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>
62 #include <tbb/parallel_for.h>
63 #include <tbb/combinable.h>
71 #if CGAL_VERSION_NR < 1041101000
72 # error Tangential_complex is only available for CGAL >= 4.11
75 #if !EIGEN_VERSION_AT_LEAST(3,1,0)
76 # error Tangential_complex is only available for Eigen3 >= 3.1.0 installed with CGAL
79 namespace sps = Gudhi::spatial_searching;
83 namespace tangential_complex {
85 using namespace internal;
89 Vertex_data(std::size_t data = (std::numeric_limits<std::size_t>::max)()) : m_data(data) {}
91 operator std::size_t() {
return m_data; }
93 operator std::size_t()
const {
return m_data; }
124 template <
typename Kernel_,
125 typename DimensionTag,
126 typename Concurrency_tag = CGAL::Parallel_tag,
typename Triangulation_ = CGAL::Default>
129 typedef typename K::FT FT;
130 typedef typename K::Point_d Point;
131 typedef typename K::Weighted_point_d Weighted_point;
132 typedef typename K::Vector_d Vector;
134 typedef typename CGAL::Default::Get<
136 CGAL::Regular_triangulation<
137 CGAL::Epick_d<DimensionTag>,
138 CGAL::Triangulation_data_structure<
139 typename CGAL::Epick_d<DimensionTag>::Dimension,
140 CGAL::Triangulation_vertex<CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> >,
142 CGAL::Triangulation_full_cell<
143 CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> > > > > >::type Triangulation;
144 typedef typename Triangulation::Geom_traits Tr_traits;
145 typedef typename Triangulation::Weighted_point Tr_point;
146 typedef typename Tr_traits::Base::Point_d Tr_bare_point;
147 typedef typename Triangulation::Vertex_handle Tr_vertex_handle;
148 typedef typename Triangulation::Full_cell_handle Tr_full_cell_handle;
149 typedef typename Tr_traits::Vector_d Tr_vector;
151 #if defined(GUDHI_USE_TBB)
152 typedef std::mutex Mutex_for_perturb;
153 typedef Vector Translation_for_perturb;
154 typedef std::vector<Atomic_wrapper<FT> > Weights;
156 typedef Vector Translation_for_perturb;
157 typedef std::vector<FT> Weights;
159 typedef std::vector<Translation_for_perturb> Translations_for_perturb;
165 Tr_and_VH() : m_tr(NULL) {}
167 Tr_and_VH(
int dim) : m_tr(
new Triangulation(dim)) {}
169 ~Tr_and_VH() { destroy_triangulation(); }
171 Triangulation &construct_triangulation(
int dim) {
173 m_tr =
new Triangulation(dim);
177 void destroy_triangulation() {
182 Triangulation &tr() {
return *m_tr; }
184 Triangulation
const &tr()
const {
return *m_tr; }
186 Tr_vertex_handle
const ¢er_vertex()
const {
return m_center_vertex; }
188 Tr_vertex_handle ¢er_vertex() {
return m_center_vertex; }
192 Tr_vertex_handle m_center_vertex;
196 typedef Basis<K> Tangent_space_basis;
197 typedef Basis<K> Orthogonal_space_basis;
198 typedef std::vector<Tangent_space_basis> TS_container;
199 typedef std::vector<Orthogonal_space_basis> OS_container;
201 typedef std::vector<Point> Points;
203 typedef boost::container::flat_set<std::size_t> Simplex;
204 typedef std::set<Simplex> Simplex_set;
211 typedef std::vector<Tr_and_VH> Tr_container;
212 typedef std::vector<Vector> Vectors;
216 typedef boost::container::flat_set<std::size_t> Incident_simplex;
217 typedef std::vector<Incident_simplex> Star;
218 typedef std::vector<Star> Stars_container;
222 static const Tr_point &vertex_handle_to_point(Tr_vertex_handle vh) {
return vh->point(); }
224 template <
typename P,
typename VH>
225 static const P &vertex_handle_to_point(VH vh) {
230 typedef internal::Simplicial_complex Simplicial_complex;
241 template <
typename Po
int_range>
243 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
244 InputIterator first_for_tse, InputIterator last_for_tse,
248 m_intrinsic_dim(intrinsic_dimension),
249 m_ambient_dim(points.empty() ? 0 : k.point_dimension_d_object()(*points.begin())),
250 m_points(points.begin(), points.end()),
251 m_weights(m_points.size(), FT(0))
252 #if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION)
254 m_p_perturb_mutexes(NULL)
257 m_points_ds(m_points),
258 m_last_max_perturb(0.),
259 m_are_tangent_spaces_computed(m_points.size(), false),
260 m_tangent_spaces(m_points.size(), Tangent_space_basis())
261 #ifdef GUDHI_TC_EXPORT_NORMALS
263 m_orth_spaces(m_points.size(), Orthogonal_space_basis())
265 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
267 m_points_for_tse(first_for_tse, last_for_tse),
268 m_points_ds_for_tse(m_points_for_tse)
275 #if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION)
276 delete[] m_p_perturb_mutexes;
286 Points
const &points()
const {
return m_points; }
293 Point
get_point(std::size_t vertex)
const {
return m_points[vertex]; }
306 void set_weights(
const Weights &weights) { m_weights = weights; }
308 void set_tangent_planes(
const TS_container &tangent_spaces
309 #ifdef GUDHI_TC_EXPORT_NORMALS
311 const OS_container &orthogonal_spaces
314 #ifdef GUDHI_TC_EXPORT_NORMALS
315 GUDHI_CHECK(m_points.size() == tangent_spaces.size() && m_points.size() == orthogonal_spaces.size(),
316 std::logic_error(
"Wrong sizes"));
318 GUDHI_CHECK(m_points.size() == tangent_spaces.size(), std::logic_error(
"Wrong sizes"));
320 m_tangent_spaces = tangent_spaces;
321 #ifdef GUDHI_TC_EXPORT_NORMALS
322 m_orth_spaces = orthogonal_spaces;
324 for (std::size_t i = 0; i < m_points.size(); ++i) m_are_tangent_spaces_computed[i] =
true;
333 #ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS
334 std::cerr << red <<
"WARNING: GUDHI_TC_PERFORM_EXTRA_CHECKS is defined. "
335 <<
"Computation might be slower than usual.\n"
339 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB)
346 m_triangulations.resize(m_points.size());
347 m_stars.resize(m_points.size());
348 m_squared_star_spheres_radii_incl_margin.resize(m_points.size(), FT(-1));
349 #ifdef GUDHI_TC_PERTURB_POSITION
350 if (m_points.empty())
351 m_translations.clear();
353 m_translations.resize(m_points.size(), m_k.construct_vector_d_object()(m_ambient_dim));
354 #if defined(GUDHI_USE_TBB)
355 delete[] m_p_perturb_mutexes;
356 m_p_perturb_mutexes =
new Mutex_for_perturb[m_points.size()];
362 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
363 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*
this));
365 #endif // GUDHI_USE_TBB
367 for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
370 #endif // GUDHI_USE_TBB
372 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB)
374 std::cerr <<
"Tangential complex computed in " << t.num_seconds() <<
" seconds.\n";
381 bool success =
false;
383 unsigned int num_steps = 0;
385 std::size_t initial_num_inconsistent_stars = 0;
387 std::size_t best_num_inconsistent_stars = 0;
389 std::size_t final_num_inconsistent_stars = 0;
400 if (time_limit == 0.)
