12 #ifndef TANGENTIAL_COMPLEX_H_ 13 #define TANGENTIAL_COMPLEX_H_ 15 #include <gudhi/Tangential_complex/config.h> 16 #include <gudhi/Tangential_complex/Simplicial_complex.h> 17 #include <gudhi/Tangential_complex/utilities.h> 18 #include <gudhi/Kd_tree_search.h> 19 #include <gudhi/console_color.h> 20 #include <gudhi/Clock.h> 21 #include <gudhi/Simplex_tree.h> 22 #include <gudhi/Debug_utils.h> 24 #include <CGAL/Default.h> 25 #include <CGAL/Dimension.h> 26 #include <CGAL/function_objects.h> 27 #include <CGAL/Epick_d.h> 28 #include <CGAL/Regular_triangulation_traits_adapter.h> 29 #include <CGAL/Regular_triangulation.h> 30 #include <CGAL/Delaunay_triangulation.h> 31 #include <CGAL/Combination_enumerator.h> 32 #include <CGAL/point_generators_d.h> 33 #include <CGAL/version.h> 36 #include <Eigen/Eigen> 37 #include <Eigen/src/Core/util/Macros.h> 39 #include <boost/optional.hpp> 40 #include <boost/iterator/transform_iterator.hpp> 41 #include <boost/range/adaptor/transformed.hpp> 42 #include <boost/range/counting_range.hpp> 43 #include <boost/math/special_functions/factorials.hpp> 44 #include <boost/container/flat_set.hpp> 61 #include <tbb/parallel_for.h> 62 #include <tbb/combinable.h> 69 #if CGAL_VERSION_NR < 1041101000 70 # error Tangential_complex is only available for CGAL >= 4.11 73 #if !EIGEN_VERSION_AT_LEAST(3,1,0) 74 # error Tangential_complex is only available for Eigen3 >= 3.1.0 installed with CGAL 81 namespace tangential_complex {
83 using namespace internal;
87 Vertex_data(std::size_t data = (std::numeric_limits<std::size_t>::max)()) : m_data(data) {}
89 operator std::size_t() {
return m_data; }
91 operator std::size_t()
const {
return m_data; }
122 template <
typename Kernel_,
123 typename DimensionTag,
124 typename Concurrency_tag = CGAL::Parallel_tag,
typename Triangulation_ = CGAL::Default>
127 typedef typename K::FT FT;
128 typedef typename K::Point_d Point;
129 typedef typename K::Weighted_point_d Weighted_point;
130 typedef typename K::Vector_d Vector;
132 typedef typename CGAL::Default::Get<
134 CGAL::Regular_triangulation<
135 CGAL::Epick_d<DimensionTag>,
136 CGAL::Triangulation_data_structure<
137 typename CGAL::Epick_d<DimensionTag>::Dimension,
138 CGAL::Triangulation_vertex<CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> >,
140 CGAL::Triangulation_full_cell<
141 CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> > > > > >::type Triangulation;
142 typedef typename Triangulation::Geom_traits Tr_traits;
143 typedef typename Triangulation::Weighted_point Tr_point;
144 typedef typename Tr_traits::Base::Point_d Tr_bare_point;
145 typedef typename Triangulation::Vertex_handle Tr_vertex_handle;
146 typedef typename Triangulation::Full_cell_handle Tr_full_cell_handle;
147 typedef typename Tr_traits::Vector_d Tr_vector;
149 #if defined(GUDHI_USE_TBB) 150 typedef std::mutex Mutex_for_perturb;
151 typedef Vector Translation_for_perturb;
152 typedef std::vector<Atomic_wrapper<FT> > Weights;
154 typedef Vector Translation_for_perturb;
155 typedef std::vector<FT> Weights;
157 typedef std::vector<Translation_for_perturb> Translations_for_perturb;
163 Tr_and_VH() : m_tr(NULL) {}
165 Tr_and_VH(
int dim) : m_tr(
new Triangulation(dim)) {}
167 ~Tr_and_VH() { destroy_triangulation(); }
169 Triangulation &construct_triangulation(
int dim) {
171 m_tr =
new Triangulation(dim);
175 void destroy_triangulation() {
180 Triangulation &tr() {
return *m_tr; }
182 Triangulation
const &tr()
const {
return *m_tr; }
184 Tr_vertex_handle
const ¢er_vertex()
const {
return m_center_vertex; }
186 Tr_vertex_handle ¢er_vertex() {
return m_center_vertex; }
190 Tr_vertex_handle m_center_vertex;
194 typedef Basis<K> Tangent_space_basis;
195 typedef Basis<K> Orthogonal_space_basis;
196 typedef std::vector<Tangent_space_basis> TS_container;
197 typedef std::vector<Orthogonal_space_basis> OS_container;
199 typedef std::vector<Point> Points;
201 typedef boost::container::flat_set<std::size_t> Simplex;
202 typedef std::set<Simplex> Simplex_set;
209 typedef std::vector<Tr_and_VH> Tr_container;
210 typedef std::vector<Vector> Vectors;
214 typedef boost::container::flat_set<std::size_t> Incident_simplex;
215 typedef std::vector<Incident_simplex> Star;
216 typedef std::vector<Star> Stars_container;
220 static const Tr_point &vertex_handle_to_point(Tr_vertex_handle vh) {
return vh->point(); }
222 template <
typename P,
typename VH>
223 static const P &vertex_handle_to_point(VH vh) {
228 typedef internal::Simplicial_complex Simplicial_complex;
239 template <
typename Po
int_range>
241 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
242 InputIterator first_for_tse, InputIterator last_for_tse,
246 m_intrinsic_dim(intrinsic_dimension),
247 m_ambient_dim(points.empty() ? 0 : k.point_dimension_d_object()(*points.begin())),
248 m_points(points.begin(), points.end()),
249 m_weights(m_points.size(), FT(0))
250 #if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION)
252 m_p_perturb_mutexes(NULL)
255 m_points_ds(m_points),
256 m_last_max_perturb(0.),
257 m_are_tangent_spaces_computed(m_points.size(), false),
258 m_tangent_spaces(m_points.size(), Tangent_space_basis())
259 #ifdef GUDHI_TC_EXPORT_NORMALS
261 m_orth_spaces(m_points.size(), Orthogonal_space_basis())
263 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
265 m_points_for_tse(first_for_tse, last_for_tse),
266 m_points_ds_for_tse(m_points_for_tse)
273 #if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION) 274 delete[] m_p_perturb_mutexes;
284 Points
const &points()
const {
return m_points; }
291 Point
get_point(std::size_t vertex)
const {
return m_points[vertex]; }
304 void set_weights(
const Weights &weights) { m_weights = weights; }
306 void set_tangent_planes(
const TS_container &tangent_spaces
307 #ifdef GUDHI_TC_EXPORT_NORMALS
309 const OS_container &orthogonal_spaces
312 #ifdef GUDHI_TC_EXPORT_NORMALS 313 GUDHI_CHECK(m_points.size() == tangent_spaces.size() && m_points.size() == orthogonal_spaces.size(),
314 std::logic_error(
"Wrong sizes"));
316 GUDHI_CHECK(m_points.size() == tangent_spaces.size(), std::logic_error(
"Wrong sizes"));
318 m_tangent_spaces = tangent_spaces;
319 #ifdef GUDHI_TC_EXPORT_NORMALS 320 m_orth_spaces = orthogonal_spaces;
322 for (std::size_t i = 0; i < m_points.size(); ++i) m_are_tangent_spaces_computed[i] =
true;
331 #ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS 332 std::cerr << red <<
"WARNING: GUDHI_TC_PERFORM_EXTRA_CHECKS is defined. " 333 <<
"Computation might be slower than usual.\n" 337 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB) 344 m_triangulations.resize(m_points.size());
345 m_stars.resize(m_points.size());
346 m_squared_star_spheres_radii_incl_margin.resize(m_points.size(), FT(-1));
347 #ifdef GUDHI_TC_PERTURB_POSITION 348 if (m_points.empty())
349 m_translations.clear();
351 m_translations.resize(m_points.size(), m_k.construct_vector_d_object()(m_ambient_dim));
352 #if defined(GUDHI_USE_TBB) 353 delete[] m_p_perturb_mutexes;
354 m_p_perturb_mutexes =
new Mutex_for_perturb[m_points.size()];
360 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
361 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*
this));
363 #endif // GUDHI_USE_TBB 365 for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
368 #endif // GUDHI_USE_TBB 370 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB) 372 std::cerr <<
"Tangential complex computed in " << t.num_seconds() <<
" seconds.\n";
379 bool success =
false;
381 unsigned int num_steps = 0;
383 std::size_t initial_num_inconsistent_stars = 0;
385 std::size_t best_num_inconsistent_stars = 0;
387 std::size_t final_num_inconsistent_stars = 0;
398 if (time_limit == 0.)
