std::clog <<
" | filt(Tau) = filt(Sigma) = " << complex.filtration(f_boundary) << std::endl;