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Tangential_complex.h
/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
* See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
* Author(s): Clement Jamin
*
* Copyright (C) 2016 Inria
*
* Modification(s):
* - 2019/08 Vincent Rouvreau: Fix issue #10 for CGAL and Eigen3
* - YYYY/MM Author: Description of the modification
*/
#ifndef TANGENTIAL_COMPLEX_H_
#define TANGENTIAL_COMPLEX_H_
#include <gudhi/Tangential_complex/config.h>
#include <gudhi/Tangential_complex/Simplicial_complex.h>
#include <gudhi/Tangential_complex/utilities.h>
#include <gudhi/Kd_tree_search.h>
#include <gudhi/console_color.h>
#include <gudhi/Clock.h>
#include <gudhi/Simplex_tree.h>
#include <gudhi/Debug_utils.h>
#include <CGAL/Default.h>
#include <CGAL/Dimension.h>
#include <CGAL/function_objects.h> // for CGAL::Identity
#include <CGAL/Epick_d.h>
#include <CGAL/Regular_triangulation_traits_adapter.h>
#include <CGAL/Regular_triangulation.h>
#include <CGAL/Delaunay_triangulation.h>
#include <CGAL/Combination_enumerator.h>
#include <CGAL/point_generators_d.h>
#include <CGAL/version.h> // for CGAL_VERSION_NR
#include <Eigen/Core>
#include <Eigen/Eigen>
#include <Eigen/src/Core/util/Macros.h> // for EIGEN_VERSION_AT_LEAST
#include <boost/iterator/transform_iterator.hpp>
#include <boost/range/adaptor/transformed.hpp>
#include <boost/range/counting_range.hpp>
#include <boost/math/special_functions/factorials.hpp>
#include <boost/container/flat_set.hpp>
#include <tuple>
#include <vector>
#include <set>
#include <utility>
#include <sstream>
#include <iostream>
#include <limits>
#include <algorithm>
#include <functional>
#include <iterator>
#include <cmath> // for std::sqrt
#include <string>
#include <cstddef> // for std::size_t
#include <optional>
#include <numeric> // for std::iota
#ifdef GUDHI_USE_TBB
#include <tbb/parallel_for.h>
#include <tbb/combinable.h>
#include <mutex>
#endif
// #define GUDHI_TC_EXPORT_NORMALS // Only for 3D surfaces (k=2, d=3)
// Make compilation fail - required for external projects - https://github.com/GUDHI/gudhi-devel/issues/10
#if CGAL_VERSION_NR < 1041101000
# error Tangential_complex is only available for CGAL >= 4.11
#endif
#if !EIGEN_VERSION_AT_LEAST(3,1,0)
# error Tangential_complex is only available for Eigen3 >= 3.1.0 installed with CGAL
#endif
namespace sps = Gudhi::spatial_searching;
namespace Gudhi {
namespace tangential_complex {
using namespace internal;
class Vertex_data {
public:
Vertex_data(std::size_t data = (std::numeric_limits<std::size_t>::max)()) : m_data(data) {}
operator std::size_t() { return m_data; }
operator std::size_t() const { return m_data; }
private:
std::size_t m_data;
};
template <typename Kernel_, // ambiant kernel
typename DimensionTag, // intrinsic dimension
typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>
class Tangential_complex {
typedef Kernel_ K;
typedef typename K::FT FT;
typedef typename K::Point_d Point;
typedef typename K::Weighted_point_d Weighted_point;
typedef typename K::Vector_d Vector;
typedef typename CGAL::Default::Get<
Triangulation_,
CGAL::Regular_triangulation<
CGAL::Epick_d<DimensionTag>,
CGAL::Triangulation_data_structure<
typename CGAL::Epick_d<DimensionTag>::Dimension,
CGAL::Triangulation_vertex<CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> >,
Vertex_data>,
CGAL::Triangulation_full_cell<
CGAL::Regular_triangulation_traits_adapter<CGAL::Epick_d<DimensionTag> > > > > >::type Triangulation;
typedef typename Triangulation::Geom_traits Tr_traits;
typedef typename Triangulation::Weighted_point Tr_point;
typedef typename Tr_traits::Base::Point_d Tr_bare_point;
typedef typename Triangulation::Vertex_handle Tr_vertex_handle;
typedef typename Triangulation::Full_cell_handle Tr_full_cell_handle;
typedef typename Tr_traits::Vector_d Tr_vector;
#if defined(GUDHI_USE_TBB)
typedef std::mutex Mutex_for_perturb;
typedef Vector Translation_for_perturb;
typedef std::vector<Atomic_wrapper<FT> > Weights;
#else
typedef Vector Translation_for_perturb;
typedef std::vector<FT> Weights;
#endif
typedef std::vector<Translation_for_perturb> Translations_for_perturb;
// Store a local triangulation and a handle to its center vertex
struct Tr_and_VH {
public:
Tr_and_VH() : m_tr(NULL) {}
Tr_and_VH(int dim) : m_tr(new Triangulation(dim)) {}
~Tr_and_VH() { destroy_triangulation(); }
Triangulation &construct_triangulation(int dim) {
delete m_tr;
m_tr = new Triangulation(dim);
return tr();
}
void destroy_triangulation() {
delete m_tr;
m_tr = NULL;
}
Triangulation &tr() { return *m_tr; }
Triangulation const &tr() const { return *m_tr; }
Tr_vertex_handle const &center_vertex() const { return m_center_vertex; }
Tr_vertex_handle &center_vertex() { return m_center_vertex; }
private:
Triangulation *m_tr;
Tr_vertex_handle m_center_vertex;
};
public:
typedef Basis<K> Tangent_space_basis;
typedef Basis<K> Orthogonal_space_basis;
typedef std::vector<Tangent_space_basis> TS_container;
typedef std::vector<Orthogonal_space_basis> OS_container;
typedef std::vector<Point> Points;
typedef boost::container::flat_set<std::size_t> Simplex;
typedef std::set<Simplex> Simplex_set;
private:
typedef sps::Kd_tree_search<K, Points> Points_ds;
typedef typename Points_ds::KNS_range KNS_range;
typedef typename Points_ds::INS_range INS_range;
typedef std::vector<Tr_and_VH> Tr_container;
typedef std::vector<Vector> Vectors;
// An Incident_simplex is the list of the vertex indices
// except the center vertex
typedef boost::container::flat_set<std::size_t> Incident_simplex;
typedef std::vector<Incident_simplex> Star;
typedef std::vector<Star> Stars_container;
// For transform_iterator
static const Tr_point &vertex_handle_to_point(Tr_vertex_handle vh) { return vh->point(); }
template <typename P, typename VH>
static const P &vertex_handle_to_point(VH vh) {
return vh->point();
}
public:
typedef internal::Simplicial_complex Simplicial_complex;
template <typename Point_range>
Tangential_complex(Point_range points, int intrinsic_dimension,
#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
InputIterator first_for_tse, InputIterator last_for_tse,
#endif
const K &k = K())
: m_k(k),
m_intrinsic_dim(intrinsic_dimension),
m_ambient_dim(points.empty() ? 0 : k.point_dimension_d_object()(*points.begin())),
m_points(points.begin(), points.end()),
m_weights(m_points.size(), FT(0))
#if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION)
,
m_p_perturb_mutexes(NULL)
#endif
,
m_points_ds(m_points),
m_last_max_perturb(0.),
m_are_tangent_spaces_computed(m_points.size(), false),
m_tangent_spaces(m_points.size(), Tangent_space_basis())
#ifdef GUDHI_TC_EXPORT_NORMALS
,
m_orth_spaces(m_points.size(), Orthogonal_space_basis())
#endif
#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
,
m_points_for_tse(first_for_tse, last_for_tse),
m_points_ds_for_tse(m_points_for_tse)
#endif
{
}
~Tangential_complex() {
#if defined(GUDHI_USE_TBB) && defined(GUDHI_TC_PERTURB_POSITION)
delete[] m_p_perturb_mutexes;
#endif
}
int intrinsic_dimension() const { return m_intrinsic_dim; }
int ambient_dimension() const { return m_ambient_dim; }
Points const &points() const { return m_points; }
Point get_point(std::size_t vertex) const { return m_points[vertex]; }
Point get_perturbed_point(std::size_t vertex) const { return compute_perturbed_point(vertex); }
std::size_t number_of_vertices() const { return m_points.size(); }
void set_weights(const Weights &weights) { m_weights = weights; }
void set_tangent_planes(const TS_container &tangent_spaces
#ifdef GUDHI_TC_EXPORT_NORMALS
,
const OS_container &orthogonal_spaces
#endif
) {
#ifdef GUDHI_TC_EXPORT_NORMALS
GUDHI_CHECK(m_points.size() == tangent_spaces.size() && m_points.size() == orthogonal_spaces.size(),
std::logic_error("Wrong sizes"));
#else
GUDHI_CHECK(m_points.size() == tangent_spaces.size(), std::logic_error("Wrong sizes"));
#endif
m_tangent_spaces = tangent_spaces;
#ifdef GUDHI_TC_EXPORT_NORMALS
m_orth_spaces = orthogonal_spaces;
#endif
for (std::size_t i = 0; i < m_points.size(); ++i) m_are_tangent_spaces_computed[i] = true;
}
void compute_tangential_complex() {
#ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS
std::cerr << red << "WARNING: GUDHI_TC_PERFORM_EXTRA_CHECKS is defined. "
<< "Computation might be slower than usual.\n"
<< white;
#endif
#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB)
Gudhi::Clock t;
#endif
// We need to do that because we don't want the container to copy the