return info;
402 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES 403 std::tuple<std::size_t, std::size_t, std::size_t> stats_before = number_of_inconsistent_simplices(
false);
405 if (std::get<1>(stats_before) == 0) {
407 std::cerr <<
"Nothing to fix.\n";
412 #endif // GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES 414 m_last_max_perturb = max_perturb;
420 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES 421 std::cerr <<
"\nBefore fix step:\n" 422 <<
" * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_before) <<
"\n" 423 <<
" * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_before)
424 << white <<
" (" << 100. * std::get<1>(stats_before) / std::get<0>(stats_before) <<
"%)\n" 425 <<
" * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_before)
426 << white <<
" (" << 100. * std::get<2>(stats_before) / m_points.size() <<
"%)\n";
429 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) 430 std::cerr << yellow <<
"\nAttempt to fix inconsistencies using perturbations - step #" << info.
num_steps + 1
434 std::size_t num_inconsistent_stars = 0;
435 std::vector<std::size_t> updated_points;
437 #ifdef GUDHI_TC_PROFILING 438 Gudhi::Clock t_fix_step;
442 #if defined(GUDHI_USE_TBB) 443 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
444 tbb::combinable<std::size_t> num_inconsistencies;
445 tbb::combinable<std::vector<std::size_t> > tls_updated_points;
446 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_triangulations.size()),
447 Try_to_solve_inconsistencies_in_a_local_triangulation(*
this, max_perturb, num_inconsistencies,
448 tls_updated_points));
449 num_inconsistent_stars = num_inconsistencies.combine(std::plus<std::size_t>());
451 tls_updated_points.combine([](std::vector<std::size_t>
const &x, std::vector<std::size_t>
const &y) {
452 std::vector<std::size_t> res;
453 res.reserve(x.size() + y.size());
454 res.insert(res.end(), x.begin(), x.end());
455 res.insert(res.end(), y.begin(), y.end());
459 #endif // GUDHI_USE_TBB 461 for (std::size_t i = 0; i < m_triangulations.size(); ++i) {
462 num_inconsistent_stars +=
463 try_to_solve_inconsistencies_in_a_local_triangulation(i, max_perturb, std::back_inserter(updated_points));
465 #if defined(GUDHI_USE_TBB) 467 #endif // GUDHI_USE_TBB 469 #ifdef GUDHI_TC_PROFILING 473 #if defined(GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES) || defined(DEBUG_TRACES) 474 std::cerr <<
"\nEncountered during fix:\n" 475 <<
" * Num stars containing inconsistent simplices: " << red << num_inconsistent_stars << white <<
" (" 476 << 100. * num_inconsistent_stars / m_points.size() <<
"%)\n";
479 #ifdef GUDHI_TC_PROFILING 480 std::cerr << yellow <<
"done in " << t_fix_step.num_seconds() <<
" seconds.\n" << white;
481 #elif defined(DEBUG_TRACES) 482 std::cerr << yellow <<
"done.\n" << white;
485 if (num_inconsistent_stars > 0) refresh_tangential_complex(updated_points);
487 #ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS 489 std::size_t num_inc_1 = std::get<1>(number_of_inconsistent_simplices(
false));
490 refresh_tangential_complex();
491 std::size_t num_inc_2 = std::get<1>(number_of_inconsistent_simplices(
false));
492 if (num_inc_1 != num_inc_2)
493 std::cerr << red <<
"REFRESHMENT CHECK: FAILED. (" << num_inc_1 <<
" vs " << num_inc_2 <<
")\n" << white;
495 std::cerr << green <<
"REFRESHMENT CHECK: PASSED.\n" << white;
498 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES 499 std::tuple<std::size_t, std::size_t, std::size_t> stats_after = number_of_inconsistent_simplices(
false);
501 std::cerr <<
"\nAfter fix:\n" 502 <<
" * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_after) <<
"\n" 503 <<
" * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_after)
504 << white <<
" (" << 100. * std::get<1>(stats_after) / std::get<0>(stats_after) <<
"%)\n" 505 <<
" * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_after) << white
506 <<
" (" << 100. * std::get<2>(stats_after) / m_points.size() <<
"%)\n";
508 stats_before = stats_after;
518 done = (num_inconsistent_stars == 0);
521 if (time_limit > 0. && t.num_seconds() > time_limit) {
523 std::cerr << red <<
"Time limit reached.\n" << white;
532 std::cerr << green <<
"Fixed!\n" << white;
541 std::size_t num_simplices = 0;
543 std::size_t num_inconsistent_simplices = 0;
545 std::size_t num_inconsistent_stars = 0;
561 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
562 bool is_star_inconsistent =
false;
565 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
566 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
567 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
569 if (is_infinite(*it_inc_simplex))
continue;
571 Simplex c = *it_inc_simplex;
574 if (!is_simplex_consistent(c)) {
576 is_star_inconsistent =
true;
585 std::cerr <<
"\n==========================================================\n" 586 <<
"Inconsistencies:\n" 587 <<
" * Total number of simplices in stars (incl. duplicates): " << stats.