return info;
404 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
405 std::tuple<std::size_t, std::size_t, std::size_t> stats_before = number_of_inconsistent_simplices(
false);
407 if (std::get<1>(stats_before) == 0) {
409 std::cerr <<
"Nothing to fix.\n";
414 #endif // GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
416 m_last_max_perturb = max_perturb;
422 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
423 std::cerr <<
"\nBefore fix step:\n"
424 <<
" * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_before) <<
"\n"
425 <<
" * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_before)
426 << white <<
" (" << 100. * std::get<1>(stats_before) / std::get<0>(stats_before) <<
"%)\n"
427 <<
" * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_before)
428 << white <<
" (" << 100. * std::get<2>(stats_before) / m_points.size() <<
"%)\n";
431 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
432 std::cerr << yellow <<
"\nAttempt to fix inconsistencies using perturbations - step #" << info.
num_steps + 1
436 std::size_t num_inconsistent_stars = 0;
437 std::vector<std::size_t> updated_points;
439 #ifdef GUDHI_TC_PROFILING
440 Gudhi::Clock t_fix_step;
444 #if defined(GUDHI_USE_TBB)
445 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
446 tbb::combinable<std::size_t> num_inconsistencies;
447 tbb::combinable<std::vector<std::size_t> > tls_updated_points;
448 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_triangulations.size()),
449 Try_to_solve_inconsistencies_in_a_local_triangulation(*
this, max_perturb, num_inconsistencies,
450 tls_updated_points));
451 num_inconsistent_stars = num_inconsistencies.combine(std::plus<std::size_t>());
453 tls_updated_points.combine([](std::vector<std::size_t>
const &x, std::vector<std::size_t>
const &y) {
454 std::vector<std::size_t> res;
455 res.reserve(x.size() + y.size());
456 res.insert(res.end(), x.begin(), x.end());
457 res.insert(res.end(), y.begin(), y.end());
461 #endif // GUDHI_USE_TBB
463 for (std::size_t i = 0; i < m_triangulations.size(); ++i) {
464 num_inconsistent_stars +=
465 try_to_solve_inconsistencies_in_a_local_triangulation(i, max_perturb, std::back_inserter(updated_points));
467 #if defined(GUDHI_USE_TBB)
469 #endif // GUDHI_USE_TBB
471 #ifdef GUDHI_TC_PROFILING
475 #if defined(GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES) || defined(DEBUG_TRACES)
476 std::cerr <<
"\nEncountered during fix:\n"
477 <<
" * Num stars containing inconsistent simplices: " << red << num_inconsistent_stars << white <<
" ("
478 << 100. * num_inconsistent_stars / m_points.size() <<
"%)\n";
481 #ifdef GUDHI_TC_PROFILING
482 std::cerr << yellow <<
"done in " << t_fix_step.num_seconds() <<
" seconds.\n" << white;
483 #elif defined(DEBUG_TRACES)
484 std::cerr << yellow <<
"done.\n" << white;
487 if (num_inconsistent_stars > 0) refresh_tangential_complex(updated_points);
489 #ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS
491 std::size_t num_inc_1 = std::get<1>(number_of_inconsistent_simplices(
false));
492 refresh_tangential_complex();
493 std::size_t num_inc_2 = std::get<1>(number_of_inconsistent_simplices(
false));
494 if (num_inc_1 != num_inc_2)
495 std::cerr << red <<
"REFRESHMENT CHECK: FAILED. (" << num_inc_1 <<
" vs " << num_inc_2 <<
")\n" << white;
497 std::cerr << green <<
"REFRESHMENT CHECK: PASSED.\n" << white;
500 #ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
501 std::tuple<std::size_t, std::size_t, std::size_t> stats_after = number_of_inconsistent_simplices(
false);
503 std::cerr <<
"\nAfter fix:\n"
504 <<
" * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_after) <<
"\n"
505 <<
" * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_after)
506 << white <<
" (" << 100. * std::get<1>(stats_after) / std::get<0>(stats_after) <<
"%)\n"
507 <<
" * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_after) << white
508 <<
" (" << 100. * std::get<2>(stats_after) / m_points.size() <<
"%)\n";
510 stats_before = stats_after;
520 done = (num_inconsistent_stars == 0);
523 if (time_limit > 0. && t.num_seconds() > time_limit) {
525 std::cerr << red <<
"Time limit reached.\n" << white;
534 std::cerr << green <<
"Fixed!\n" << white;
543 std::size_t num_simplices = 0;
545 std::size_t num_inconsistent_simplices = 0;
547 std::size_t num_inconsistent_stars = 0;
563 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
564 bool is_star_inconsistent =
false;
567 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
568 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
569 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
571 if (is_infinite(*it_inc_simplex))
continue;
573 Simplex c = *it_inc_simplex;
576 if (!is_simplex_consistent(c)) {
578 is_star_inconsistent =
true;
587 std::cerr <<
"\n==========================================================\n"
588 <<
"Inconsistencies:\n"
589 <<
" * Total number of simplices in stars (incl. duplicates): " << stats.