// already-computed triangulations (while resizing) since it would
// invalidate the vertex handles stored beside the triangulations
m_triangulations.resize(m_points.size());
m_stars.resize(m_points.size());
m_squared_star_spheres_radii_incl_margin.resize(m_points.size(), FT(-1));
#ifdef GUDHI_TC_PERTURB_POSITION
if (m_points.empty()) {
m_translations.clear();
} else {
m_translations.resize(m_points.size(), m_k.construct_vector_d_object()(m_ambient_dim));
}
#if defined(GUDHI_USE_TBB)
delete[] m_p_perturb_mutexes;
m_p_perturb_mutexes = new Mutex_for_perturb[m_points.size()];
#endif
#endif
#ifdef GUDHI_USE_TBB
// Parallel
if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*this));
} else {
#endif // GUDHI_USE_TBB
// Sequential
for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
#ifdef GUDHI_USE_TBB
}
#endif // GUDHI_USE_TBB
#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_USE_TBB)
t.end();
std::cerr << "Tangential complex computed in " << t.num_seconds() << " seconds.\n";
#endif
}
struct Fix_inconsistencies_info {
bool success = false;
unsigned int num_steps = 0;
std::size_t initial_num_inconsistent_stars = 0;
std::size_t best_num_inconsistent_stars = 0;
std::size_t final_num_inconsistent_stars = 0;
};
Fix_inconsistencies_info fix_inconsistencies_using_perturbation(double max_perturb, double time_limit = -1.) {
Fix_inconsistencies_info info;
if (time_limit == 0.) return info;
Gudhi::Clock t;
#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
std::tuple<std::size_t, std::size_t, std::size_t> stats_before = number_of_inconsistent_simplices(false);
if (std::get<1>(stats_before) == 0) {
#ifdef DEBUG_TRACES
std::cerr << "Nothing to fix.\n";
#endif
info.success = false;
return info;
}
#endif // GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
m_last_max_perturb = max_perturb;
bool done = false;
info.best_num_inconsistent_stars = m_triangulations.size();
info.num_steps = 0;
while (!done) {
#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
std::cerr << "\nBefore fix step:\n"
<< " * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_before) << "\n"
<< " * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_before)
<< white << " (" << 100. * std::get<1>(stats_before) / std::get<0>(stats_before) << "%)\n"
<< " * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_before)
<< white << " (" << 100. * std::get<2>(stats_before) / m_points.size() << "%)\n";
#endif
#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
std::cerr << yellow << "\nAttempt to fix inconsistencies using perturbations - step #" << info.num_steps + 1
<< "... " << white;
#endif
std::size_t num_inconsistent_stars = 0;
std::vector<std::size_t> updated_points;
#ifdef GUDHI_TC_PROFILING
Gudhi::Clock t_fix_step;
#endif
// Parallel
#if defined(GUDHI_USE_TBB)
if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
tbb::combinable<std::size_t> num_inconsistencies;
tbb::combinable<std::vector<std::size_t> > tls_updated_points;
tbb::parallel_for(tbb::blocked_range<size_t>(0, m_triangulations.size()),
[&]( tbb::blocked_range<size_t> r ) {
for (size_t i = r.begin(); i != r.end(); ++i) {
num_inconsistencies.local() += try_to_solve_inconsistencies_in_a_local_triangulation(
i, max_perturb, std::back_inserter(tls_updated_points.local()));
}
});
num_inconsistent_stars = num_inconsistencies.combine(std::plus<std::size_t>());
updated_points =
tls_updated_points.combine([](std::vector<std::size_t> const &x, std::vector<std::size_t> const &y) {
std::vector<std::size_t> res;
res.reserve(x.size() + y.size());
res.insert(res.end(), x.begin(), x.end());
res.insert(res.end(), y.begin(), y.end());
return res;
});
} else {
#endif // GUDHI_USE_TBB
// Sequential
for (std::size_t i = 0; i < m_triangulations.size(); ++i) {
num_inconsistent_stars +=
try_to_solve_inconsistencies_in_a_local_triangulation(i, max_perturb, std::back_inserter(updated_points));
}
#if defined(GUDHI_USE_TBB)
}
#endif // GUDHI_USE_TBB
#ifdef GUDHI_TC_PROFILING
t_fix_step.end();
#endif
#if defined(GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES) || defined(DEBUG_TRACES)
std::cerr << "\nEncountered during fix:\n"
<< " * Num stars containing inconsistent simplices: " << red << num_inconsistent_stars << white << " ("
<< 100. * num_inconsistent_stars / m_points.size() << "%)\n";
#endif
#ifdef GUDHI_TC_PROFILING
std::cerr << yellow << "done in " << t_fix_step.num_seconds() << " seconds.\n" << white;
#elif defined(DEBUG_TRACES)
std::cerr << yellow << "done.\n" << white;
#endif
if (num_inconsistent_stars > 0) refresh_tangential_complex(updated_points);
#ifdef GUDHI_TC_PERFORM_EXTRA_CHECKS
// Confirm that all stars were actually refreshed
std::size_t num_inc_1 = std::get<1>(number_of_inconsistent_simplices(false));
refresh_tangential_complex();
std::size_t num_inc_2 = std::get<1>(number_of_inconsistent_simplices(false));
if (num_inc_1 != num_inc_2)
std::cerr << red << "REFRESHMENT CHECK: FAILED. (" << num_inc_1 << " vs " << num_inc_2 << ")\n" << white;
else
std::cerr << green << "REFRESHMENT CHECK: PASSED.\n" << white;
#endif
#ifdef GUDHI_TC_SHOW_DETAILED_STATS_FOR_INCONSISTENCIES
std::tuple<std::size_t, std::size_t, std::size_t> stats_after = number_of_inconsistent_simplices(false);
std::cerr << "\nAfter fix:\n"
<< " * Total number of simplices in stars (incl. duplicates): " << std::get<0>(stats_after) << "\n"
<< " * Num inconsistent simplices in stars (incl. duplicates): " << red << std::get<1>(stats_after)
<< white << " (" << 100. * std::get<1>(stats_after) / std::get<0>(stats_after) << "%)\n"
<< " * Number of stars containing inconsistent simplices: " << red << std::get<2>(stats_after) << white
<< " (" << 100. * std::get<2>(stats_after) / m_points.size() << "%)\n";
stats_before = stats_after;
#endif
if (info.num_steps == 0) info.initial_num_inconsistent_stars = num_inconsistent_stars;
if (num_inconsistent_stars < info.best_num_inconsistent_stars)
info.best_num_inconsistent_stars = num_inconsistent_stars;
info.final_num_inconsistent_stars = num_inconsistent_stars;
done = (num_inconsistent_stars == 0);
if (!done) {
++info.num_steps;
if (time_limit > 0. && t.num_seconds() > time_limit) {
#ifdef DEBUG_TRACES
std::cerr << red << "Time limit reached.\n" << white;
#endif
info.success = false;
return info;
}
}
}
#ifdef DEBUG_TRACES
std::cerr << green << "Fixed!\n" << white;
#endif
info.success = true;
return info;
}
struct Num_inconsistencies {
std::size_t num_simplices = 0;
std::size_t num_inconsistent_simplices = 0;
std::size_t num_inconsistent_stars = 0;
};
Num_inconsistencies number_of_inconsistent_simplices(
#ifdef DEBUG_TRACES
bool verbose = true
#else
bool verbose = false
#endif
) const {
Num_inconsistencies stats;
// For each triangulation
for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
bool is_star_inconsistent = false;
// For each cell
Star::const_iterator it_inc_simplex = m_stars[idx].begin();
Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
// Don't check infinite cells
if (is_infinite(*it_inc_simplex)) continue;
Simplex c = *it_inc_simplex;
c.insert(idx); // Add the missing index
if (!is_simplex_consistent(c)) {
++stats.num_inconsistent_simplices;
is_star_inconsistent = true;
}
++stats.num_simplices;
}
stats.num_inconsistent_stars += is_star_inconsistent;
}
if (verbose) {
std::cerr << "\n==========================================================\n"
<< "Inconsistencies:\n"
<< " * Total number of simplices in stars (incl. duplicates): " << stats.num_simplices << "\n"
<< " * Number of inconsistent simplices in stars (incl. duplicates): "
<< stats.num_inconsistent_simplices << " ("
<< 100. * stats.num_inconsistent_simplices / stats.num_simplices << "%)\n"
<< " * Number of stars containing inconsistent simplices: " << stats.num_inconsistent_stars << " ("
<< 100. * stats.num_inconsistent_stars / m_points.size() << "%)\n"
<< "==========================================================\n";
}
return stats;
}
template <typename Simplex_tree_>
int create_complex(Simplex_tree_ &tree,
bool export_inconsistent_simplices = true
,
bool export_infinite_simplices = false, Simplex_set *p_inconsistent_simplices = NULL
) const {
#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
std::cerr << yellow << "\nExporting the TC as a Simplex_tree... " << white;
#endif
#ifdef GUDHI_TC_PROFILING
Gudhi::Clock t;
#endif
int max_dim = -1;
// Ordered vertices to be inserted first by the create_complex method to avoid quadratic complexity.