num_simplices <<
"\n" 588 <<
" * Number of inconsistent simplices in stars (incl. duplicates): " 593 <<
"==========================================================\n";
609 template <
typename Simplex_tree_>
611 bool export_inconsistent_simplices =
true 614 bool export_infinite_simplices =
false, Simplex_set *p_inconsistent_simplices = NULL
617 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) 618 std::cerr << yellow <<
"\nExporting the TC as a Simplex_tree... " << white;
620 #ifdef GUDHI_TC_PROFILING 627 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
629 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
630 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
631 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
632 Simplex c = *it_inc_simplex;
635 if (!export_infinite_simplices && is_infinite(c))
continue;
637 if (static_cast<int>(c.size()) > max_dim) max_dim =
static_cast<int>(c.size());
641 if (!export_inconsistent_simplices && !is_simplex_consistent(c))
continue;
644 bool inserted = tree.insert_simplex_and_subfaces(c).second;
647 if (p_inconsistent_simplices && inserted && !is_simplex_consistent(c)) {
648 p_inconsistent_simplices->insert(c);
653 #ifdef GUDHI_TC_PROFILING 655 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
656 #elif defined(DEBUG_TRACES) 657 std::cerr << yellow <<
"done.\n" << white;
673 int create_complex(Simplicial_complex &complex,
bool export_inconsistent_simplices =
true,
674 bool export_infinite_simplices =
false,
int check_lower_and_higher_dim_simplices = 2,
675 Simplex_set *p_inconsistent_simplices = NULL)
const {
676 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) 677 std::cerr << yellow <<
"\nExporting the TC as a Simplicial_complex... " << white;
679 #ifdef GUDHI_TC_PROFILING 687 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
689 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
690 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
691 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
692 Simplex c = *it_inc_simplex;
695 if (!export_infinite_simplices && is_infinite(c))
continue;
697 if (static_cast<int>(c.size()) > max_dim) max_dim =
static_cast<int>(c.size());
701 if (!export_inconsistent_simplices && !is_simplex_consistent(c))
continue;
704 if (check_lower_and_higher_dim_simplices == 2 && max_dim != -1 && static_cast<int>(c.size()) != max_dim) {
707 <<
"Info: check_lower_and_higher_dim_simplices ACTIVATED. " 708 "Export might be take some time...\n" 710 check_lower_and_higher_dim_simplices = 1;
714 bool added = complex.add_simplex(c, check_lower_and_higher_dim_simplices == 1);
717 if (p_inconsistent_simplices && added && !is_simplex_consistent(c)) {
718 p_inconsistent_simplices->insert(c);
723 #ifdef GUDHI_TC_PROFILING 725 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
726 #elif defined(DEBUG_TRACES) 727 std::cerr << yellow <<
"done.\n" << white;
733 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
734 std::ostream &export_to_off(
const Simplicial_complex &complex, std::ostream &os,
735 Simplex_set
const *p_simpl_to_color_in_red = NULL,
736 Simplex_set
const *p_simpl_to_color_in_green = NULL,
737 Simplex_set
const *p_simpl_to_color_in_blue = NULL,
738 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
739 return export_to_off(os,
false, p_simpl_to_color_in_red, p_simpl_to_color_in_green, p_simpl_to_color_in_blue,
740 &complex, point_projection);
743 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
744 std::ostream &export_to_off(std::ostream &os,
bool color_inconsistencies =
false,
745 Simplex_set
const *p_simpl_to_color_in_red = NULL,
746 Simplex_set
const *p_simpl_to_color_in_green = NULL,
747 Simplex_set
const *p_simpl_to_color_in_blue = NULL,
748 const Simplicial_complex *p_complex = NULL,
749 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
750 if (m_points.empty())
return os;
752 if (m_ambient_dim < 2) {
753 std::cerr <<
"Error: export_to_off => ambient dimension should be >= 2.\n";
754 os <<
"Error: export_to_off => ambient dimension should be >= 2.\n";
757 if (m_ambient_dim > 3) {
758 std::cerr <<
"Warning: export_to_off => ambient dimension should be " 759 "<= 3. Only the first 3 coordinates will be exported.\n";
762 if (m_intrinsic_dim < 1 || m_intrinsic_dim > 3) {
763 std::cerr <<
"Error: export_to_off => intrinsic dimension should be " 764 "between 1 and 3.\n";
765 os <<
"Error: export_to_off => intrinsic dimension should be " 766 "between 1 and 3.\n";
770 std::stringstream output;
771 std::size_t num_simplices, num_vertices;
772 export_vertices_to_off(output, num_vertices,
false, point_projection);
774 export_simplices_to_off(*p_complex, output, num_simplices, p_simpl_to_color_in_red, p_simpl_to_color_in_green,
775 p_simpl_to_color_in_blue);
777 export_simplices_to_off(output, num_simplices, color_inconsistencies, p_simpl_to_color_in_red,
778 p_simpl_to_color_in_green, p_simpl_to_color_in_blue);
781 #ifdef GUDHI_TC_EXPORT_NORMALS 786 << num_vertices <<
" " << num_simplices <<
" " 794 void refresh_tangential_complex() {
795 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) 796 std::cerr << yellow <<
"\nRefreshing TC... " << white;
799 #ifdef GUDHI_TC_PROFILING 804 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
805 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*
this));
807 #endif // GUDHI_USE_TBB 809 for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
812 #endif // GUDHI_USE_TBB 814 #ifdef GUDHI_TC_PROFILING 816 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
817 #elif defined(DEBUG_TRACES) 818 std::cerr << yellow <<
"done.\n" << white;
823 template <
typename Po
int_indices_range>
824 void refresh_tangential_complex(Point_indices_range
const &perturbed_points_indices) {
825 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING) 826 std::cerr << yellow <<
"\nRefreshing TC... " << white;
829 #ifdef GUDHI_TC_PROFILING 834 Points_ds updated_pts_ds(m_points, perturbed_points_indices);
838 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
839 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()),
840 Refresh_tangent_triangulation(*
this, updated_pts_ds));
842 #endif // GUDHI_USE_TBB 844 for (std::size_t i = 0; i < m_points.size(); ++i) refresh_tangent_triangulation(i, updated_pts_ds);
847 #endif // GUDHI_USE_TBB 849 #ifdef GUDHI_TC_PROFILING 851 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
852 #elif defined(DEBUG_TRACES) 853 std::cerr << yellow <<
"done.\n" << white;
857 void export_inconsistent_stars_to_OFF_files(std::string
const &filename_base)
const {
859 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
861 Simplicial_complex sc;
863 bool is_inconsistent =
false;
864 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
865 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
866 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