num_simplices <<
"\n"
590 <<
" * Number of inconsistent simplices in stars (incl. duplicates): "
595 <<
"==========================================================\n";
611 template <
typename Simplex_tree_>
613 bool export_inconsistent_simplices =
true
616 bool export_infinite_simplices =
false, Simplex_set *p_inconsistent_simplices = NULL
619 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
620 std::cerr << yellow <<
"\nExporting the TC as a Simplex_tree... " << white;
622 #ifdef GUDHI_TC_PROFILING
629 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
631 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
632 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
633 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
634 Simplex c = *it_inc_simplex;
637 if (!export_infinite_simplices && is_infinite(c))
continue;
639 if (
static_cast<int>(c.size()) > max_dim) max_dim =
static_cast<int>(c.size());
643 if (!export_inconsistent_simplices && !is_simplex_consistent(c))
continue;
646 bool inserted = tree.insert_simplex_and_subfaces(c).second;
649 if (p_inconsistent_simplices && inserted && !is_simplex_consistent(c)) {
650 p_inconsistent_simplices->insert(c);
655 #ifdef GUDHI_TC_PROFILING
657 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
658 #elif defined(DEBUG_TRACES)
659 std::cerr << yellow <<
"done.\n" << white;
675 int create_complex(Simplicial_complex &complex,
bool export_inconsistent_simplices =
true,
676 bool export_infinite_simplices =
false,
int check_lower_and_higher_dim_simplices = 2,
677 Simplex_set *p_inconsistent_simplices = NULL)
const {
678 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
679 std::cerr << yellow <<
"\nExporting the TC as a Simplicial_complex... " << white;
681 #ifdef GUDHI_TC_PROFILING
689 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
691 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
692 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
693 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
694 Simplex c = *it_inc_simplex;
697 if (!export_infinite_simplices && is_infinite(c))
continue;
699 if (
static_cast<int>(c.size()) > max_dim) max_dim =
static_cast<int>(c.size());
703 if (!export_inconsistent_simplices && !is_simplex_consistent(c))
continue;
706 if (check_lower_and_higher_dim_simplices == 2 && max_dim != -1 &&
static_cast<int>(c.size()) != max_dim) {
709 <<
"Info: check_lower_and_higher_dim_simplices ACTIVATED. "
710 "Export might be take some time...\n"
712 check_lower_and_higher_dim_simplices = 1;
716 bool added = complex.add_simplex(c, check_lower_and_higher_dim_simplices == 1);
719 if (p_inconsistent_simplices && added && !is_simplex_consistent(c)) {
720 p_inconsistent_simplices->insert(c);
725 #ifdef GUDHI_TC_PROFILING
727 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
728 #elif defined(DEBUG_TRACES)
729 std::cerr << yellow <<
"done.\n" << white;
735 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
736 std::ostream &export_to_off(
const Simplicial_complex &complex, std::ostream &os,
737 Simplex_set
const *p_simpl_to_color_in_red = NULL,
738 Simplex_set
const *p_simpl_to_color_in_green = NULL,
739 Simplex_set
const *p_simpl_to_color_in_blue = NULL,
740 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
741 return export_to_off(os,
false, p_simpl_to_color_in_red, p_simpl_to_color_in_green, p_simpl_to_color_in_blue,
742 &complex, point_projection);
745 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
746 std::ostream &export_to_off(std::ostream &os,
bool color_inconsistencies =
false,
747 Simplex_set
const *p_simpl_to_color_in_red = NULL,
748 Simplex_set
const *p_simpl_to_color_in_green = NULL,
749 Simplex_set
const *p_simpl_to_color_in_blue = NULL,
750 const Simplicial_complex *p_complex = NULL,
751 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
752 if (m_points.empty())
return os;
754 if (m_ambient_dim < 2) {
755 std::cerr <<
"Error: export_to_off => ambient dimension should be >= 2.\n";
756 os <<
"Error: export_to_off => ambient dimension should be >= 2.\n";
759 if (m_ambient_dim > 3) {
760 std::cerr <<
"Warning: export_to_off => ambient dimension should be "
761 "<= 3. Only the first 3 coordinates will be exported.\n";
764 if (m_intrinsic_dim < 1 || m_intrinsic_dim > 3) {
765 std::cerr <<
"Error: export_to_off => intrinsic dimension should be "
766 "between 1 and 3.\n";
767 os <<
"Error: export_to_off => intrinsic dimension should be "
768 "between 1 and 3.\n";
772 std::stringstream output;
773 std::size_t num_simplices, num_vertices;
774 export_vertices_to_off(output, num_vertices,
false, point_projection);
776 export_simplices_to_off(*p_complex, output, num_simplices, p_simpl_to_color_in_red, p_simpl_to_color_in_green,
777 p_simpl_to_color_in_blue);
779 export_simplices_to_off(output, num_simplices, color_inconsistencies, p_simpl_to_color_in_red,
780 p_simpl_to_color_in_green, p_simpl_to_color_in_blue);
783 #ifdef GUDHI_TC_EXPORT_NORMALS
788 << num_vertices <<
" " << num_simplices <<
" "
796 void refresh_tangential_complex() {
797 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
798 std::cerr << yellow <<
"\nRefreshing TC... " << white;
801 #ifdef GUDHI_TC_PROFILING
806 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
807 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*
this));
809 #endif // GUDHI_USE_TBB
811 for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
814 #endif // GUDHI_USE_TBB
816 #ifdef GUDHI_TC_PROFILING
818 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
819 #elif defined(DEBUG_TRACES)
820 std::cerr << yellow <<
"done.\n" << white;
825 template <
typename Po
int_indices_range>
826 void refresh_tangential_complex(Point_indices_range
const &perturbed_points_indices) {
827 #if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
828 std::cerr << yellow <<
"\nRefreshing TC... " << white;
831 #ifdef GUDHI_TC_PROFILING
836 Points_ds updated_pts_ds(m_points, perturbed_points_indices);
840 if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
841 tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()),
842 Refresh_tangent_triangulation(*
this, updated_pts_ds));
844 #endif // GUDHI_USE_TBB
846 for (std::size_t i = 0; i < m_points.size(); ++i) refresh_tangent_triangulation(i, updated_pts_ds);
849 #endif // GUDHI_USE_TBB
851 #ifdef GUDHI_TC_PROFILING
853 std::cerr << yellow <<
"done in " << t.num_seconds() <<
" seconds.\n" << white;
854 #elif defined(DEBUG_TRACES)
855 std::cerr << yellow <<
"done.\n" << white;
859 void export_inconsistent_stars_to_OFF_files(std::string
const &filename_base)
const {
861 for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
863 Simplicial_complex sc;
865 bool is_inconsistent =