std::vector<typename Simplex_tree_::Vertex_handle> vertices(m_points.size());
std::iota(vertices.begin(), vertices.end(), 0);
tree.insert_batch_vertices(vertices);
// For each triangulation
for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
// For each cell of the star
Star::const_iterator it_inc_simplex = m_stars[idx].begin();
Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
Simplex c = *it_inc_simplex;
// Don't export infinite cells
if (!export_infinite_simplices && is_infinite(c)) continue;
if (static_cast<int>(c.size()) > max_dim) max_dim = static_cast<int>(c.size());
// Add the missing center vertex
c.insert(idx);
if (!export_inconsistent_simplices && !is_simplex_consistent(c)) continue;
// Try to insert the simplex
bool inserted = tree.insert_simplex_and_subfaces(c).second;
// Inconsistent?
if (p_inconsistent_simplices && inserted && !is_simplex_consistent(c)) {
p_inconsistent_simplices->insert(c);
}
}
}
#ifdef GUDHI_TC_PROFILING
t.end();
std::cerr << yellow << "done in " << t.num_seconds() << " seconds.\n" << white;
#elif defined(DEBUG_TRACES)
std::cerr << yellow << "done.\n" << white;
#endif
return max_dim;
}
// First clears the complex then exports the TC into it
// Returns the max dimension of the simplices
// check_lower_and_higher_dim_simplices : 0 (false), 1 (true), 2 (auto)
// If the check is enabled, the function:
// - won't insert the simplex if it is already in a higher dim simplex
// - will erase any lower-dim simplices that are faces of the new simplex
// "auto" (= 2) will enable the check as a soon as it encounters a
// simplex whose dimension is different from the previous ones.
// N.B.: The check is quite expensive.
int create_complex(Simplicial_complex &complex, bool export_inconsistent_simplices = true,
bool export_infinite_simplices = false, int check_lower_and_higher_dim_simplices = 2,
Simplex_set *p_inconsistent_simplices = NULL) const {
#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
std::cerr << yellow << "\nExporting the TC as a Simplicial_complex... " << white;
#endif
#ifdef GUDHI_TC_PROFILING
Gudhi::Clock t;
#endif
int max_dim = -1;
complex.clear();
// For each triangulation
for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
// For each cell of the star
Star::const_iterator it_inc_simplex = m_stars[idx].begin();
Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
Simplex c = *it_inc_simplex;
// Don't export infinite cells
if (!export_infinite_simplices && is_infinite(c)) continue;
if (static_cast<int>(c.size()) > max_dim) max_dim = static_cast<int>(c.size());
// Add the missing center vertex
c.insert(idx);
if (!export_inconsistent_simplices && !is_simplex_consistent(c)) continue;
// Unusual simplex dim?
if (check_lower_and_higher_dim_simplices == 2 && max_dim != -1 && static_cast<int>(c.size()) != max_dim) {
// Let's activate the check
std::cerr << red
<< "Info: check_lower_and_higher_dim_simplices ACTIVATED. "
"Export might be take some time...\n"
<< white;
check_lower_and_higher_dim_simplices = 1;
}
// Try to insert the simplex
bool added = complex.add_simplex(c, check_lower_and_higher_dim_simplices == 1);
// Inconsistent?
if (p_inconsistent_simplices && added && !is_simplex_consistent(c)) {
p_inconsistent_simplices->insert(c);
}
}
}
#ifdef GUDHI_TC_PROFILING
t.end();
std::cerr << yellow << "done in " << t.num_seconds() << " seconds.\n" << white;
#elif defined(DEBUG_TRACES)
std::cerr << yellow << "done.\n" << white;
#endif
return max_dim;
}
template <typename ProjectionFunctor = CGAL::Identity<Point> >
std::ostream &export_to_off(const Simplicial_complex &complex, std::ostream &os,
Simplex_set const *p_simpl_to_color_in_red = NULL,
Simplex_set const *p_simpl_to_color_in_green = NULL,
Simplex_set const *p_simpl_to_color_in_blue = NULL,
ProjectionFunctor const &point_projection = ProjectionFunctor()) const {
return export_to_off(os, false, p_simpl_to_color_in_red, p_simpl_to_color_in_green, p_simpl_to_color_in_blue,
&complex, point_projection);
}
template <typename ProjectionFunctor = CGAL::Identity<Point> >
std::ostream &export_to_off(std::ostream &os, bool color_inconsistencies = false,
Simplex_set const *p_simpl_to_color_in_red = NULL,
Simplex_set const *p_simpl_to_color_in_green = NULL,
Simplex_set const *p_simpl_to_color_in_blue = NULL,
const Simplicial_complex *p_complex = NULL,
ProjectionFunctor const &point_projection = ProjectionFunctor()) const {
if (m_points.empty()) return os;
if (m_ambient_dim < 2) {
std::cerr << "Error: export_to_off => ambient dimension should be >= 2.\n";
os << "Error: export_to_off => ambient dimension should be >= 2.\n";
return os;
}
if (m_ambient_dim > 3) {
std::cerr << "Warning: export_to_off => ambient dimension should be "
"<= 3. Only the first 3 coordinates will be exported.\n";
}
if (m_intrinsic_dim < 1 || m_intrinsic_dim > 3) {
std::cerr << "Error: export_to_off => intrinsic dimension should be "
"between 1 and 3.\n";
os << "Error: export_to_off => intrinsic dimension should be "
"between 1 and 3.\n";
return os;
}
std::stringstream output;
std::size_t num_simplices, num_vertices;
export_vertices_to_off(output, num_vertices, false, point_projection);
if (p_complex) {
export_simplices_to_off(*p_complex, output, num_simplices, p_simpl_to_color_in_red, p_simpl_to_color_in_green,
p_simpl_to_color_in_blue);
} else {
export_simplices_to_off(output, num_simplices, color_inconsistencies, p_simpl_to_color_in_red,
p_simpl_to_color_in_green, p_simpl_to_color_in_blue);
}
#ifdef GUDHI_TC_EXPORT_NORMALS
os << "N";
#endif
os << "OFF \n"
<< num_vertices << " " << num_simplices << " "
<< "0 \n"
<< output.str();
return os;
}
private:
void refresh_tangential_complex() {
#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
std::cerr << yellow << "\nRefreshing TC... " << white;
#endif
#ifdef GUDHI_TC_PROFILING
Gudhi::Clock t;
#endif
#ifdef GUDHI_USE_TBB
// Parallel
if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()), Compute_tangent_triangulation(*this));
} else {
#endif // GUDHI_USE_TBB
// Sequential
for (std::size_t i = 0; i < m_points.size(); ++i) compute_tangent_triangulation(i);
#ifdef GUDHI_USE_TBB
}
#endif // GUDHI_USE_TBB
#ifdef GUDHI_TC_PROFILING
t.end();
std::cerr << yellow << "done in " << t.num_seconds() << " seconds.\n" << white;
#elif defined(DEBUG_TRACES)
std::cerr << yellow << "done.\n" << white;
#endif
}
// If the list of perturbed points is provided, it is much faster
template <typename Point_indices_range>
void refresh_tangential_complex(Point_indices_range const &perturbed_points_indices) {
#if defined(DEBUG_TRACES) || defined(GUDHI_TC_PROFILING)
std::cerr << yellow << "\nRefreshing TC... " << white;
#endif
#ifdef GUDHI_TC_PROFILING
Gudhi::Clock t;
#endif
// ANN tree containing only the perturbed points
Points_ds updated_pts_ds(m_points, perturbed_points_indices);
#ifdef GUDHI_USE_TBB
// Parallel
if (boost::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value) {
tbb::parallel_for(tbb::blocked_range<size_t>(0, m_points.size()),
Refresh_tangent_triangulation(*this, updated_pts_ds));
} else {
#endif // GUDHI_USE_TBB
// Sequential
for (std::size_t i = 0; i < m_points.size(); ++i) refresh_tangent_triangulation(i, updated_pts_ds);
#ifdef GUDHI_USE_TBB
}
#endif // GUDHI_USE_TBB
#ifdef GUDHI_TC_PROFILING
t.end();
std::cerr << yellow << "done in " << t.num_seconds() << " seconds.\n" << white;
#elif defined(DEBUG_TRACES)
std::cerr << yellow << "done.\n" << white;
#endif
}
void export_inconsistent_stars_to_OFF_files(std::string const &filename_base) const {
// For each triangulation
for (std::size_t idx = 0; idx < m_points.size(); ++idx) {
// We build a SC along the way in case it's inconsistent
Simplicial_complex sc;
// For each cell
bool is_inconsistent = false;
Star::const_iterator it_inc_simplex = m_stars[idx].begin();
Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
// Skip infinite cells
if (is_infinite(*it_inc_simplex)) continue;
Simplex c = *it_inc_simplex;
c.insert(idx); // Add the missing index
sc.add_simplex(c);
// If we do not already know this star is inconsistent, test it
if (!is_inconsistent && !is_simplex_consistent(c)) is_inconsistent = true;
}
if (is_inconsistent) {
// Export star to OFF file
std::stringstream output_filename;
output_filename << filename_base << "_" << idx << ".off";
std::ofstream off_stream(output_filename.str().c_str());
export_to_off(sc, off_stream);