868 if (is_infinite(*it_inc_simplex))
continue;
870 Simplex c = *it_inc_simplex;
876 if (!is_inconsistent && !is_simplex_consistent(c)) is_inconsistent =
true;
879 if (is_inconsistent) {
881 std::stringstream output_filename;
882 output_filename << filename_base <<
"_" << idx <<
".off";
883 std::ofstream off_stream(output_filename.str().c_str());
884 export_to_off(sc, off_stream);
889 class Compare_distance_to_ref_point {
891 Compare_distance_to_ref_point(Point
const &ref, K
const &k) : m_ref(ref), m_k(k) {}
893 bool operator()(Point
const &p1, Point
const &p2) {
894 typename K::Squared_distance_d sqdist = m_k.squared_distance_d_object();
895 return sqdist(p1, m_ref) < sqdist(p2, m_ref);
905 class Compute_tangent_triangulation {
913 Compute_tangent_triangulation(
const Compute_tangent_triangulation &ctt) : m_tc(ctt.m_tc) {}
916 void operator()(
const tbb::blocked_range<size_t> &r)
const {
917 for (
size_t i = r.begin(); i != r.end(); ++i) m_tc.compute_tangent_triangulation(i);
922 class Refresh_tangent_triangulation {
924 Points_ds
const &m_updated_pts_ds;
928 Refresh_tangent_triangulation(
Tangential_complex &tc, Points_ds
const &updated_pts_ds)
929 : m_tc(tc), m_updated_pts_ds(updated_pts_ds) {}
932 Refresh_tangent_triangulation(
const Refresh_tangent_triangulation &ctt)
933 : m_tc(ctt.m_tc), m_updated_pts_ds(ctt.m_updated_pts_ds) {}
936 void operator()(
const tbb::blocked_range<size_t> &r)
const {
937 for (
size_t i = r.begin(); i != r.end(); ++i) m_tc.refresh_tangent_triangulation(i, m_updated_pts_ds);
940 #endif // GUDHI_USE_TBB 942 bool is_infinite(Simplex
const &s)
const {
return *s.rbegin() == (std::numeric_limits<std::size_t>::max)(); }
947 Tr_vertex_handle compute_star(std::size_t i,
const Point ¢er_pt,
const Tangent_space_basis &tsb,
948 Triangulation &triangulation,
bool verbose =
false) {
949 int tangent_space_dim = tsb.dimension();
950 const Tr_traits &local_tr_traits = triangulation.geom_traits();
953 typename K::Squared_distance_d k_sqdist = m_k.squared_distance_d_object();
956 typename Tr_traits::Compute_weight_d point_weight = local_tr_traits.compute_weight_d_object();
957 #if CGAL_VERSION_NR < 1050200000 958 typename Tr_traits::Power_center_d power_center = local_tr_traits.power_center_d_object();
960 typename Tr_traits::Construct_power_sphere_d power_center = local_tr_traits.construct_power_sphere_d_object();
970 if (i == tsb.origin()) {
972 proj_wp = local_tr_traits.construct_weighted_point_d_object()(
973 local_tr_traits.construct_point_d_object()(tangent_space_dim, CGAL::ORIGIN), m_weights[i]);
975 const Weighted_point &wp = compute_perturbed_weighted_point(i);
976 proj_wp = project_point_and_compute_weight(wp, tsb, local_tr_traits);
979 Tr_vertex_handle center_vertex = triangulation.insert(proj_wp);
980 center_vertex->data() = i;
981 if (verbose) std::cerr <<
"* Inserted point #" << i <<
"\n";
983 #ifdef GUDHI_TC_VERY_VERBOSE 984 std::size_t num_attempts_to_insert_points = 1;
985 std::size_t num_inserted_points = 1;
989 INS_range ins_range = m_points_ds.incremental_nearest_neighbors(center_pt);
997 boost::optional<FT> squared_star_sphere_radius_plus_margin = m_max_squared_edge_length;
1000 for (
auto nn_it = ins_range.begin(); nn_it != ins_range.end(); ++nn_it) {
1001 std::size_t neighbor_point_idx = nn_it->first;
1004 if (neighbor_point_idx != i) {
1009 compute_perturbed_weighted_point(neighbor_point_idx, neighbor_pt, neighbor_weight);
1010 GUDHI_CHECK(!m_max_squared_edge_length ||
1011 squared_star_sphere_radius_plus_margin.value() <= m_max_squared_edge_length.value(),
1012 std::invalid_argument(
"Tangential_complex::compute_star - set a bigger value with set_max_squared_edge_length."));
1013 if (squared_star_sphere_radius_plus_margin &&
1014 k_sqdist(center_pt, neighbor_pt) > squared_star_sphere_radius_plus_margin.value()) {
1015 GUDHI_CHECK(triangulation.current_dimension() >= tangent_space_dim,
1016 std::invalid_argument(
"Tangential_complex::compute_star - Dimension of the star is only " + \
1017 std::to_string(triangulation.current_dimension())));
1021 Tr_point proj_pt = project_point_and_compute_weight(neighbor_pt, neighbor_weight, tsb, local_tr_traits);
1023 #ifdef GUDHI_TC_VERY_VERBOSE 1024 ++num_attempts_to_insert_points;
1027 Tr_vertex_handle vh = triangulation.insert_if_in_star(proj_pt, center_vertex);
1029 if (vh != Tr_vertex_handle() && vh->data() == (std::numeric_limits<std::size_t>::max)()) {
1030 #ifdef GUDHI_TC_VERY_VERBOSE 1031 ++num_inserted_points;
1033 if (verbose) std::cerr <<
"* Inserted point #" << neighbor_point_idx <<
"\n";
1035 vh->data() = neighbor_point_idx;
1038 if (triangulation.current_dimension() >= tangent_space_dim) {
1039 squared_star_sphere_radius_plus_margin = boost::none;
1041 std::vector<Tr_full_cell_handle> incident_cells;
1042 triangulation.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
1043 for (
typename std::vector<Tr_full_cell_handle>::iterator cit = incident_cells.begin();
1044 cit != incident_cells.end(); ++cit) {
1045 Tr_full_cell_handle cell = *cit;
1046 if (triangulation.is_infinite(cell)) {
1047 squared_star_sphere_radius_plus_margin = boost::none;
1053 power_center(boost::make_transform_iterator(cell->vertices_begin(),
1054 vertex_handle_to_point<Tr_point, Tr_vertex_handle>),
1055 boost::make_transform_iterator(cell->vertices_end(),
1056 vertex_handle_to_point<Tr_point, Tr_vertex_handle>));
1058 FT sq_power_sphere_diam = 4 * point_weight(c);
1060 if (!squared_star_sphere_radius_plus_margin ||
1061 sq_power_sphere_diam > squared_star_sphere_radius_plus_margin.value()) {
1062 squared_star_sphere_radius_plus_margin = sq_power_sphere_diam;
1069 if (squared_star_sphere_radius_plus_margin) {
1071 squared_star_sphere_radius_plus_margin =
1072 CGAL::square(std::sqrt(squared_star_sphere_radius_plus_margin.value()) + 2 * m_last_max_perturb);
1075 if (m_max_squared_edge_length && squared_star_sphere_radius_plus_margin.value() > m_max_squared_edge_length.value()) {
1076 squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
1080 m_squared_star_spheres_radii_incl_margin[i] = squared_star_sphere_radius_plus_margin.value();
1082 if (m_max_squared_edge_length) {
1083 squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
1084 m_squared_star_spheres_radii_incl_margin[i] = m_max_squared_edge_length.value();
1086 m_squared_star_spheres_radii_incl_margin[i] = FT(-1);
1094 return center_vertex;
1097 void refresh_tangent_triangulation(std::size_t i, Points_ds
const &updated_pts_ds,
bool verbose =
false) {
1098 if (verbose) std::cerr <<
"** Refreshing tangent tri #" << i <<
" **\n";
1100 if (m_squared_star_spheres_radii_incl_margin[i] == FT(-1))
return compute_tangent_triangulation(i, verbose);
1102 Point center_point = compute_perturbed_point(i);
1104 std::size_t closest_pt_index = updated_pts_ds.