false;
866 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
867 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
868 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
870 if (is_infinite(*it_inc_simplex))
continue;
872 Simplex c = *it_inc_simplex;
878 if (!is_inconsistent && !is_simplex_consistent(c)) is_inconsistent =
true;
881 if (is_inconsistent) {
883 std::stringstream output_filename;
884 output_filename << filename_base <<
"_" << idx <<
".off";
885 std::ofstream off_stream(output_filename.str().c_str());
886 export_to_off(sc, off_stream);
891 class Compare_distance_to_ref_point {
893 Compare_distance_to_ref_point(Point
const &ref, K
const &k) : m_ref(ref), m_k(k) {}
895 bool operator()(Point
const &p1, Point
const &p2) {
896 typename K::Squared_distance_d sqdist = m_k.squared_distance_d_object();
897 return sqdist(p1, m_ref) < sqdist(p2, m_ref);
907 class Compute_tangent_triangulation {
908 Tangential_complex &m_tc;
912 Compute_tangent_triangulation(Tangential_complex &tc) : m_tc(tc) {}
915 Compute_tangent_triangulation(
const Compute_tangent_triangulation &ctt) : m_tc(ctt.m_tc) {}
918 void operator()(
const tbb::blocked_range<size_t> &r)
const {
919 for (
size_t i = r.begin(); i != r.end(); ++i) m_tc.compute_tangent_triangulation(i);
924 class Refresh_tangent_triangulation {
925 Tangential_complex &m_tc;
926 Points_ds
const &m_updated_pts_ds;
930 Refresh_tangent_triangulation(Tangential_complex &tc, Points_ds
const &updated_pts_ds)
931 : m_tc(tc), m_updated_pts_ds(updated_pts_ds) {}
934 Refresh_tangent_triangulation(
const Refresh_tangent_triangulation &ctt)
935 : m_tc(ctt.m_tc), m_updated_pts_ds(ctt.m_updated_pts_ds) {}
938 void operator()(
const tbb::blocked_range<size_t> &r)
const {
939 for (
size_t i = r.begin(); i != r.end(); ++i) m_tc.refresh_tangent_triangulation(i, m_updated_pts_ds);
942 #endif // GUDHI_USE_TBB
944 bool is_infinite(Simplex
const &s)
const {
return *s.rbegin() == (std::numeric_limits<std::size_t>::max)(); }
949 Tr_vertex_handle compute_star(std::size_t i,
const Point ¢er_pt,
const Tangent_space_basis &tsb,
950 Triangulation &triangulation,
bool verbose =
false) {
951 int tangent_space_dim = tsb.dimension();
952 const Tr_traits &local_tr_traits = triangulation.geom_traits();
955 typename K::Squared_distance_d k_sqdist = m_k.squared_distance_d_object();
958 typename Tr_traits::Compute_weight_d point_weight = local_tr_traits.compute_weight_d_object();
959 typename Tr_traits::Power_center_d power_center = local_tr_traits.power_center_d_object();
968 if (i == tsb.origin()) {
970 proj_wp = local_tr_traits.construct_weighted_point_d_object()(
971 local_tr_traits.construct_point_d_object()(tangent_space_dim, CGAL::ORIGIN), m_weights[i]);
973 const Weighted_point &wp = compute_perturbed_weighted_point(i);
974 proj_wp = project_point_and_compute_weight(wp, tsb, local_tr_traits);
977 Tr_vertex_handle center_vertex = triangulation.insert(proj_wp);
978 center_vertex->data() = i;
979 if (verbose) std::cerr <<
"* Inserted point #" << i <<
"\n";
981 #ifdef GUDHI_TC_VERY_VERBOSE
982 std::size_t num_attempts_to_insert_points = 1;
983 std::size_t num_inserted_points = 1;
987 INS_range ins_range = m_points_ds.incremental_nearest_neighbors(center_pt);
995 boost::optional<FT> squared_star_sphere_radius_plus_margin = m_max_squared_edge_length;
998 for (
auto nn_it = ins_range.begin(); nn_it != ins_range.end(); ++nn_it) {
999 std::size_t neighbor_point_idx = nn_it->first;
1002 if (neighbor_point_idx != i) {
1007 compute_perturbed_weighted_point(neighbor_point_idx, neighbor_pt, neighbor_weight);
1008 GUDHI_CHECK(!m_max_squared_edge_length ||
1009 squared_star_sphere_radius_plus_margin.value() <= m_max_squared_edge_length.value(),
1010 std::invalid_argument(
"Tangential_complex::compute_star - set a bigger value with set_max_squared_edge_length."));
1011 if (squared_star_sphere_radius_plus_margin &&
1012 k_sqdist(center_pt, neighbor_pt) > squared_star_sphere_radius_plus_margin.value()) {
1013 GUDHI_CHECK(triangulation.current_dimension() >= tangent_space_dim,
1014 std::invalid_argument(
"Tangential_complex::compute_star - Dimension of the star is only " + \
1015 std::to_string(triangulation.current_dimension())));
1019 Tr_point proj_pt = project_point_and_compute_weight(neighbor_pt, neighbor_weight, tsb, local_tr_traits);
1021 #ifdef GUDHI_TC_VERY_VERBOSE
1022 ++num_attempts_to_insert_points;
1025 Tr_vertex_handle vh = triangulation.insert_if_in_star(proj_pt, center_vertex);
1027 if (vh != Tr_vertex_handle() && vh->data() == (std::numeric_limits<std::size_t>::max)()) {
1028 #ifdef GUDHI_TC_VERY_VERBOSE
1029 ++num_inserted_points;
1031 if (verbose) std::cerr <<
"* Inserted point #" << neighbor_point_idx <<
"\n";
1033 vh->data() = neighbor_point_idx;
1036 if (triangulation.current_dimension() >= tangent_space_dim) {
1037 squared_star_sphere_radius_plus_margin = boost::none;
1039 std::vector<Tr_full_cell_handle> incident_cells;
1040 triangulation.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
1041 for (
typename std::vector<Tr_full_cell_handle>::iterator cit = incident_cells.begin();
1042 cit != incident_cells.end(); ++cit) {
1043 Tr_full_cell_handle cell = *cit;
1044 if (triangulation.is_infinite(cell)) {
1045 squared_star_sphere_radius_plus_margin = boost::none;
1051 power_center(boost::make_transform_iterator(cell->vertices_begin(),
1052 vertex_handle_to_point<Tr_point, Tr_vertex_handle>),
1053 boost::make_transform_iterator(cell->vertices_end(),
1054 vertex_handle_to_point<Tr_point, Tr_vertex_handle>));
1056 FT sq_power_sphere_diam = 4 * point_weight(c);
1058 if (!squared_star_sphere_radius_plus_margin ||
1059 sq_power_sphere_diam > squared_star_sphere_radius_plus_margin.value()) {
1060 squared_star_sphere_radius_plus_margin = sq_power_sphere_diam;
1067 if (squared_star_sphere_radius_plus_margin) {
1069 squared_star_sphere_radius_plus_margin =
1070 CGAL::square(std::sqrt(squared_star_sphere_radius_plus_margin.value()) + 2 * m_last_max_perturb);
1073 if (m_max_squared_edge_length && squared_star_sphere_radius_plus_margin.value() > m_max_squared_edge_length.value()) {
1074 squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
1078 m_squared_star_spheres_radii_incl_margin[i] = squared_star_sphere_radius_plus_margin.value();
1080 if (m_max_squared_edge_length) {
1081 squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
1082 m_squared_star_spheres_radii_incl_margin[i] = m_max_squared_edge_length.value();
1084 m_squared_star_spheres_radii_incl_margin[i] = FT(-1);
1092 return center_vertex;
1095 void refresh_tangent_triangulation(std::size_t i, Points_ds
const &updated_pts_ds,
bool verbose =
false) {
1096 if (verbose) std::cerr <<