}
}
}
class Compare_distance_to_ref_point {
public:
Compare_distance_to_ref_point(Point const &ref, K const &k) : m_ref(ref), m_k(k) {}
bool operator()(Point const &p1, Point const &p2) {
typename K::Squared_distance_d sqdist = m_k.squared_distance_d_object();
return sqdist(p1, m_ref) < sqdist(p2, m_ref);
}
private:
Point const &m_ref;
K const &m_k;
};
#ifdef GUDHI_USE_TBB
// Functor for compute_tangential_complex function
class Compute_tangent_triangulation {
Tangential_complex &m_tc;
public:
// Constructor
Compute_tangent_triangulation(Tangential_complex &tc) : m_tc(tc) {}
// Constructor
Compute_tangent_triangulation(const Compute_tangent_triangulation &ctt) : m_tc(ctt.m_tc) {}
// operator()
void operator()(const tbb::blocked_range<size_t> &r) const {
for (size_t i = r.begin(); i != r.end(); ++i) m_tc.compute_tangent_triangulation(i);
}
};
// Functor for refresh_tangential_complex function
class Refresh_tangent_triangulation {
Tangential_complex &m_tc;
Points_ds const &m_updated_pts_ds;
public:
// Constructor
Refresh_tangent_triangulation(Tangential_complex &tc, Points_ds const &updated_pts_ds)
: m_tc(tc), m_updated_pts_ds(updated_pts_ds) {}
// Constructor
Refresh_tangent_triangulation(const Refresh_tangent_triangulation &ctt)
: m_tc(ctt.m_tc), m_updated_pts_ds(ctt.m_updated_pts_ds) {}
// operator()
void operator()(const tbb::blocked_range<size_t> &r) const {
for (size_t i = r.begin(); i != r.end(); ++i) m_tc.refresh_tangent_triangulation(i, m_updated_pts_ds);
}
};
#endif // GUDHI_USE_TBB
bool is_infinite(Simplex const &s) const { return *s.rbegin() == (std::numeric_limits<std::size_t>::max)(); }
// Output: "triangulation" is a Regular Triangulation containing at least the
// star of "center_pt"
// Returns the handle of the center vertex
Tr_vertex_handle compute_star(std::size_t i, const Point &center_pt, const Tangent_space_basis &tsb,
Triangulation &triangulation, bool verbose = false) {
int tangent_space_dim = tsb.dimension();
const Tr_traits &local_tr_traits = triangulation.geom_traits();
// Kernel functor & objects
typename K::Squared_distance_d k_sqdist = m_k.squared_distance_d_object();
// Triangulation's traits functor & objects
typename Tr_traits::Compute_weight_d point_weight = local_tr_traits.compute_weight_d_object();
#if CGAL_VERSION_NR < 1050200000
typename Tr_traits::Power_center_d power_center = local_tr_traits.power_center_d_object();
#else
typename Tr_traits::Construct_power_sphere_d power_center = local_tr_traits.construct_power_sphere_d_object();
#endif
//***************************************************
// Build a minimal triangulation in the tangent space
// (we only need the star of p)
//***************************************************
// Insert p
Tr_point proj_wp;
if (i == tsb.origin()) {
// Insert {(0, 0, 0...), m_weights[i]}
proj_wp = local_tr_traits.construct_weighted_point_d_object()(
local_tr_traits.construct_point_d_object()(tangent_space_dim, CGAL::ORIGIN), m_weights[i]);
} else {
const Weighted_point &wp = compute_perturbed_weighted_point(i);
proj_wp = project_point_and_compute_weight(wp, tsb, local_tr_traits);
}
Tr_vertex_handle center_vertex = triangulation.insert(proj_wp);
center_vertex->data() = i;
if (verbose) std::cerr << "* Inserted point #" << i << "\n";
#ifdef GUDHI_TC_VERY_VERBOSE
std::size_t num_attempts_to_insert_points = 1;
std::size_t num_inserted_points = 1;
#endif
// const int NUM_NEIGHBORS = 150;
// KNS_range ins_range = m_points_ds.k_nearest_neighbors(center_pt, NUM_NEIGHBORS);
INS_range ins_range = m_points_ds.incremental_nearest_neighbors(center_pt);
// While building the local triangulation, we keep the radius
// of the sphere "star sphere" centered at "center_vertex"
// and which contains all the
// circumspheres of the star of "center_vertex"
// If th the m_max_squared_edge_length is set the maximal radius of the "star sphere"
// is at most square root of m_max_squared_edge_length
std::optional<FT> squared_star_sphere_radius_plus_margin = m_max_squared_edge_length;
// Insert points until we find a point which is outside "star sphere"
for (auto nn_it = ins_range.begin(); nn_it != ins_range.end(); ++nn_it) {
std::size_t neighbor_point_idx = nn_it->first;
// ith point = p, which is already inserted
if (neighbor_point_idx != i) {
// No need to lock the Mutex_for_perturb here since this will not be
// called while other threads are perturbing the positions
Point neighbor_pt;
FT neighbor_weight;
compute_perturbed_weighted_point(neighbor_point_idx, neighbor_pt, neighbor_weight);
GUDHI_CHECK(!m_max_squared_edge_length ||
squared_star_sphere_radius_plus_margin.value() <= m_max_squared_edge_length.value(),
std::invalid_argument("Tangential_complex::compute_star - set a bigger value with set_max_squared_edge_length."));
if (squared_star_sphere_radius_plus_margin &&
k_sqdist(center_pt, neighbor_pt) > squared_star_sphere_radius_plus_margin.value()) {
GUDHI_CHECK(triangulation.current_dimension() >= tangent_space_dim,
std::invalid_argument("Tangential_complex::compute_star - Dimension of the star is only " + \
std::to_string(triangulation.current_dimension())));
break;
}
Tr_point proj_pt = project_point_and_compute_weight(neighbor_pt, neighbor_weight, tsb, local_tr_traits);
#ifdef GUDHI_TC_VERY_VERBOSE
++num_attempts_to_insert_points;
#endif
Tr_vertex_handle vh = triangulation.insert_if_in_star(proj_pt, center_vertex);
// Tr_vertex_handle vh = triangulation.insert(proj_pt);
if (vh != Tr_vertex_handle() && vh->data() == (std::numeric_limits<std::size_t>::max)()) {
#ifdef GUDHI_TC_VERY_VERBOSE
++num_inserted_points;
#endif
if (verbose) std::cerr << "* Inserted point #" << neighbor_point_idx << "\n";
vh->data() = neighbor_point_idx;
// Let's recompute squared_star_sphere_radius_plus_margin
if (triangulation.current_dimension() >= tangent_space_dim) {
squared_star_sphere_radius_plus_margin = std::nullopt;
// Get the incident cells and look for the biggest circumsphere
std::vector<Tr_full_cell_handle> incident_cells;
triangulation.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
for (typename std::vector<Tr_full_cell_handle>::iterator cit = incident_cells.begin();
cit != incident_cells.end(); ++cit) {
Tr_full_cell_handle cell = *cit;
if (triangulation.is_infinite(cell)) {
squared_star_sphere_radius_plus_margin = std::nullopt;
break;
} else {
// Note that this uses the perturbed point since it uses
// the points of the local triangulation
Tr_point c =
power_center(boost::make_transform_iterator(cell->vertices_begin(),
vertex_handle_to_point<Tr_point, Tr_vertex_handle>),
boost::make_transform_iterator(cell->vertices_end(),
vertex_handle_to_point<Tr_point, Tr_vertex_handle>));
FT sq_power_sphere_diam = 4 * point_weight(c);
if (!squared_star_sphere_radius_plus_margin ||
sq_power_sphere_diam > squared_star_sphere_radius_plus_margin.value()) {
squared_star_sphere_radius_plus_margin = sq_power_sphere_diam;
}
}
}
// Let's add the margin, now
// The value depends on whether we perturb weight or position
if (squared_star_sphere_radius_plus_margin) {
// "2*m_last_max_perturb" because both points can be perturbed
squared_star_sphere_radius_plus_margin =
CGAL::square(std::sqrt(squared_star_sphere_radius_plus_margin.value()) + 2 * m_last_max_perturb);
// Reduce the square radius to m_max_squared_edge_length if necessary
if (m_max_squared_edge_length && squared_star_sphere_radius_plus_margin.value() > m_max_squared_edge_length.value()) {
squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
}
// Save it in `m_squared_star_spheres_radii_incl_margin`
m_squared_star_spheres_radii_incl_margin[i] = squared_star_sphere_radius_plus_margin.value();
} else {
if (m_max_squared_edge_length) {
squared_star_sphere_radius_plus_margin = m_max_squared_edge_length.value();
m_squared_star_spheres_radii_incl_margin[i] = m_max_squared_edge_length.value();
} else {
m_squared_star_spheres_radii_incl_margin[i] = FT(-1);
}
}
}
}
}
}
return center_vertex;
}
void refresh_tangent_triangulation(std::size_t i, Points_ds const &updated_pts_ds, bool verbose = false) {
if (verbose) std::cerr << "** Refreshing tangent tri #" << i << " **\n";
if (m_squared_star_spheres_radii_incl_margin[i] == FT(-1)) return compute_tangent_triangulation(i, verbose);
Point center_point = compute_perturbed_point(i);
// Among updated point, what is the closer from our center point?