k_nearest_neighbors(center_point, 1,
false).begin()->first;
1106 typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
1107 #if CGAL_VERSION_NR < 1050200000 1108 typename K::Power_distance_d k_power_dist = m_k.power_distance_d_object();
1110 typename K::Compute_power_product_d k_power_dist = m_k.compute_power_product_d_object();
1114 Weighted_point star_sphere = k_constr_wp(compute_perturbed_point(i), m_squared_star_spheres_radii_incl_margin[i]);
1115 Weighted_point closest_updated_point = compute_perturbed_weighted_point(closest_pt_index);
1118 if (k_power_dist(star_sphere, closest_updated_point) <= FT(0)) compute_tangent_triangulation(i, verbose);
1121 void compute_tangent_triangulation(std::size_t i,
bool verbose =
false) {
1122 if (verbose) std::cerr <<
"** Computing tangent tri #" << i <<
" **\n";
1127 const Point center_pt = compute_perturbed_point(i);
1128 Tangent_space_basis &tsb = m_tangent_spaces[i];
1131 if (!m_are_tangent_spaces_computed[i]) {
1132 #ifdef GUDHI_TC_EXPORT_NORMALS 1133 tsb = compute_tangent_space(center_pt, i,
true , &m_orth_spaces[i]);
1135 tsb = compute_tangent_space(center_pt, i);
1139 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) 1142 int tangent_space_dim = tangent_basis_dim(i);
1143 Triangulation &local_tr = m_triangulations[i].construct_triangulation(tangent_space_dim);
1145 m_triangulations[i].center_vertex() = compute_star(i, center_pt, tsb, local_tr, verbose);
1147 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) 1149 std::cerr <<
" - triangulation construction: " << t.num_seconds() <<
" s.\n";
1153 #ifdef GUDHI_TC_VERY_VERBOSE 1154 std::cerr <<
"Inserted " << num_inserted_points <<
" points / " << num_attempts_to_insert_points
1155 <<
" attemps to compute the star\n";
1160 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE) 1162 std::cerr <<
" - update_star: " << t.num_seconds() <<
" s.\n";
1168 void update_star(std::size_t i) {
1169 Star &star = m_stars[i];
1171 Triangulation &local_tr = m_triangulations[i].tr();
1172 Tr_vertex_handle center_vertex = m_triangulations[i].center_vertex();
1173 int cur_dim_plus_1 = local_tr.current_dimension() + 1;
1175 std::vector<Tr_full_cell_handle> incident_cells;
1176 local_tr.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
1178 typename std::vector<Tr_full_cell_handle>::const_iterator it_c = incident_cells.begin();
1179 typename std::vector<Tr_full_cell_handle>::const_iterator it_c_end = incident_cells.end();
1181 for (; it_c != it_c_end; ++it_c) {
1183 Incident_simplex incident_simplex;
1184 for (
int j = 0; j < cur_dim_plus_1; ++j) {
1185 std::size_t index = (*it_c)->vertex(j)->data();
1186 if (index != i) incident_simplex.insert(index);
1188 GUDHI_CHECK(incident_simplex.size() == cur_dim_plus_1 - 1,
1189 std::logic_error(
"update_star: wrong size of incident simplex"));
1190 star.push_back(incident_simplex);
1196 Tangent_space_basis compute_tangent_space(
const Point &p,
const std::size_t i,
bool normalize_basis =
true,
1197 Orthogonal_space_basis *p_orth_space_basis = NULL) {
1198 unsigned int num_pts_for_pca =
1199 (std::min)(static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
1200 static_cast<unsigned int>(m_points.size()));
1203 typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
1204 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1206 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM 1207 KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca,
false);
1208 const Points &points_for_pca = m_points_for_tse;
1210 KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca,
false);
1211 const Points &points_for_pca = m_points;
1215 Eigen::MatrixXd mat_points(num_pts_for_pca, m_ambient_dim);
1216 auto nn_it = kns_range.begin();
1217 for (
unsigned int j = 0; j < num_pts_for_pca && nn_it != kns_range.end(); ++j, ++nn_it) {
1218 for (
int i = 0; i < m_ambient_dim; ++i) {
1219 mat_points(j, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
1222 Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
1223 Eigen::MatrixXd cov = centered.adjoint() * centered;
1224 Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
1226 Tangent_space_basis tsb(i);
1230 for (
int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
1231 if (normalize_basis) {
1232 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1233 eig.eigenvectors().col(j).data() + m_ambient_dim);
1234 tsb.push_back(normalize_vector(v, m_k));
1236 tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1237 eig.eigenvectors().col(j).data() + m_ambient_dim));
1241 if (p_orth_space_basis) {
1242 p_orth_space_basis->set_origin(i);
1243 for (
int j = m_ambient_dim - m_intrinsic_dim - 1; j >= 0; --j) {
1244 if (normalize_basis) {
1245 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1246 eig.eigenvectors().col(j).data() + m_ambient_dim);
1247 p_orth_space_basis->push_back(normalize_vector(v, m_k));
1249 p_orth_space_basis->push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1250 eig.eigenvectors().col(j).data() + m_ambient_dim));
1255 m_are_tangent_spaces_computed[i] =
true;
1265 Tangent_space_basis compute_tangent_space(
const Simplex &s,
bool normalize_basis =
true) {
1266 unsigned int num_pts_for_pca =
1267 (std::min)(static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
1268 static_cast<unsigned int>(m_points.size()));
1271 typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
1272 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1273 typename K::Squared_length_d sqlen = m_k.squared_length_d_object();
1274 typename K::Scaled_vector_d scaled_vec = m_k.scaled_vector_d_object();
1275 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1276 typename K::Difference_of_vectors_d diff_vec = m_k.difference_of_vectors_d_object();
1279 Eigen::MatrixXd mat_points(s.size() * num_pts_for_pca, m_ambient_dim);
1280 unsigned int current_row = 0;
1282 for (Simplex::const_iterator it_index = s.begin(); it_index != s.end(); ++it_index) {
1283 const Point &p = m_points[*it_index];
1285 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM 1286 KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca,
false);
1287 const Points &points_for_pca = m_points_for_tse;
1289 KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca,
false);
1290 const Points &points_for_pca = m_points;
1293 auto nn_it = kns_range.begin();
1294 for (; current_row < num_pts_for_pca && nn_it != kns_range.end(); ++current_row, ++nn_it) {
1295 for (
int i = 0; i < m_ambient_dim; ++i) {
1296 mat_points(current_row, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
1300 Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
1301 Eigen::MatrixXd cov = centered.adjoint() * centered;
1302 Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
1304 Tangent_space_basis tsb;
1308 for (
int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
1309 if (normalize_basis) {
1310 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1311 eig.eigenvectors().col(j).data() + m_ambient_dim);
1312 tsb.push_back(normalize_vector(v, m_k));
1314 tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1315 eig.eigenvectors().col(j).data() + m_ambient_dim));
1324 int tangent_basis_dim(std::size_t i)
const {
return m_tangent_spaces[i].dimension(); }
1326 Point compute_perturbed_point(std::size_t pt_idx)
const {
1327 #ifdef GUDHI_TC_PERTURB_POSITION 1328 return m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
1330 return m_points[pt_idx];
1334 void compute_perturbed_weighted_point(std::size_t pt_idx, Point &p, FT &w)
const {
1335 #ifdef GUDHI_TC_PERTURB_POSITION 1336 p = m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