"** Refreshing tangent tri #" << i <<
" **\n";
1098 if (m_squared_star_spheres_radii_incl_margin[i] == FT(-1))
return compute_tangent_triangulation(i, verbose);
1100 Point center_point = compute_perturbed_point(i);
1102 std::size_t closest_pt_index = updated_pts_ds.k_nearest_neighbors(center_point, 1,
false).begin()->first;
1104 typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
1105 typename K::Power_distance_d k_power_dist = m_k.power_distance_d_object();
1108 Weighted_point star_sphere = k_constr_wp(compute_perturbed_point(i), m_squared_star_spheres_radii_incl_margin[i]);
1109 Weighted_point closest_updated_point = compute_perturbed_weighted_point(closest_pt_index);
1112 if (k_power_dist(star_sphere, closest_updated_point) <= FT(0)) compute_tangent_triangulation(i, verbose);
1115 void compute_tangent_triangulation(std::size_t i,
bool verbose =
false) {
1116 if (verbose) std::cerr <<
"** Computing tangent tri #" << i <<
" **\n";
1121 const Point center_pt = compute_perturbed_point(i);
1122 Tangent_space_basis &tsb = m_tangent_spaces[i];
1125 if (!m_are_tangent_spaces_computed[i]) {
1126 #ifdef GUDHI_TC_EXPORT_NORMALS
1127 tsb = compute_tangent_space(center_pt, i,
true , &m_orth_spaces[i]);
1129 tsb = compute_tangent_space(center_pt, i);
1133 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
1136 int tangent_space_dim = tangent_basis_dim(i);
1137 Triangulation &local_tr = m_triangulations[i].construct_triangulation(tangent_space_dim);
1139 m_triangulations[i].center_vertex() = compute_star(i, center_pt, tsb, local_tr, verbose);
1141 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
1143 std::cerr <<
" - triangulation construction: " << t.num_seconds() <<
" s.\n";
1147 #ifdef GUDHI_TC_VERY_VERBOSE
1148 std::cerr <<
"Inserted " << num_inserted_points <<
" points / " << num_attempts_to_insert_points
1149 <<
" attemps to compute the star\n";
1154 #if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
1156 std::cerr <<
" - update_star: " << t.num_seconds() <<
" s.\n";
1162 void update_star(std::size_t i) {
1163 Star &star = m_stars[i];
1165 Triangulation &local_tr = m_triangulations[i].tr();
1166 Tr_vertex_handle center_vertex = m_triangulations[i].center_vertex();
1167 int cur_dim_plus_1 = local_tr.current_dimension() + 1;
1169 std::vector<Tr_full_cell_handle> incident_cells;
1170 local_tr.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
1172 typename std::vector<Tr_full_cell_handle>::const_iterator it_c = incident_cells.begin();
1173 typename std::vector<Tr_full_cell_handle>::const_iterator it_c_end = incident_cells.end();
1175 for (; it_c != it_c_end; ++it_c) {
1177 Incident_simplex incident_simplex;
1178 for (
int j = 0; j < cur_dim_plus_1; ++j) {
1179 std::size_t index = (*it_c)->vertex(j)->data();
1180 if (index != i) incident_simplex.insert(index);
1182 GUDHI_CHECK(incident_simplex.size() == cur_dim_plus_1 - 1,
1183 std::logic_error(
"update_star: wrong size of incident simplex"));
1184 star.push_back(incident_simplex);
1190 Tangent_space_basis compute_tangent_space(
const Point &p,
const std::size_t i,
bool normalize_basis =
true,
1191 Orthogonal_space_basis *p_orth_space_basis = NULL) {
1192 unsigned int num_pts_for_pca =
1193 (std::min)(
static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
1194 static_cast<unsigned int>(m_points.size()));
1197 typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
1198 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1200 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
1201 KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca,
false);
1202 const Points &points_for_pca = m_points_for_tse;
1204 KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca,
false);
1205 const Points &points_for_pca = m_points;
1209 Eigen::MatrixXd mat_points(num_pts_for_pca, m_ambient_dim);
1210 auto nn_it = kns_range.begin();
1211 for (
unsigned int j = 0; j < num_pts_for_pca && nn_it != kns_range.end(); ++j, ++nn_it) {
1212 for (
int i = 0; i < m_ambient_dim; ++i) {
1213 mat_points(j, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
1216 Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
1217 Eigen::MatrixXd cov = centered.adjoint() * centered;
1218 Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
1220 Tangent_space_basis tsb(i);
1224 for (
int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
1225 if (normalize_basis) {
1226 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1227 eig.eigenvectors().col(j).data() + m_ambient_dim);
1228 tsb.push_back(normalize_vector(v, m_k));
1230 tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1231 eig.eigenvectors().col(j).data() + m_ambient_dim));
1235 if (p_orth_space_basis) {
1236 p_orth_space_basis->set_origin(i);
1237 for (
int j = m_ambient_dim - m_intrinsic_dim - 1; j >= 0; --j) {
1238 if (normalize_basis) {
1239 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1240 eig.eigenvectors().col(j).data() + m_ambient_dim);
1241 p_orth_space_basis->push_back(normalize_vector(v, m_k));
1243 p_orth_space_basis->push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1244 eig.eigenvectors().col(j).data() + m_ambient_dim));
1249 m_are_tangent_spaces_computed[i] =
true;
1259 Tangent_space_basis compute_tangent_space(
const Simplex &s,
bool normalize_basis =
true) {
1260 unsigned int num_pts_for_pca =
1261 (std::min)(
static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
1262 static_cast<unsigned int>(m_points.size()));
1265 typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
1266 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1267 typename K::Squared_length_d sqlen = m_k.squared_length_d_object();
1268 typename K::Scaled_vector_d scaled_vec = m_k.scaled_vector_d_object();
1269 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1270 typename K::Difference_of_vectors_d diff_vec = m_k.difference_of_vectors_d_object();
1273 Eigen::MatrixXd mat_points(s.size() * num_pts_for_pca, m_ambient_dim);
1274 unsigned int current_row = 0;
1276 for (Simplex::const_iterator it_index = s.begin(); it_index != s.end(); ++it_index) {
1277 const Point &p = m_points[*it_index];
1279 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
1280 KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca,
false);
1281 const Points &points_for_pca = m_points_for_tse;
1283 KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca,
false);
1284 const Points &points_for_pca = m_points;
1287 auto nn_it = kns_range.begin();
1288 for (; current_row < num_pts_for_pca && nn_it != kns_range.end(); ++current_row, ++nn_it) {
1289 for (
int i = 0; i < m_ambient_dim; ++i) {
1290 mat_points(current_row, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