std::size_t closest_pt_index = updated_pts_ds.k_nearest_neighbors(center_point, 1, false).begin()->first;
typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
#if CGAL_VERSION_NR < 1050200000
typename K::Power_distance_d k_power_dist = m_k.power_distance_d_object();
#else
typename K::Compute_power_product_d k_power_dist = m_k.compute_power_product_d_object();
#endif
// Construct a weighted point equivalent to the star sphere
Weighted_point star_sphere = k_constr_wp(compute_perturbed_point(i), m_squared_star_spheres_radii_incl_margin[i]);
Weighted_point closest_updated_point = compute_perturbed_weighted_point(closest_pt_index);
// Is the "closest point" inside our star sphere?
if (k_power_dist(star_sphere, closest_updated_point) <= FT(0)) compute_tangent_triangulation(i, verbose);
}
void compute_tangent_triangulation(std::size_t i, bool verbose = false) {
if (verbose) std::cerr << "** Computing tangent tri #" << i << " **\n";
// std::cerr << "***********************************************\n";
// No need to lock the mutex here since this will not be called while
// other threads are perturbing the positions
const Point center_pt = compute_perturbed_point(i);
Tangent_space_basis &tsb = m_tangent_spaces[i];
// Estimate the tangent space
if (!m_are_tangent_spaces_computed[i]) {
#ifdef GUDHI_TC_EXPORT_NORMALS
tsb = compute_tangent_space(center_pt, i, true /*normalize*/, &m_orth_spaces[i]);
#else
tsb = compute_tangent_space(center_pt, i);
#endif
}
#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
Gudhi::Clock t;
#endif
int tangent_space_dim = tangent_basis_dim(i);
Triangulation &local_tr = m_triangulations[i].construct_triangulation(tangent_space_dim);
m_triangulations[i].center_vertex() = compute_star(i, center_pt, tsb, local_tr, verbose);
#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
t.end();
std::cerr << " - triangulation construction: " << t.num_seconds() << " s.\n";
t.reset();
#endif
#ifdef GUDHI_TC_VERY_VERBOSE
std::cerr << "Inserted " << num_inserted_points << " points / " << num_attempts_to_insert_points
<< " attempts to compute the star\n";
#endif
update_star(i);
#if defined(GUDHI_TC_PROFILING) && defined(GUDHI_TC_VERY_VERBOSE)
t.end();
std::cerr << " - update_star: " << t.num_seconds() << " s.\n";
#endif
}
// Updates m_stars[i] directly from m_triangulations[i]
void update_star(std::size_t i) {
Star &star = m_stars[i];
star.clear();
Triangulation &local_tr = m_triangulations[i].tr();
Tr_vertex_handle center_vertex = m_triangulations[i].center_vertex();
int cur_dim_plus_1 = local_tr.current_dimension() + 1;
std::vector<Tr_full_cell_handle> incident_cells;
local_tr.incident_full_cells(center_vertex, std::back_inserter(incident_cells));
typename std::vector<Tr_full_cell_handle>::const_iterator it_c = incident_cells.begin();
typename std::vector<Tr_full_cell_handle>::const_iterator it_c_end = incident_cells.end();
// For each cell
for (; it_c != it_c_end; ++it_c) {
// Will contain all indices except center_vertex
Incident_simplex incident_simplex;
for (int j = 0; j < cur_dim_plus_1; ++j) {
std::size_t index = (*it_c)->vertex(j)->data();
if (index != i) incident_simplex.insert(index);
}
GUDHI_CHECK(incident_simplex.size() == cur_dim_plus_1 - 1,
std::logic_error("update_star: wrong size of incident simplex"));
star.push_back(incident_simplex);
}
}
// Estimates tangent subspaces using PCA
Tangent_space_basis compute_tangent_space(const Point &p, const std::size_t i, bool normalize_basis = true,
Orthogonal_space_basis *p_orth_space_basis = NULL) {
unsigned int num_pts_for_pca =
(std::min)(static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
static_cast<unsigned int>(m_points.size()));
// Kernel functors
typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca, false);
const Points &points_for_pca = m_points_for_tse;
#else
KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca, false);
const Points &points_for_pca = m_points;
#endif
// One row = one point
Eigen::MatrixXd mat_points(num_pts_for_pca, m_ambient_dim);
auto nn_it = kns_range.begin();
for (unsigned int j = 0; j < num_pts_for_pca && nn_it != kns_range.end(); ++j, ++nn_it) {
for (int i = 0; i < m_ambient_dim; ++i) {
mat_points(j, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
}
}
Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
Eigen::MatrixXd cov = centered.adjoint() * centered;
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
Tangent_space_basis tsb(i); // p = compute_perturbed_point(i) here
// The eigenvectors are sorted in increasing order of their corresponding
// eigenvalues
for (int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
if (normalize_basis) {
Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim);
tsb.push_back(normalize_vector(v, m_k));
} else {
tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim));
}
}
if (p_orth_space_basis) {
p_orth_space_basis->set_origin(i);
for (int j = m_ambient_dim - m_intrinsic_dim - 1; j >= 0; --j) {
if (normalize_basis) {
Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim);
p_orth_space_basis->push_back(normalize_vector(v, m_k));
} else {
p_orth_space_basis->push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim));
}
}
}
m_are_tangent_spaces_computed[i] = true;
return tsb;
}
// Compute the space tangent to a simplex (p1, p2, ... pn)
// TODO(CJ): Improve this?
// Basically, it takes all the neighbor points to p1, p2... pn and runs PCA
// on it. Note that most points are duplicated.