1338 p = m_points[pt_idx];
1340 w = m_weights[pt_idx];
1343 Weighted_point compute_perturbed_weighted_point(std::size_t pt_idx)
const {
1344 typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
1346 Weighted_point wp = k_constr_wp(
1347 #ifdef GUDHI_TC_PERTURB_POSITION
1348 m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]),
1357 Point unproject_point(
const Tr_point &p,
const Tangent_space_basis &tsb,
const Tr_traits &tr_traits)
const {
1358 typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
1359 typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
1360 typename Tr_traits::Compute_coordinate_d coord = tr_traits.compute_coordinate_d_object();
1362 Point global_point = compute_perturbed_point(tsb.origin());
1363 for (
int i = 0; i < m_intrinsic_dim; ++i) global_point = k_transl(global_point, k_scaled_vec(tsb[i], coord(p, i)));
1365 return global_point;
1370 Tr_bare_point project_point(
const Point &p,
const Tangent_space_basis &tsb,
const Tr_traits &tr_traits)
const {
1371 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1372 typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
1374 Vector v = diff_points(p, compute_perturbed_point(tsb.origin()));
1376 std::vector<FT> coords;
1378 coords.reserve(tsb.dimension());
1379 for (std::size_t i = 0; i < m_intrinsic_dim; ++i) {
1381 FT coord = scalar_pdct(v, tsb[i]);
1382 coords.push_back(coord);
1385 return tr_traits.construct_point_d_object()(
static_cast<int>(coords.size()), coords.begin(), coords.end());
1392 Tr_point project_point_and_compute_weight(
const Weighted_point &wp,
const Tangent_space_basis &tsb,
1393 const Tr_traits &tr_traits)
const {
1394 typename K::Point_drop_weight_d k_drop_w = m_k.point_drop_weight_d_object();
1395 typename K::Compute_weight_d k_point_weight = m_k.compute_weight_d_object();
1396 return project_point_and_compute_weight(k_drop_w(wp), k_point_weight(wp), tsb, tr_traits);
1400 Tr_point project_point_and_compute_weight(
const Point &p,
const FT w,
const Tangent_space_basis &tsb,
1401 const Tr_traits &tr_traits)
const {
1402 const int point_dim = m_k.point_dimension_d_object()(p);
1404 typename K::Construct_point_d constr_pt = m_k.construct_point_d_object();
1405 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1406 typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
1407 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1408 typename K::Construct_cartesian_const_iterator_d ccci = m_k.construct_cartesian_const_iterator_d_object();
1410 Point origin = compute_perturbed_point(tsb.origin());
1411 Vector v = diff_points(p, origin);
1414 bool same_dim = (point_dim == tsb.dimension());
1416 std::vector<FT> coords;
1418 std::vector<FT> p_proj(ccci(origin), ccci(origin, 0));
1419 coords.reserve(tsb.dimension());
1420 for (
int i = 0; i < tsb.dimension(); ++i) {
1422 FT c = scalar_pdct(v, tsb[i]);
1423 coords.push_back(c);
1427 for (
int j = 0; j < point_dim; ++j) p_proj[j] += c * coord(tsb[i], j);
1432 FT sq_dist_to_proj_pt = 0;
1434 Point projected_pt = constr_pt(point_dim, p_proj.begin(), p_proj.end());
1435 sq_dist_to_proj_pt = m_k.squared_distance_d_object()(p, projected_pt);
1438 return tr_traits.construct_weighted_point_d_object()(
1439 tr_traits.construct_point_d_object()(
static_cast<int>(coords.size()), coords.begin(), coords.end()),
1440 w - sq_dist_to_proj_pt);
1445 template <
typename Indexed_po
int_range>
1446 std::vector<Tr_point> project_points_and_compute_weights(
const Indexed_point_range &point_indices,
1447 const Tangent_space_basis &tsb,
1448 const Tr_traits &tr_traits)
const {
1449 std::vector<Tr_point> ret;
1450 for (
typename Indexed_point_range::const_iterator it = point_indices.begin(), it_end = point_indices.end();
1451 it != it_end; ++it) {
1452 ret.push_back(project_point_and_compute_weight(compute_perturbed_weighted_point(*it), tsb, tr_traits));
1459 bool is_simplex_consistent(Tr_full_cell_handle fch,
int cur_dim)
const {
1461 for (
int i = 0; i < cur_dim + 1; ++i) {
1462 std::size_t data = fch->vertex(i)->data();
1465 return is_simplex_consistent(c);
1471 bool is_simplex_consistent(Simplex
const &simplex)
const {
1473 Simplex::const_iterator it_point_idx = simplex.begin();
1476 for (; it_point_idx != simplex.end(); ++it_point_idx) {
1477 std::size_t point_idx = *it_point_idx;
1479 if (point_idx == (std::numeric_limits<std::size_t>::max)())
continue;
1481 Star
const &star = m_stars[point_idx];
1484 Incident_simplex is_to_find = simplex;
1485 is_to_find.erase(point_idx);
1488 if (std::find(star.begin(), star.end(), is_to_find) == star.end())
return false;
1500 template <
typename OutputIterator>
1501 bool is_simplex_consistent(std::size_t center_point,
1502 Incident_simplex
const &s,
1503 OutputIterator points_whose_star_does_not_contain_s,
1504 bool check_also_in_non_maximal_faces =
false)
const {
1505 Simplex full_simplex = s;
1506 full_simplex.insert(center_point);
1509 Incident_simplex::const_iterator it_point_idx = s.begin();
1512 for (; it_point_idx != s.end(); ++it_point_idx) {
1513 std::size_t point_idx = *it_point_idx;
1515 if (point_idx == (std::numeric_limits<std::size_t>::max)())
continue;
1517 Star
const &star = m_stars[point_idx];
1520 Incident_simplex is_to_find = full_simplex;
1521 is_to_find.erase(point_idx);
1523 if (check_also_in_non_maximal_faces) {
1527 for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
1528 if (std::includes(is->begin(), is->end(), is_to_find.begin(), is_to_find.end())) found =
true;
1531 if (!found) *points_whose_star_does_not_contain_s++ = point_idx;
1534 if (std::find(star.begin(), star.end(), is_to_find) == star.end())
1535 *points_whose_star_does_not_contain_s++ = point_idx;
1545 bool is_simplex_in_star(std::size_t p, Incident_simplex
const &s,
bool check_also_in_non_maximal_faces =
true)
const {
1546 Star
const &star = m_stars[p];
1548 if (check_also_in_non_maximal_faces) {
1552 for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
1553 if (std::includes(is->begin(), is->end(), s.begin(), s.end())) found =
true;
1558 return !(std::find(star.begin(), star.end(), s) == star.end());
1562 #ifdef GUDHI_USE_TBB 1564 class Try_to_solve_inconsistencies_in_a_local_triangulation {
1566 double m_max_perturb;
1567 tbb::combinable<std::size_t> &m_num_inconsistencies;
1568 tbb::combinable<std::vector<std::size_t> > &m_updated_points;
1572 Try_to_solve_inconsistencies_in_a_local_triangulation(
Tangential_complex &tc,
double max_perturb,
1573 tbb::combinable<std::size_t> &num_inconsistencies,
1574 tbb::combinable<std::vector<std::size_t> > &updated_points)
1576 m_max_perturb(max_perturb),
1577 m_num_inconsistencies(num_inconsistencies),
1578 m_updated_points(updated_points) {}
1581 Try_to_solve_inconsistencies_in_a_local_triangulation(
1582 const Try_to_solve_inconsistencies_in_a_local_triangulation &tsilt)
1584 m_max_perturb(tsilt.m_max_perturb),
1585 m_num_inconsistencies(tsilt.m_num_inconsistencies),
1586 m_updated_points(tsilt.m_updated_points) {}
1589 void operator()(
const tbb::blocked_range<size_t> &r)
const {
1590 for (
size_t i = r.begin(); i != r.end(); ++i) {
1591 m_num_inconsistencies.local() += m_tc.try_to_solve_inconsistencies_in_a_local_triangulation(
1592 i, m_max_perturb, std::back_inserter(m_updated_points.local()));
1596 #endif // GUDHI_USE_TBB 1598 void perturb(std::size_t point_idx,
double max_perturb) {
1599 const Tr_traits &local_tr_traits = m_triangulations[point_idx].tr().geom_traits();
1600 typename Tr_traits::Compute_coordinate_d coord = local_tr_traits.compute_coordinate_d_object();
1601 typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