1294 Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
1295 Eigen::MatrixXd cov = centered.adjoint() * centered;
1296 Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
1298 Tangent_space_basis tsb;
1302 for (
int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
1303 if (normalize_basis) {
1304 Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1305 eig.eigenvectors().col(j).data() + m_ambient_dim);
1306 tsb.push_back(normalize_vector(v, m_k));
1308 tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
1309 eig.eigenvectors().col(j).data() + m_ambient_dim));
1318 int tangent_basis_dim(std::size_t i)
const {
return m_tangent_spaces[i].dimension(); }
1320 Point compute_perturbed_point(std::size_t pt_idx)
const {
1321 #ifdef GUDHI_TC_PERTURB_POSITION
1322 return m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
1324 return m_points[pt_idx];
1328 void compute_perturbed_weighted_point(std::size_t pt_idx, Point &p, FT &w)
const {
1329 #ifdef GUDHI_TC_PERTURB_POSITION
1330 p = m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
1332 p = m_points[pt_idx];
1334 w = m_weights[pt_idx];
1337 Weighted_point compute_perturbed_weighted_point(std::size_t pt_idx)
const {
1338 typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
1340 Weighted_point wp = k_constr_wp(
1341 #ifdef GUDHI_TC_PERTURB_POSITION
1342 m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]),
1351 Point unproject_point(
const Tr_point &p,
const Tangent_space_basis &tsb,
const Tr_traits &tr_traits)
const {
1352 typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
1353 typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
1354 typename Tr_traits::Compute_coordinate_d coord = tr_traits.compute_coordinate_d_object();
1356 Point global_point = compute_perturbed_point(tsb.origin());
1357 for (
int i = 0; i < m_intrinsic_dim; ++i) global_point = k_transl(global_point, k_scaled_vec(tsb[i], coord(p, i)));
1359 return global_point;
1364 Tr_bare_point project_point(
const Point &p,
const Tangent_space_basis &tsb,
const Tr_traits &tr_traits)
const {
1365 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1366 typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
1368 Vector v = diff_points(p, compute_perturbed_point(tsb.origin()));
1370 std::vector<FT> coords;
1372 coords.reserve(tsb.dimension());
1373 for (std::size_t i = 0; i < m_intrinsic_dim; ++i) {
1375 FT coord = scalar_pdct(v, tsb[i]);
1376 coords.push_back(coord);
1379 return tr_traits.construct_point_d_object()(
static_cast<int>(coords.size()), coords.begin(), coords.end());
1386 Tr_point project_point_and_compute_weight(
const Weighted_point &wp,
const Tangent_space_basis &tsb,
1387 const Tr_traits &tr_traits)
const {
1388 typename K::Point_drop_weight_d k_drop_w = m_k.point_drop_weight_d_object();
1389 typename K::Compute_weight_d k_point_weight = m_k.compute_weight_d_object();
1390 return project_point_and_compute_weight(k_drop_w(wp), k_point_weight(wp), tsb, tr_traits);
1394 Tr_point project_point_and_compute_weight(
const Point &p,
const FT w,
const Tangent_space_basis &tsb,
1395 const Tr_traits &tr_traits)
const {
1396 const int point_dim = m_k.point_dimension_d_object()(p);
1398 typename K::Construct_point_d constr_pt = m_k.construct_point_d_object();
1399 typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
1400 typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
1401 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1402 typename K::Construct_cartesian_const_iterator_d ccci = m_k.construct_cartesian_const_iterator_d_object();
1404 Point origin = compute_perturbed_point(tsb.origin());
1405 Vector v = diff_points(p, origin);
1408 bool same_dim = (point_dim == tsb.dimension());
1410 std::vector<FT> coords;
1412 std::vector<FT> p_proj(ccci(origin), ccci(origin, 0));
1413 coords.reserve(tsb.dimension());
1414 for (
int i = 0; i < tsb.dimension(); ++i) {
1416 FT c = scalar_pdct(v, tsb[i]);
1417 coords.push_back(c);
1421 for (
int j = 0; j < point_dim; ++j) p_proj[j] += c * coord(tsb[i], j);
1426 FT sq_dist_to_proj_pt = 0;
1428 Point projected_pt = constr_pt(point_dim, p_proj.begin(), p_proj.end());
1429 sq_dist_to_proj_pt = m_k.squared_distance_d_object()(p, projected_pt);
1432 return tr_traits.construct_weighted_point_d_object()(
1433 tr_traits.construct_point_d_object()(
static_cast<int>(coords.size()), coords.begin(), coords.end()),
1434 w - sq_dist_to_proj_pt);
1439 template <
typename Indexed_po
int_range>
1440 std::vector<Tr_point> project_points_and_compute_weights(
const Indexed_point_range &point_indices,
1441 const Tangent_space_basis &tsb,
1442 const Tr_traits &tr_traits)
const {
1443 std::vector<Tr_point> ret;
1444 for (
typename Indexed_point_range::const_iterator it = point_indices.begin(), it_end = point_indices.end();
1445 it != it_end; ++it) {
1446 ret.push_back(project_point_and_compute_weight(compute_perturbed_weighted_point(*it), tsb, tr_traits));
1453 bool is_simplex_consistent(Tr_full_cell_handle fch,
int cur_dim)
const {
1455 for (
int i = 0; i < cur_dim + 1; ++i) {
1456 std::size_t data = fch->vertex(i)->data();
1459 return is_simplex_consistent(c);
1465 bool is_simplex_consistent(Simplex
const &simplex)
const {
1467 Simplex::const_iterator it_point_idx = simplex.begin();
1470 for (; it_point_idx != simplex.end(); ++it_point_idx) {
1471 std::size_t point_idx = *it_point_idx;
1473 if (point_idx == (std::numeric_limits<std::size_t>::max)())
continue;
1475 Star
const &star = m_stars[point_idx];
1478 Incident_simplex is_to_find = simplex;
1479 is_to_find.erase(point_idx);
1482 if (std::find(star.begin(), star.end(), is_to_find) == star.end())
return false;
1494 template <
typename OutputIterator>
1495 bool is_simplex_consistent(std::size_t center_point,
1496 Incident_simplex
const &s,
1497 OutputIterator points_whose_star_does_not_contain_s,
1498 bool check_also_in_non_maximal_faces =
false)
const {
1499 Simplex full_simplex = s;
1500 full_simplex.insert(center_point);
1503 Incident_simplex::const_iterator it_point_idx = s.begin();
1506 for (; it_point_idx != s.end(); ++it_point_idx) {
1507 std::size_t point_idx = *it_point_idx;
1509 if (point_idx == (std::numeric_limits<std::size_t>::max)())
continue;
1511 Star
const &star = m_stars[point_idx];
1514 Incident_simplex is_to_find = full_simplex;
1515 is_to_find.erase(point_idx);
1517 if (check_also_in_non_maximal_faces) {
1521 for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
1522 if (std::includes(is->begin(), is->end(), is_to_find.begin(), is_to_find.end())) found =
true;
1525 if (!found) *points_whose_star_does_not_contain_s++ = point_idx;
1528 if (std::find(star.begin(), star.end(), is_to_find) == star.end())