Tangent_space_basis compute_tangent_space(const Simplex &s, bool normalize_basis = true) {
unsigned int num_pts_for_pca =
(std::min)(static_cast<unsigned int>(std::pow(GUDHI_TC_BASE_VALUE_FOR_PCA, m_intrinsic_dim)),
static_cast<unsigned int>(m_points.size()));
// Kernel functors
typename K::Construct_vector_d constr_vec = m_k.construct_vector_d_object();
typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
typename K::Squared_length_d sqlen = m_k.squared_length_d_object();
typename K::Scaled_vector_d scaled_vec = m_k.scaled_vector_d_object();
typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
typename K::Difference_of_vectors_d diff_vec = m_k.difference_of_vectors_d_object();
// One row = one point
Eigen::MatrixXd mat_points(s.size() * num_pts_for_pca, m_ambient_dim);
unsigned int current_row = 0;
for (Simplex::const_iterator it_index = s.begin(); it_index != s.end(); ++it_index) {
const Point &p = m_points[*it_index];
#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
KNS_range kns_range = m_points_ds_for_tse.k_nearest_neighbors(p, num_pts_for_pca, false);
const Points &points_for_pca = m_points_for_tse;
#else
KNS_range kns_range = m_points_ds.k_nearest_neighbors(p, num_pts_for_pca, false);
const Points &points_for_pca = m_points;
#endif
auto nn_it = kns_range.begin();
for (; current_row < num_pts_for_pca && nn_it != kns_range.end(); ++current_row, ++nn_it) {
for (int i = 0; i < m_ambient_dim; ++i) {
mat_points(current_row, i) = CGAL::to_double(coord(points_for_pca[nn_it->first], i));
}
}
}
Eigen::MatrixXd centered = mat_points.rowwise() - mat_points.colwise().mean();
Eigen::MatrixXd cov = centered.adjoint() * centered;
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
Tangent_space_basis tsb;
// The eigenvectors are sorted in increasing order of their corresponding
// eigenvalues
for (int j = m_ambient_dim - 1; j >= m_ambient_dim - m_intrinsic_dim; --j) {
if (normalize_basis) {
Vector v = constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim);
tsb.push_back(normalize_vector(v, m_k));
} else {
tsb.push_back(constr_vec(m_ambient_dim, eig.eigenvectors().col(j).data(),
eig.eigenvectors().col(j).data() + m_ambient_dim));
}
}
return tsb;
}
// Returns the dimension of the ith local triangulation
int tangent_basis_dim(std::size_t i) const { return m_tangent_spaces[i].dimension(); }
Point compute_perturbed_point(std::size_t pt_idx) const {
#ifdef GUDHI_TC_PERTURB_POSITION
return m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
#else
return m_points[pt_idx];
#endif
}
void compute_perturbed_weighted_point(std::size_t pt_idx, Point &p, FT &w) const {
#ifdef GUDHI_TC_PERTURB_POSITION
p = m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]);
#else
p = m_points[pt_idx];
#endif
w = m_weights[pt_idx];
}
Weighted_point compute_perturbed_weighted_point(std::size_t pt_idx) const {
typename K::Construct_weighted_point_d k_constr_wp = m_k.construct_weighted_point_d_object();
Weighted_point wp = k_constr_wp(
#ifdef GUDHI_TC_PERTURB_POSITION
m_k.translated_point_d_object()(m_points[pt_idx], m_translations[pt_idx]),
#else
m_points[pt_idx],
#endif
m_weights[pt_idx]);
return wp;
}
Point unproject_point(const Tr_point &p, const Tangent_space_basis &tsb, const Tr_traits &tr_traits) const {
typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
typename Tr_traits::Compute_coordinate_d coord = tr_traits.compute_coordinate_d_object();
Point global_point = compute_perturbed_point(tsb.origin());
for (int i = 0; i < m_intrinsic_dim; ++i) global_point = k_transl(global_point, k_scaled_vec(tsb[i], coord(p, i)));
return global_point;
}
// Project the point in the tangent space
// Resulting point coords are expressed in tsb's space
Tr_bare_point project_point(const Point &p, const Tangent_space_basis &tsb, const Tr_traits &tr_traits) const {
typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
Vector v = diff_points(p, compute_perturbed_point(tsb.origin()));
std::vector<FT> coords;
// Ambiant-space coords of the projected point
coords.reserve(tsb.dimension());
for (std::size_t i = 0; i < m_intrinsic_dim; ++i) {
// Local coords are given by the scalar product with the vectors of tsb
FT coord = scalar_pdct(v, tsb[i]);
coords.push_back(coord);
}
return tr_traits.construct_point_d_object()(static_cast<int>(coords.size()), coords.begin(), coords.end());
}
// Project the point in the tangent space
// The weight will be the squared distance between p and the projection of p
// Resulting point coords are expressed in tsb's space
Tr_point project_point_and_compute_weight(const Weighted_point &wp, const Tangent_space_basis &tsb,
const Tr_traits &tr_traits) const {
typename K::Point_drop_weight_d k_drop_w = m_k.point_drop_weight_d_object();
typename K::Compute_weight_d k_point_weight = m_k.compute_weight_d_object();
return project_point_and_compute_weight(k_drop_w(wp), k_point_weight(wp), tsb, tr_traits);
}
// Same as above, with slightly different parameters
Tr_point project_point_and_compute_weight(const Point &p, const FT w, const Tangent_space_basis &tsb,
const Tr_traits &tr_traits) const {
const int point_dim = m_k.point_dimension_d_object()(p);
typename K::Construct_point_d constr_pt = m_k.construct_point_d_object();
typename K::Scalar_product_d scalar_pdct = m_k.scalar_product_d_object();
typename K::Difference_of_points_d diff_points = m_k.difference_of_points_d_object();
typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
typename K::Construct_cartesian_const_iterator_d ccci = m_k.construct_cartesian_const_iterator_d_object();
Point origin = compute_perturbed_point(tsb.origin());
Vector v = diff_points(p, origin);
// Same dimension? Then the weight is 0
bool same_dim = (point_dim == tsb.dimension());
std::vector<FT> coords;
// Ambiant-space coords of the projected point
std::vector<FT> p_proj(ccci(origin), ccci(origin, 0));
coords.reserve(tsb.dimension());
for (int i = 0; i < tsb.dimension(); ++i) {
// Local coords are given by the scalar product with the vectors of tsb
FT c = scalar_pdct(v, tsb[i]);
coords.push_back(c);
// p_proj += c * tsb[i]
if (!same_dim) {
for (int j = 0; j < point_dim; ++j) p_proj[j] += c * coord(tsb[i], j);
}
}
// Same dimension? Then the weight is 0
FT sq_dist_to_proj_pt = 0;
if (!same_dim) {
Point projected_pt = constr_pt(point_dim, p_proj.begin(), p_proj.end());
sq_dist_to_proj_pt = m_k.squared_distance_d_object()(p, projected_pt);
}
return tr_traits.construct_weighted_point_d_object()(
tr_traits.construct_point_d_object()(static_cast<int>(coords.size()), coords.begin(), coords.end()),
w - sq_dist_to_proj_pt);
}
// Project all the points in the tangent space
template <typename Indexed_point_range>
std::vector<Tr_point> project_points_and_compute_weights(const Indexed_point_range &point_indices,
const Tangent_space_basis &tsb,
const Tr_traits &tr_traits) const {
std::vector<Tr_point> ret;
for (typename Indexed_point_range::const_iterator it = point_indices.begin(), it_end = point_indices.end();
it != it_end; ++it) {
ret.push_back(project_point_and_compute_weight(compute_perturbed_weighted_point(*it), tsb, tr_traits));
}
return ret;
}
// A simplex here is a local tri's full cell handle
bool is_simplex_consistent(Tr_full_cell_handle fch, int cur_dim) const {
Simplex c;
for (int i = 0; i < cur_dim + 1; ++i) {
std::size_t data = fch->vertex(i)->data();
c.insert(data);
}
return is_simplex_consistent(c);
}
// A simplex here is a list of point indices
// TODO(CJ): improve it like the other "is_simplex_consistent" below
bool is_simplex_consistent(Simplex const &simplex) const {
// Check if the simplex is in the stars of all its vertices
Simplex::const_iterator it_point_idx = simplex.begin();
// For each point p of the simplex, we parse the incidents cells of p
// and we check if "simplex" is among them
for (; it_point_idx != simplex.end(); ++it_point_idx) {
std::size_t point_idx = *it_point_idx;
// Don't check infinite simplices
if (point_idx == (std::numeric_limits<std::size_t>::max)()) continue;
Star const &star = m_stars[point_idx];
// What we're looking for is "simplex" \ point_idx
Incident_simplex is_to_find = simplex;
is_to_find.erase(point_idx);
// For each cell
if (std::find(star.begin(), star.end(), is_to_find) == star.end()) return false;
}
return true;
}
// A simplex here is a list of point indices
// "s" contains all the points of the simplex except "center_point"
// This function returns the points whose star doesn't contain the simplex
// N.B.: the function assumes that the simplex is contained in
// star(center_point)
template <typename OutputIterator> // value_type = std::size_t
bool is_simplex_consistent(std::size_t center_point,
Incident_simplex const &s, // without "center_point"
OutputIterator points_whose_star_does_not_contain_s,
bool check_also_in_non_maximal_faces = false) const {
Simplex full_simplex = s;
full_simplex.insert(center_point);
// Check if the simplex is in the stars of all its vertices
Incident_simplex::const_iterator it_point_idx = s.begin();
// For each point p of the simplex, we parse the incidents cells of p
// and we check if "simplex" is among them
for (; it_point_idx != s.end(); ++it_point_idx) {
std::size_t point_idx = *it_point_idx;
// Don't check infinite simplices
if (point_idx == (std::numeric_limits<std::size_t>::max)()) continue;
Star const &star = m_stars[point_idx];
// What we're looking for is full_simplex \ point_idx
Incident_simplex is_to_find = full_simplex;
is_to_find.erase(point_idx);
if (check_also_in_non_maximal_faces) {
// For each simplex "is" of the star, check if ic_to_simplex is
// included in "is"
bool found = false;
for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
if (std::includes(is->begin(), is->end(), is_to_find.begin(), is_to_find.end())) found = true;
}
if (!found) *points_whose_star_does_not_contain_s++ = point_idx;
} else {
// Does the star contain is_to_find?
if (std::find(star.begin(), star.end(), is_to_find) == star.end())
*points_whose_star_does_not_contain_s++ = point_idx;
}
}
return true;
}
// A simplex here is a list of point indices
// It looks for s in star(p).