1602 typename K::Construct_vector_d k_constr_vec = m_k.construct_vector_d_object();
1603 typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
1605 CGAL::Random_points_in_ball_d<Tr_bare_point> tr_point_in_ball_generator(
1606 m_intrinsic_dim, m_random_generator.get_double(0., max_perturb));
1608 Tr_point local_random_transl =
1609 local_tr_traits.construct_weighted_point_d_object()(*tr_point_in_ball_generator++, 0);
1610 Translation_for_perturb global_transl = k_constr_vec(m_ambient_dim);
1611 const Tangent_space_basis &tsb = m_tangent_spaces[point_idx];
1612 for (
int i = 0; i < m_intrinsic_dim; ++i) {
1613 global_transl = k_transl(global_transl, k_scaled_vec(tsb[i], coord(local_random_transl, i)));
1616 #if defined(GUDHI_USE_TBB) 1617 m_p_perturb_mutexes[point_idx].lock();
1618 m_translations[point_idx] = global_transl;
1619 m_p_perturb_mutexes[point_idx].unlock();
1622 m_translations[point_idx] = global_transl;
1627 template <
typename OutputIt>
1628 bool try_to_solve_inconsistencies_in_a_local_triangulation(
1629 std::size_t tr_index,
double max_perturb, OutputIt perturbed_pts_indices = CGAL::Emptyset_iterator()) {
1630 bool is_inconsistent =
false;
1632 Star
const &star = m_stars[tr_index];
1635 Star::const_iterator it_inc_simplex = star.begin();
1636 Star::const_iterator it_inc_simplex_end = star.end();
1637 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
1638 const Incident_simplex &incident_simplex = *it_inc_simplex;
1641 if (is_infinite(incident_simplex))
continue;
1643 Simplex c = incident_simplex;
1647 if (!is_simplex_consistent(c)) {
1648 is_inconsistent =
true;
1650 std::size_t idx = tr_index;
1652 perturb(tr_index, max_perturb);
1653 *perturbed_pts_indices++ = idx;
1660 return is_inconsistent;
1665 std::ostream &export_point_set(std::ostream &os,
bool use_perturbed_points =
false,
1666 const char *coord_separator =
" ")
const {
1667 if (use_perturbed_points) {
1668 std::vector<Point> perturbed_points;
1669 perturbed_points.reserve(m_points.size());
1670 for (std::size_t i = 0; i < m_points.size(); ++i) perturbed_points.push_back(compute_perturbed_point(i));
1672 return export_point_set(m_k, perturbed_points, os, coord_separator);
1674 return export_point_set(m_k, m_points, os, coord_separator);
1678 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
1679 std::ostream &export_vertices_to_off(std::ostream &os, std::size_t &num_vertices,
bool use_perturbed_points =
false,
1680 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
1681 if (m_points.empty()) {
1689 const int N = (m_intrinsic_dim == 1 ? 2 : 1);
1692 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1694 #ifdef GUDHI_TC_EXPORT_ALL_COORDS_IN_OFF 1695 int num_coords = m_ambient_dim;
1697 int num_coords = (std::min)(m_ambient_dim, 3);
1700 #ifdef GUDHI_TC_EXPORT_NORMALS 1701 OS_container::const_iterator it_os = m_orth_spaces.begin();
1703 typename Points::const_iterator it_p = m_points.begin();
1704 typename Points::const_iterator it_p_end = m_points.end();
1706 for (std::size_t i = 0; it_p != it_p_end; ++it_p, ++i) {
1707 Point p = point_projection(use_perturbed_points ? compute_perturbed_point(i) : *it_p);
1708 for (
int ii = 0; ii < N; ++ii) {
1710 for (; j < num_coords; ++j) os << CGAL::to_double(coord(p, j)) <<
" ";
1711 if (j == 2) os <<
"0";
1713 #ifdef GUDHI_TC_EXPORT_NORMALS 1714 for (j = 0; j < num_coords; ++j) os <<
" " << CGAL::to_double(coord(*it_os->begin(), j));
1718 #ifdef GUDHI_TC_EXPORT_NORMALS 1723 num_vertices = N * m_points.size();
1727 std::ostream &export_simplices_to_off(std::ostream &os, std::size_t &num_OFF_simplices,
1728 bool color_inconsistencies =
false,
1729 Simplex_set
const *p_simpl_to_color_in_red = NULL,
1730 Simplex_set
const *p_simpl_to_color_in_green = NULL,
1731 Simplex_set
const *p_simpl_to_color_in_blue = NULL)
const {
1734 num_OFF_simplices = 0;
1735 std::size_t num_maximal_simplices = 0;
1736 std::size_t num_inconsistent_maximal_simplices = 0;
1737 std::size_t num_inconsistent_stars = 0;
1738 typename Tr_container::const_iterator it_tr = m_triangulations.begin();
1739 typename Tr_container::const_iterator it_tr_end = m_triangulations.end();
1741 for (std::size_t idx = 0; it_tr != it_tr_end; ++it_tr, ++idx) {
1742 bool is_star_inconsistent =
false;
1744 Triangulation
const &tr = it_tr->tr();
1746 if (tr.current_dimension() < m_intrinsic_dim)
continue;
1749 std::stringstream color;
1751 color << 128 <<
" " << 128 <<
" " << 128;
1754 typedef std::vector<std::pair<Simplex, int> > Star_using_triangles;
1755 Star_using_triangles star_using_triangles;
1758 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
1759 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
1760 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
1761 Simplex c = *it_inc_simplex;
1763 std::size_t num_vertices = c.size();
1764 ++num_maximal_simplices;
1766 int color_simplex = -1;
1767 if (color_inconsistencies && !is_simplex_consistent(c)) {
1768 ++num_inconsistent_maximal_simplices;
1770 is_star_inconsistent =
true;
1772 if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(),
1773 c) != p_simpl_to_color_in_red->end()) {
1775 }
else if (p_simpl_to_color_in_green &&
1776 std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
1777 p_simpl_to_color_in_green->end()) {
1779 }
else if (p_simpl_to_color_in_blue &&
1780 std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
1781 p_simpl_to_color_in_blue->end()) {
1790 if (m_intrinsic_dim == 1) {
1792 Simplex::iterator it = c.begin();
1793 for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
1794 if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
1799 if (num_vertices <= 3) {
1800 star_using_triangles.push_back(std::make_pair(c, color_simplex));
1803 std::vector<bool> booleans(num_vertices,
false);
1804 std::fill(booleans.begin() + num_vertices - 3, booleans.end(),
true);
1807 Simplex::iterator it = c.begin();
1808 for (
int i = 0; it != c.end(); ++i, ++it) {
1809 if (booleans[i]) triangle.insert(*it);
1811 star_using_triangles.push_back(std::make_pair(triangle, color_simplex));
1812 }
while (std::next_permutation(booleans.begin(), booleans.end()));
1817 Star_using_triangles::const_iterator it_simplex = star_using_triangles.begin();
1818 Star_using_triangles::const_iterator it_simplex_end = star_using_triangles.end();
1819 for (; it_simplex != it_simplex_end; ++it_simplex) {
1820 const Simplex &c = it_simplex->first;
1823 if (is_infinite(c))
continue;
1825 int color_simplex = it_simplex->second;
1827 std::stringstream sstr_c;
1829 Simplex::const_iterator it_point_idx = c.begin();
1830 for (; it_point_idx != c.end(); ++it_point_idx) {
1831 sstr_c << *it_point_idx <<
" ";
1834 os << 3 <<
" " << sstr_c.str();
1835 if (color_inconsistencies || p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
1836 switch (color_simplex) {
1850 os <<
" " << color.str();
1854 ++num_OFF_simplices;
1857 if (is_star_inconsistent) ++num_inconsistent_stars;
1861 std::cerr <<
"\n==========================================================\n" 1862 <<
"Export from list of stars to OFF:\n" 1863 <<
" * Number of vertices: " << m_points.size() <<
"\n" 1864 <<
" * Total number of maximal simplices: " << num_maximal_simplices <<
"\n";
1865 if (color_inconsistencies) {
1866 std::cerr <<
" * Number of inconsistent stars: " << num_inconsistent_stars <<
" (" 1867 << (m_points.size() > 0 ? 100. * num_inconsistent_stars / m_points.size() : 0.) <<
"%)\n" 1868 <<
" * Number of inconsistent maximal simplices: " << num_inconsistent_maximal_simplices <<
" (" 1869 << (num_maximal_simplices > 0 ? 100. * num_inconsistent_maximal_simplices / num_maximal_simplices : 0.)