1529 *points_whose_star_does_not_contain_s++ = point_idx;
1539 bool is_simplex_in_star(std::size_t p, Incident_simplex
const &s,
bool check_also_in_non_maximal_faces =
true)
const {
1540 Star
const &star = m_stars[p];
1542 if (check_also_in_non_maximal_faces) {
1546 for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
1547 if (std::includes(is->begin(), is->end(), s.begin(), s.end())) found =
true;
1552 return !(std::find(star.begin(), star.end(), s) == star.end());
1556 #ifdef GUDHI_USE_TBB
1558 class Try_to_solve_inconsistencies_in_a_local_triangulation {
1559 Tangential_complex &m_tc;
1560 double m_max_perturb;
1561 tbb::combinable<std::size_t> &m_num_inconsistencies;
1562 tbb::combinable<std::vector<std::size_t> > &m_updated_points;
1566 Try_to_solve_inconsistencies_in_a_local_triangulation(Tangential_complex &tc,
double max_perturb,
1567 tbb::combinable<std::size_t> &num_inconsistencies,
1568 tbb::combinable<std::vector<std::size_t> > &updated_points)
1570 m_max_perturb(max_perturb),
1571 m_num_inconsistencies(num_inconsistencies),
1572 m_updated_points(updated_points) {}
1575 Try_to_solve_inconsistencies_in_a_local_triangulation(
1576 const Try_to_solve_inconsistencies_in_a_local_triangulation &tsilt)
1578 m_max_perturb(tsilt.m_max_perturb),
1579 m_num_inconsistencies(tsilt.m_num_inconsistencies),
1580 m_updated_points(tsilt.m_updated_points) {}
1583 void operator()(
const tbb::blocked_range<size_t> &r)
const {
1584 for (
size_t i = r.begin(); i != r.end(); ++i) {
1585 m_num_inconsistencies.local() += m_tc.try_to_solve_inconsistencies_in_a_local_triangulation(
1586 i, m_max_perturb, std::back_inserter(m_updated_points.local()));
1590 #endif // GUDHI_USE_TBB
1592 void perturb(std::size_t point_idx,
double max_perturb) {
1593 const Tr_traits &local_tr_traits = m_triangulations[point_idx].tr().geom_traits();
1594 typename Tr_traits::Compute_coordinate_d coord = local_tr_traits.compute_coordinate_d_object();
1595 typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
1596 typename K::Construct_vector_d k_constr_vec = m_k.construct_vector_d_object();
1597 typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
1599 CGAL::Random_points_in_ball_d<Tr_bare_point> tr_point_in_ball_generator(
1600 m_intrinsic_dim, m_random_generator.get_double(0., max_perturb));
1602 Tr_point local_random_transl =
1603 local_tr_traits.construct_weighted_point_d_object()(*tr_point_in_ball_generator++, 0);
1604 Translation_for_perturb global_transl = k_constr_vec(m_ambient_dim);
1605 const Tangent_space_basis &tsb = m_tangent_spaces[point_idx];
1606 for (
int i = 0; i < m_intrinsic_dim; ++i) {
1607 global_transl = k_transl(global_transl, k_scaled_vec(tsb[i], coord(local_random_transl, i)));
1610 #if defined(GUDHI_USE_TBB)
1611 m_p_perturb_mutexes[point_idx].lock();
1612 m_translations[point_idx] = global_transl;
1613 m_p_perturb_mutexes[point_idx].unlock();
1616 m_translations[point_idx] = global_transl;
1621 template <
typename OutputIt>
1622 bool try_to_solve_inconsistencies_in_a_local_triangulation(
1623 std::size_t tr_index,
double max_perturb, OutputIt perturbed_pts_indices = CGAL::Emptyset_iterator()) {
1624 bool is_inconsistent =
false;
1626 Star
const &star = m_stars[tr_index];
1629 Star::const_iterator it_inc_simplex = star.begin();
1630 Star::const_iterator it_inc_simplex_end = star.end();
1631 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
1632 const Incident_simplex &incident_simplex = *it_inc_simplex;
1635 if (is_infinite(incident_simplex))
continue;
1637 Simplex c = incident_simplex;
1641 if (!is_simplex_consistent(c)) {
1642 is_inconsistent =
true;
1644 std::size_t idx = tr_index;
1646 perturb(tr_index, max_perturb);
1647 *perturbed_pts_indices++ = idx;
1654 return is_inconsistent;
1659 std::ostream &export_point_set(std::ostream &os,
bool use_perturbed_points =
false,
1660 const char *coord_separator =
" ")
const {
1661 if (use_perturbed_points) {
1662 std::vector<Point> perturbed_points;
1663 perturbed_points.reserve(m_points.size());
1664 for (std::size_t i = 0; i < m_points.size(); ++i) perturbed_points.push_back(compute_perturbed_point(i));
1666 return export_point_set(m_k, perturbed_points, os, coord_separator);
1668 return export_point_set(m_k, m_points, os, coord_separator);
1672 template <
typename ProjectionFunctor = CGAL::Identity<Po
int> >
1673 std::ostream &export_vertices_to_off(std::ostream &os, std::size_t &num_vertices,
bool use_perturbed_points =
false,
1674 ProjectionFunctor
const &point_projection = ProjectionFunctor())
const {
1675 if (m_points.empty()) {
1683 const int N = (m_intrinsic_dim == 1 ? 2 : 1);
1686 typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
1688 #ifdef GUDHI_TC_EXPORT_ALL_COORDS_IN_OFF
1689 int num_coords = m_ambient_dim;
1691 int num_coords = (std::min)(m_ambient_dim, 3);
1694 #ifdef GUDHI_TC_EXPORT_NORMALS
1695 OS_container::const_iterator it_os = m_orth_spaces.begin();
1697 typename Points::const_iterator it_p = m_points.begin();
1698 typename Points::const_iterator it_p_end = m_points.end();
1700 for (std::size_t i = 0; it_p != it_p_end; ++it_p, ++i) {
1701 Point p = point_projection(use_perturbed_points ? compute_perturbed_point(i) : *it_p);
1702 for (
int ii = 0; ii < N; ++ii) {
1704 for (; j < num_coords; ++j) os << CGAL::to_double(coord(p, j)) <<
" ";
1705 if (j == 2) os <<
"0";
1707 #ifdef GUDHI_TC_EXPORT_NORMALS
1708 for (j = 0; j < num_coords; ++j) os <<
" " << CGAL::to_double(coord(*it_os->begin(), j));
1712 #ifdef GUDHI_TC_EXPORT_NORMALS
1717 num_vertices = N * m_points.size();
1721 std::ostream &export_simplices_to_off(std::ostream &os, std::size_t &num_OFF_simplices,
1722 bool color_inconsistencies =
false,
1723 Simplex_set
const *p_simpl_to_color_in_red = NULL,
1724 Simplex_set
const *p_simpl_to_color_in_green = NULL,
1725 Simplex_set
const *p_simpl_to_color_in_blue = NULL)
const {
1728 num_OFF_simplices = 0;
1729 std::size_t num_maximal_simplices = 0;
1730 std::size_t num_inconsistent_maximal_simplices = 0;
1731 std::size_t num_inconsistent_stars = 0;
1732 typename Tr_container::const_iterator it_tr = m_triangulations.begin();
1733 typename Tr_container::const_iterator it_tr_end = m_triangulations.end();
1735 for (std::size_t idx = 0; it_tr != it_tr_end; ++it_tr, ++idx) {
1736 bool is_star_inconsistent =
false;
1738 Triangulation
const &tr = it_tr->tr();
1740 if (tr.current_dimension() < m_intrinsic_dim)
continue;
1743 std::stringstream color;
1745 color << 128 <<
" " << 128 <<
" " << 128;
1748 typedef std::vector<std::pair<Simplex, int> > Star_using_triangles;
1749 Star_using_triangles star_using_triangles;
1752 Star::const_iterator it_inc_simplex = m_stars[idx].begin();
1753 Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