// "s" contains all the points of the simplex except p.
bool is_simplex_in_star(std::size_t p, Incident_simplex const &s, bool check_also_in_non_maximal_faces = true) const {
Star const &star = m_stars[p];
if (check_also_in_non_maximal_faces) {
// For each simplex "is" of the star, check if ic_to_simplex is
// included in "is"
bool found = false;
for (Star::const_iterator is = star.begin(), is_end = star.end(); !found && is != is_end; ++is) {
if (std::includes(is->begin(), is->end(), s.begin(), s.end())) found = true;
}
return found;
} else {
return !(std::find(star.begin(), star.end(), s) == star.end());
}
}
void perturb(std::size_t point_idx, double max_perturb) {
const Tr_traits &local_tr_traits = m_triangulations[point_idx].tr().geom_traits();
typename Tr_traits::Compute_coordinate_d coord = local_tr_traits.compute_coordinate_d_object();
typename K::Translated_point_d k_transl = m_k.translated_point_d_object();
typename K::Construct_vector_d k_constr_vec = m_k.construct_vector_d_object();
typename K::Scaled_vector_d k_scaled_vec = m_k.scaled_vector_d_object();
CGAL::Random_points_in_ball_d<Tr_bare_point> tr_point_in_ball_generator(
m_intrinsic_dim, CGAL::get_default_random().get_double(0., max_perturb));
Tr_point local_random_transl =
local_tr_traits.construct_weighted_point_d_object()(*tr_point_in_ball_generator++, 0);
Translation_for_perturb global_transl = k_constr_vec(m_ambient_dim);
const Tangent_space_basis &tsb = m_tangent_spaces[point_idx];
for (int i = 0; i < m_intrinsic_dim; ++i) {
global_transl = k_transl(global_transl, k_scaled_vec(tsb[i], coord(local_random_transl, i)));
}
// Parallel
#if defined(GUDHI_USE_TBB)
m_p_perturb_mutexes[point_idx].lock();
m_translations[point_idx] = global_transl;
m_p_perturb_mutexes[point_idx].unlock();
// Sequential
#else
m_translations[point_idx] = global_transl;
#endif
}
// Return true if inconsistencies were found
template <typename OutputIt>
bool try_to_solve_inconsistencies_in_a_local_triangulation(
std::size_t tr_index, double max_perturb, OutputIt perturbed_pts_indices = CGAL::Emptyset_iterator()) {
bool is_inconsistent = false;
Star const &star = m_stars[tr_index];
// For each incident simplex
Star::const_iterator it_inc_simplex = star.begin();
Star::const_iterator it_inc_simplex_end = star.end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
const Incident_simplex &incident_simplex = *it_inc_simplex;
// Don't check infinite cells
if (is_infinite(incident_simplex)) continue;
Simplex c = incident_simplex;
c.insert(tr_index); // Add the missing index
// Perturb the center point
if (!is_simplex_consistent(c)) {
is_inconsistent = true;
std::size_t idx = tr_index;
perturb(tr_index, max_perturb);
*perturbed_pts_indices++ = idx;
// We will try the other cells next time
break;
}
}
return is_inconsistent;
}
// 1st line: number of points
// Then one point per line
std::ostream &export_point_set(std::ostream &os, bool use_perturbed_points = false,
const char *coord_separator = " ") const {
if (use_perturbed_points) {
std::vector<Point> perturbed_points;
perturbed_points.reserve(m_points.size());
for (std::size_t i = 0; i < m_points.size(); ++i) perturbed_points.push_back(compute_perturbed_point(i));
return export_point_set(m_k, perturbed_points, os, coord_separator);
} else {
return export_point_set(m_k, m_points, os, coord_separator);
}
}
template <typename ProjectionFunctor = CGAL::Identity<Point> >
std::ostream &export_vertices_to_off(std::ostream &os, std::size_t &num_vertices, bool use_perturbed_points = false,
ProjectionFunctor const &point_projection = ProjectionFunctor()) const {
if (m_points.empty()) {
num_vertices = 0;
return os;
}
// If m_intrinsic_dim = 1, we output each point two times
// to be able to export each segment as a flat triangle with 3 different
// indices (otherwise, Meshlab detects degenerated simplices)
const int N = (m_intrinsic_dim == 1 ? 2 : 1);
// Kernel functors
typename K::Compute_coordinate_d coord = m_k.compute_coordinate_d_object();
#ifdef GUDHI_TC_EXPORT_ALL_COORDS_IN_OFF
int num_coords = m_ambient_dim;
#else
int num_coords = (std::min)(m_ambient_dim, 3);
#endif
#ifdef GUDHI_TC_EXPORT_NORMALS
OS_container::const_iterator it_os = m_orth_spaces.begin();
#endif
typename Points::const_iterator it_p = m_points.begin();
typename Points::const_iterator it_p_end = m_points.end();
// For each point p
for (std::size_t i = 0; it_p != it_p_end; ++it_p, ++i) {
Point p = point_projection(use_perturbed_points ? compute_perturbed_point(i) : *it_p);
for (int ii = 0; ii < N; ++ii) {
int j = 0;
for (; j < num_coords; ++j) os << CGAL::to_double(coord(p, j)) << " ";
if (j == 2) os << "0";
#ifdef GUDHI_TC_EXPORT_NORMALS
for (j = 0; j < num_coords; ++j) os << " " << CGAL::to_double(coord(*it_os->begin(), j));
#endif
os << "\n";
}
#ifdef GUDHI_TC_EXPORT_NORMALS
++it_os;
#endif
}
num_vertices = N * m_points.size();
return os;
}
std::ostream &export_simplices_to_off(std::ostream &os, std::size_t &num_OFF_simplices,
bool color_inconsistencies = false,
Simplex_set const *p_simpl_to_color_in_red = NULL,
Simplex_set const *p_simpl_to_color_in_green = NULL,
Simplex_set const *p_simpl_to_color_in_blue = NULL) const {
// If m_intrinsic_dim = 1, each point is output two times
// (see export_vertices_to_off)
num_OFF_simplices = 0;
std::size_t num_maximal_simplices = 0;
std::size_t num_inconsistent_maximal_simplices = 0;
std::size_t num_inconsistent_stars = 0;
typename Tr_container::const_iterator it_tr = m_triangulations.begin();
typename Tr_container::const_iterator it_tr_end = m_triangulations.end();
// For each triangulation
for (std::size_t idx = 0; it_tr != it_tr_end; ++it_tr, ++idx) {
bool is_star_inconsistent = false;
Triangulation const &tr = it_tr->tr();
if (tr.current_dimension() < m_intrinsic_dim) continue;
// Color for this star
std::stringstream color;
// color << rand()%256 << " " << 100+rand()%156 << " " << 100+rand()%156;
color << 128 << " " << 128 << " " << 128;
// Gather the triangles here, with an int telling its color
typedef std::vector<std::pair<Simplex, int> > Star_using_triangles;
Star_using_triangles star_using_triangles;
// For each cell of the star
Star::const_iterator it_inc_simplex = m_stars[idx].begin();
Star::const_iterator it_inc_simplex_end = m_stars[idx].end();
for (; it_inc_simplex != it_inc_simplex_end; ++it_inc_simplex) {
Simplex c = *it_inc_simplex;
c.insert(idx);
std::size_t num_vertices = c.size();
++num_maximal_simplices;
int color_simplex = -1; // -1=no color, 0=yellow, 1=red, 2=green, 3=blue
if (color_inconsistencies && !is_simplex_consistent(c)) {
++num_inconsistent_maximal_simplices;
color_simplex = 0;
is_star_inconsistent = true;
} else {
if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(),
c) != p_simpl_to_color_in_red->end()) {
color_simplex = 1;
} else if (p_simpl_to_color_in_green &&
std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
p_simpl_to_color_in_green->end()) {
color_simplex = 2;
} else if (p_simpl_to_color_in_blue &&
std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
p_simpl_to_color_in_blue->end()) {
color_simplex = 3;
}
}
// If m_intrinsic_dim = 1, each point is output two times,
// so we need to multiply each index by 2
// And if only 2 vertices, add a third one (each vertex is duplicated in
// the file when m_intrinsic dim = 2)
if (m_intrinsic_dim == 1) {
Simplex tmp_c;
Simplex::iterator it = c.begin();
for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
c = tmp_c;
}
if (num_vertices <= 3) {
star_using_triangles.push_back(std::make_pair(c, color_simplex));
} else {
// num_vertices >= 4: decompose the simplex in triangles
std::vector<bool> booleans(num_vertices, false);
std::fill(booleans.begin() + num_vertices - 3, booleans.end(), true);
do {
Simplex triangle;
Simplex::iterator it = c.begin();
for (int i = 0; it != c.end(); ++i, ++it) {
if (booleans[i]) triangle.insert(*it);
}
star_using_triangles.push_back(std::make_pair(triangle, color_simplex));
} while (std::next_permutation(booleans.begin(), booleans.end()));
}
}
// For each cell
Star_using_triangles::const_iterator it_simplex = star_using_triangles.begin();
Star_using_triangles::const_iterator it_simplex_end = star_using_triangles.end();
for (; it_simplex != it_simplex_end; ++it_simplex) {
const Simplex &c = it_simplex->first;
// Don't export infinite cells
if (is_infinite(c)) continue;
int color_simplex = it_simplex->second;
std::stringstream sstr_c;
Simplex::const_iterator it_point_idx = c.begin();
for (; it_point_idx != c.end(); ++it_point_idx) {
sstr_c << *it_point_idx << " ";
}
os << 3 << " " << sstr_c.str();
if (color_inconsistencies || p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
switch (color_simplex) {
case 0:
os << " 255 255 0";
break;
case 1:
os << " 255 0 0";
break;
case 2:
os << " 0 255 0";
break;
case 3:
os << " 0 0 255";
break;
default:
os << " " << color.str();
break;
}
}
++num_OFF_simplices;
os << "\n";
}
if (is_star_inconsistent) ++num_inconsistent_stars;
}
#ifdef DEBUG_TRACES
std::cerr << "\n==========================================================\n"
<< "Export from list of stars to OFF:\n"
<< " * Number of vertices: " << m_points.size() << "\n"
<< " * Total number of maximal simplices: " << num_maximal_simplices << "\n";
if (color_inconsistencies) {
std::cerr << " * Number of inconsistent stars: " << num_inconsistent_stars << " ("
<< (m_points.size() > 0 ? 100. * num_inconsistent_stars / m_points.size() : 0.) << "%)\n"
<< " * Number of inconsistent maximal simplices: " << num_inconsistent_maximal_simplices << " ("
<< (num_maximal_simplices > 0 ? 100. * num_inconsistent_maximal_simplices / num_maximal_simplices : 0.)