1872 std::cerr <<
"==========================================================\n";
1879 std::ostream &export_simplices_to_off(
const Simplicial_complex &complex, std::ostream &os,
1880 std::size_t &num_OFF_simplices,
1881 Simplex_set
const *p_simpl_to_color_in_red = NULL,
1882 Simplex_set
const *p_simpl_to_color_in_green = NULL,
1883 Simplex_set
const *p_simpl_to_color_in_blue = NULL)
const {
1884 typedef Simplicial_complex::Simplex Simplex;
1885 typedef Simplicial_complex::Simplex_set Simplex_set;
1889 num_OFF_simplices = 0;
1890 std::size_t num_maximal_simplices = 0;
1892 typename Simplex_set::const_iterator it_s = complex.simplex_range().begin();
1893 typename Simplex_set::const_iterator it_s_end = complex.simplex_range().end();
1895 for (; it_s != it_s_end; ++it_s) {
1897 ++num_maximal_simplices;
1899 int color_simplex = -1;
1900 if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(), c) !=
1901 p_simpl_to_color_in_red->end()) {
1903 }
else if (p_simpl_to_color_in_green &&
1904 std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
1905 p_simpl_to_color_in_green->end()) {
1907 }
else if (p_simpl_to_color_in_blue &&
1908 std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
1909 p_simpl_to_color_in_blue->end()) {
1914 typedef std::vector<Simplex> Triangles;
1915 Triangles triangles;
1917 int num_vertices =
static_cast<int>(c.size());
1919 if (num_vertices < m_intrinsic_dim + 1)
continue;
1925 if (m_intrinsic_dim == 1) {
1927 Simplex::iterator it = c.begin();
1928 for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
1929 if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
1934 if (num_vertices <= 3) {
1935 triangles.push_back(c);
1938 std::vector<bool> booleans(num_vertices,
false);
1939 std::fill(booleans.begin() + num_vertices - 3, booleans.end(),
true);
1942 Simplex::iterator it = c.begin();
1943 for (
int i = 0; it != c.end(); ++i, ++it) {
1944 if (booleans[i]) triangle.insert(*it);
1946 triangles.push_back(triangle);
1947 }
while (std::next_permutation(booleans.begin(), booleans.end()));
1951 Triangles::const_iterator it_tri = triangles.begin();
1952 Triangles::const_iterator it_tri_end = triangles.end();
1953 for (; it_tri != it_tri_end; ++it_tri) {
1955 if (is_infinite(*it_tri))
continue;
1958 Simplex::const_iterator it_point_idx = it_tri->begin();
1959 for (; it_point_idx != it_tri->end(); ++it_point_idx) {
1960 os << *it_point_idx <<
" ";
1963 if (p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
1964 switch (color_simplex) {
1978 os <<
" 128 128 128";
1983 ++num_OFF_simplices;
1989 std::cerr <<
"\n==========================================================\n" 1990 <<
"Export from complex to OFF:\n" 1991 <<
" * Number of vertices: " << m_points.size() <<
"\n" 1992 <<
" * Total number of maximal simplices: " << num_maximal_simplices <<
"\n" 1993 <<
"==========================================================\n";
2010 const int m_intrinsic_dim;
2011 const int m_ambient_dim;
2015 #ifdef GUDHI_TC_PERTURB_POSITION 2016 Translations_for_perturb m_translations;
2017 #if defined(GUDHI_USE_TBB) 2018 Mutex_for_perturb *m_p_perturb_mutexes;
2022 Points_ds m_points_ds;
2023 double m_last_max_perturb;
2024 std::vector<bool> m_are_tangent_spaces_computed;
2025 TS_container m_tangent_spaces;
2026 #ifdef GUDHI_TC_EXPORT_NORMALS 2027 OS_container m_orth_spaces;
2029 Tr_container m_triangulations;
2031 Stars_container m_stars;
2032 std::vector<FT> m_squared_star_spheres_radii_incl_margin;
2033 boost::optional<FT> m_max_squared_edge_length;
2035 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM 2036 Points m_points_for_tse;
2037 Points_ds m_points_ds_for_tse;
2040 mutable CGAL::Random m_random_generator;
2046 #endif // TANGENTIAL_COMPLEX_H_
std::size_t num_inconsistent_simplices
Number of inconsistent simplices.
Definition: Tangential_complex.h:543
void set_max_squared_edge_length(FT max_squared_edge_length)
Sets the maximal possible squared edge length for the edges in the triangulations.
Definition: Tangential_complex.h:2006
Type returned by Tangential_complex::fix_inconsistencies_using_perturbation.
Definition: Tangential_complex.h:377
Point get_point(std::size_t vertex) const
Returns the point corresponding to the vertex given as parameter.
Definition: Tangential_complex.h:291
Tangential complex data structure.
Definition: Tangential_complex.h:125
Incremental_neighbor_search INS_range
The range returned by an incremental nearest or furthest neighbor search. Its value type is std::pair...
Definition: Kd_tree_search.h:112
K_neighbor_search KNS_range
The range returned by a k-nearest or k-furthest neighbor search. Its value type is std::pair<std::siz...
Definition: Kd_tree_search.h:104
KNS_range k_nearest_neighbors(Point const &p, unsigned int k, bool sorted=true, FT eps=FT(0)) const
Search for the k-nearest neighbors from a query point.
Definition: Kd_tree_search.h:245
std::size_t final_num_inconsistent_stars
final number of inconsistent stars
Definition: Tangential_complex.h:387
Definition: SimplicialComplexForAlpha.h:14
~Tangential_complex()
Destructor.
Definition: Tangential_complex.h:272
std::size_t num_simplices
Total number of simplices in stars (including duplicates that appear in several stars) ...
Definition: Tangential_complex.h:541
std::size_t best_num_inconsistent_stars
best number of inconsistent stars during the process
Definition: Tangential_complex.h:385
std::size_t num_inconsistent_stars
Number of stars containing at least one inconsistent simplex.
Definition: Tangential_complex.h:545
int create_complex(Simplex_tree_ &tree, bool export_inconsistent_simplices=true) const
Exports the complex into a Simplex_tree.
Definition: Tangential_complex.h:610
Fix_inconsistencies_info fix_inconsistencies_using_perturbation(double max_perturb, double time_limit=-1.)
Attempts to fix inconsistencies by perturbing the point positions.
Definition: Tangential_complex.h:395
std::size_t initial_num_inconsistent_stars
initial number of inconsistent stars
Definition: Tangential_complex.h:383
Tangential_complex(Point_range points, int intrinsic_dimension, const K &k=K())
Constructor from a range of points. Points are copied into the instance, and a search data structure ...
Definition: Tangential_complex.h:240
Num_inconsistencies number_of_inconsistent_simplices(bool verbose=false) const
Definition: Tangential_complex.h:551
bool success
true if all inconsistencies could be removed, false if the time limit has been reached before ...
Definition: Tangential_complex.h:379
int intrinsic_dimension() const
Returns the intrinsic dimension of the manifold.
Definition: Tangential_complex.h:279
Definition: Intro_spatial_searching.h:16
void compute_tangential_complex()
Computes the tangential complex.
Definition: Tangential_complex.h:330
int ambient_dimension() const
Returns the ambient dimension.
Definition: Tangential_complex.h:282
Type returned by Tangential_complex::number_of_inconsistent_simplices.
Definition: Tangential_complex.h:539
std::size_t number_of_vertices() const
Returns the number of vertices.
Definition: Tangential_complex.h:302
unsigned int num_steps
number of steps performed
Definition: Tangential_complex.h:381
Point get_perturbed_point(std::size_t vertex) const
Returns the perturbed position of the point corresponding to the vertex given as parameter.
Definition: Tangential_complex.h:298