1754 for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
1755 Simplex c = *it_inc_simplex;
1757 std::size_t num_vertices = c.size();
1758 ++num_maximal_simplices;
1760 int color_simplex = -1;
1761 if (color_inconsistencies && !is_simplex_consistent(c)) {
1762 ++num_inconsistent_maximal_simplices;
1764 is_star_inconsistent =
true;
1766 if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(),
1767 c) != p_simpl_to_color_in_red->end()) {
1769 }
else if (p_simpl_to_color_in_green &&
1770 std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
1771 p_simpl_to_color_in_green->end()) {
1773 }
else if (p_simpl_to_color_in_blue &&
1774 std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
1775 p_simpl_to_color_in_blue->end()) {
1784 if (m_intrinsic_dim == 1) {
1786 Simplex::iterator it = c.begin();
1787 for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
1788 if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
1793 if (num_vertices <= 3) {
1794 star_using_triangles.push_back(std::make_pair(c, color_simplex));
1797 std::vector<bool> booleans(num_vertices,
false);
1798 std::fill(booleans.begin() + num_vertices - 3, booleans.end(),
true);
1801 Simplex::iterator it = c.begin();
1802 for (
int i = 0; it != c.end(); ++i, ++it) {
1803 if (booleans[i]) triangle.insert(*it);
1805 star_using_triangles.push_back(std::make_pair(triangle, color_simplex));
1806 }
while (std::next_permutation(booleans.begin(), booleans.end()));
1811 Star_using_triangles::const_iterator it_simplex = star_using_triangles.begin();
1812 Star_using_triangles::const_iterator it_simplex_end = star_using_triangles.end();
1813 for (; it_simplex != it_simplex_end; ++it_simplex) {
1814 const Simplex &c = it_simplex->first;
1817 if (is_infinite(c))
continue;
1819 int color_simplex = it_simplex->second;
1821 std::stringstream sstr_c;
1823 Simplex::const_iterator it_point_idx = c.begin();
1824 for (; it_point_idx != c.end(); ++it_point_idx) {
1825 sstr_c << *it_point_idx <<
" ";
1828 os << 3 <<
" " << sstr_c.str();
1829 if (color_inconsistencies || p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
1830 switch (color_simplex) {
1844 os <<
" " << color.str();
1848 ++num_OFF_simplices;
1851 if (is_star_inconsistent) ++num_inconsistent_stars;
1855 std::cerr <<
"\n==========================================================\n"
1856 <<
"Export from list of stars to OFF:\n"
1857 <<
" * Number of vertices: " << m_points.size() <<
"\n"
1858 <<
" * Total number of maximal simplices: " << num_maximal_simplices <<
"\n";
1859 if (color_inconsistencies) {
1860 std::cerr <<
" * Number of inconsistent stars: " << num_inconsistent_stars <<
" ("
1861 << (m_points.size() > 0 ? 100. * num_inconsistent_stars / m_points.size() : 0.) <<
"%)\n"
1862 <<
" * Number of inconsistent maximal simplices: " << num_inconsistent_maximal_simplices <<
" ("
1863 << (num_maximal_simplices > 0 ? 100. * num_inconsistent_maximal_simplices / num_maximal_simplices : 0.)
1866 std::cerr <<
"==========================================================\n";
1873 std::ostream &export_simplices_to_off(
const Simplicial_complex &complex, std::ostream &os,
1874 std::size_t &num_OFF_simplices,
1875 Simplex_set
const *p_simpl_to_color_in_red = NULL,
1876 Simplex_set
const *p_simpl_to_color_in_green = NULL,
1877 Simplex_set
const *p_simpl_to_color_in_blue = NULL)
const {
1878 typedef Simplicial_complex::Simplex Simplex;
1879 typedef Simplicial_complex::Simplex_set Simplex_set;
1883 num_OFF_simplices = 0;
1884 std::size_t num_maximal_simplices = 0;
1886 typename Simplex_set::const_iterator it_s = complex.simplex_range().begin();
1887 typename Simplex_set::const_iterator it_s_end = complex.simplex_range().end();
1889 for (; it_s != it_s_end; ++it_s) {
1891 ++num_maximal_simplices;
1893 int color_simplex = -1;
1894 if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(), c) !=
1895 p_simpl_to_color_in_red->end()) {
1897 }
else if (p_simpl_to_color_in_green &&
1898 std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
1899 p_simpl_to_color_in_green->end()) {
1901 }
else if (p_simpl_to_color_in_blue &&
1902 std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
1903 p_simpl_to_color_in_blue->end()) {
1908 typedef std::vector<Simplex> Triangles;
1909 Triangles triangles;
1911 int num_vertices =
static_cast<int>(c.size());
1913 if (num_vertices < m_intrinsic_dim + 1)
continue;
1919 if (m_intrinsic_dim == 1) {
1921 Simplex::iterator it = c.begin();
1922 for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
1923 if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
1928 if (num_vertices <= 3) {
1929 triangles.push_back(c);
1932 std::vector<bool> booleans(num_vertices,
false);
1933 std::fill(booleans.begin() + num_vertices - 3, booleans.end(),
true);
1936 Simplex::iterator it = c.begin();
1937 for (
int i = 0; it != c.end(); ++i, ++it) {
1938 if (booleans[i]) triangle.insert(*it);
1940 triangles.push_back(triangle);
1941 }
while (std::next_permutation(booleans.begin(), booleans.end()));
1945 Triangles::const_iterator it_tri = triangles.begin();
1946 Triangles::const_iterator it_tri_end = triangles.end();
1947 for (; it_tri != it_tri_end; ++it_tri) {
1949 if (is_infinite(*it_tri))
continue;
1952 Simplex::const_iterator it_point_idx = it_tri->begin();
1953 for (; it_point_idx != it_tri->end(); ++it_point_idx) {
1954 os << *it_point_idx <<
" ";
1957 if (p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
1958 switch (color_simplex) {
1972 os <<
" 128 128 128";
1977 ++num_OFF_simplices;
1983 std::cerr <<
"\n==========================================================\n"
1984 <<
"Export from complex to OFF:\n"
1985 <<
" * Number of vertices: " << m_points.size() <<
"\n"
1986 <<
" * Total number of maximal simplices: " << num_maximal_simplices <<
"\n"
1987 <<
"==========================================================\n";
2004 const int m_intrinsic_dim;
2005 const int m_ambient_dim;
2009 #ifdef GUDHI_TC_PERTURB_POSITION
2010 Translations_for_perturb m_translations;
2011 #if defined(GUDHI_USE_TBB)
2012 Mutex_for_perturb *m_p_perturb_mutexes;
2016 Points_ds m_points_ds;
2017 double m_last_max_perturb;
2018 std::vector<bool> m_are_tangent_spaces_computed;
2019 TS_container m_tangent_spaces;
2020 #ifdef GUDHI_TC_EXPORT_NORMALS
2021 OS_container m_orth_spaces;
2023 Tr_container m_triangulations;
2025 Stars_container m_stars;
2026 std::vector<FT> m_squared_star_spheres_radii_incl_margin;
2027 boost::optional<FT> m_max_squared_edge_length;
2029 #ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
2030 Points m_points_for_tse;
2031 Points_ds m_points_ds_for_tse;
2034 mutable CGAL::Random m_random_generator;
2040 #endif // TANGENTIAL_COMPLEX_H_