<< "%)\n";
}
std::cerr << "==========================================================\n";
#endif
return os;
}
public:
std::ostream &export_simplices_to_off(const Simplicial_complex &complex, std::ostream &os,
std::size_t &num_OFF_simplices,
Simplex_set const *p_simpl_to_color_in_red = NULL,
Simplex_set const *p_simpl_to_color_in_green = NULL,
Simplex_set const *p_simpl_to_color_in_blue = NULL) const {
typedef Simplicial_complex::Simplex Simplex;
typedef Simplicial_complex::Simplex_set Simplex_set;
// If m_intrinsic_dim = 1, each point is output two times
// (see export_vertices_to_off)
num_OFF_simplices = 0;
std::size_t num_maximal_simplices = 0;
typename Simplex_set::const_iterator it_s = complex.simplex_range().begin();
typename Simplex_set::const_iterator it_s_end = complex.simplex_range().end();
// For each simplex
for (; it_s != it_s_end; ++it_s) {
Simplex c = *it_s;
++num_maximal_simplices;
int color_simplex = -1; // -1=no color, 0=yellow, 1=red, 2=green, 3=blue
if (p_simpl_to_color_in_red && std::find(p_simpl_to_color_in_red->begin(), p_simpl_to_color_in_red->end(), c) !=
p_simpl_to_color_in_red->end()) {
color_simplex = 1;
} else if (p_simpl_to_color_in_green &&
std::find(p_simpl_to_color_in_green->begin(), p_simpl_to_color_in_green->end(), c) !=
p_simpl_to_color_in_green->end()) {
color_simplex = 2;
} else if (p_simpl_to_color_in_blue &&
std::find(p_simpl_to_color_in_blue->begin(), p_simpl_to_color_in_blue->end(), c) !=
p_simpl_to_color_in_blue->end()) {
color_simplex = 3;
}
// Gather the triangles here
typedef std::vector<Simplex> Triangles;
Triangles triangles;
int num_vertices = static_cast<int>(c.size());
// Do not export smaller dimension simplices
if (num_vertices < m_intrinsic_dim + 1) continue;
// If m_intrinsic_dim = 1, each point is output two times,
// so we need to multiply each index by 2
// And if only 2 vertices, add a third one (each vertex is duplicated in
// the file when m_intrinsic dim = 2)
if (m_intrinsic_dim == 1) {
Simplex tmp_c;
Simplex::iterator it = c.begin();
for (; it != c.end(); ++it) tmp_c.insert(*it * 2);
if (num_vertices == 2) tmp_c.insert(*tmp_c.rbegin() + 1);
c = tmp_c;
}
if (num_vertices <= 3) {
triangles.push_back(c);
} else {
// num_vertices >= 4: decompose the simplex in triangles
std::vector<bool> booleans(num_vertices, false);
std::fill(booleans.begin() + num_vertices - 3, booleans.end(), true);
do {
Simplex triangle;
Simplex::iterator it = c.begin();
for (int i = 0; it != c.end(); ++i, ++it) {
if (booleans[i]) triangle.insert(*it);
}
triangles.push_back(triangle);
} while (std::next_permutation(booleans.begin(), booleans.end()));
}
// For each cell
Triangles::const_iterator it_tri = triangles.begin();
Triangles::const_iterator it_tri_end = triangles.end();
for (; it_tri != it_tri_end; ++it_tri) {
// Don't export infinite cells
if (is_infinite(*it_tri)) continue;
os << 3 << " ";
Simplex::const_iterator it_point_idx = it_tri->begin();
for (; it_point_idx != it_tri->end(); ++it_point_idx) {
os << *it_point_idx << " ";
}
if (p_simpl_to_color_in_red || p_simpl_to_color_in_green || p_simpl_to_color_in_blue) {
switch (color_simplex) {
case 0:
os << " 255 255 0";
break;
case 1:
os << " 255 0 0";
break;
case 2:
os << " 0 255 0";
break;
case 3:
os << " 0 0 255";
break;
default:
os << " 128 128 128";
break;
}
}
++num_OFF_simplices;
os << "\n";
}
}
#ifdef DEBUG_TRACES
std::cerr << "\n==========================================================\n"
<< "Export from complex to OFF:\n"
<< " * Number of vertices: " << m_points.size() << "\n"
<< " * Total number of maximal simplices: " << num_maximal_simplices << "\n"
<< "==========================================================\n";
#endif
return os;
}
void set_max_squared_edge_length(FT max_squared_edge_length) { m_max_squared_edge_length = max_squared_edge_length; }
private:
const K m_k;
const int m_intrinsic_dim;
const int m_ambient_dim;
Points m_points;
Weights m_weights;
#ifdef GUDHI_TC_PERTURB_POSITION
Translations_for_perturb m_translations;
#if defined(GUDHI_USE_TBB)
Mutex_for_perturb *m_p_perturb_mutexes;
#endif
#endif
Points_ds m_points_ds;
double m_last_max_perturb;
std::vector<bool> m_are_tangent_spaces_computed;
TS_container m_tangent_spaces;
#ifdef GUDHI_TC_EXPORT_NORMALS
OS_container m_orth_spaces;
#endif
Tr_container m_triangulations; // Contains the triangulations
// and their center vertex
Stars_container m_stars;
std::vector<FT> m_squared_star_spheres_radii_incl_margin;
std::optional<FT> m_max_squared_edge_length;
#ifdef GUDHI_TC_USE_ANOTHER_POINT_SET_FOR_TANGENT_SPACE_ESTIM
Points m_points_for_tse;
Points_ds m_points_ds_for_tse;
#endif
}; // /class Tangential_complex
} // end namespace tangential_complex
} // end namespace Gudhi
#endif // TANGENTIAL_COMPLEX_H_
Gudhi::spatial_searching::Kd_tree_search
Spatial tree data structure to perform (approximate) nearest and furthest neighbor search.
Definition Kd_tree_search.h:70
Gudhi::spatial_searching::Kd_tree_search< K, Points >::KNS_range
K_neighbor_search KNS_range
Definition Kd_tree_search.h:104
Gudhi::spatial_searching::Kd_tree_search< K, Points >::INS_range
Incremental_neighbor_search INS_range
Definition Kd_tree_search.h:112
Gudhi::tangential_complex::Tangential_complex::Tangential_complex
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:241
Gudhi::tangential_complex::Tangential_complex::fix_inconsistencies_using_perturbation
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:397
Gudhi::tangential_complex::Tangential_complex::compute_tangential_complex
void compute_tangential_complex()
Computes the tangential complex.
Definition Tangential_complex.h:331
Gudhi::tangential_complex::Tangential_complex< Kernel, CGAL::Dynamic_dimension_tag, CGAL::Parallel_tag >::intrinsic_dimension
int intrinsic_dimension() const
Definition Tangential_complex.h:280
Gudhi::tangential_complex::Tangential_complex::get_perturbed_point
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:299
Gudhi::tangential_complex::Tangential_complex::set_max_squared_edge_length
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:1983
Gudhi::tangential_complex::Tangential_complex::get_point
Point get_point(std::size_t vertex) const
Returns the point corresponding to the vertex given as parameter.
Definition Tangential_complex.h:292
Gudhi::tangential_complex::Tangential_complex::number_of_inconsistent_simplices
Num_inconsistencies number_of_inconsistent_simplices(bool verbose=false) const
Definition Tangential_complex.h:559
Gudhi::tangential_complex::Tangential_complex::ambient_dimension
int ambient_dimension() const
Returns the ambient dimension.
Definition Tangential_complex.h:283
Gudhi::tangential_complex::Tangential_complex::number_of_vertices
std::size_t number_of_vertices() const
Returns the number of vertices.
Definition Tangential_complex.h:303
Gudhi::tangential_complex::Tangential_complex::create_complex
int create_complex(Simplex_tree_ &tree, bool export_inconsistent_simplices=true) const
Exports the complex into a Simplex_tree.
Definition Tangential_complex.h:618
Gudhi::tangential_complex::Tangential_complex::~Tangential_complex
~Tangential_complex()
Destructor.
Definition Tangential_complex.h:273
std::get
constexpr auto & get(Gudhi::persistence_matrix::Persistence_interval< Dimension, Event_value > &i) noexcept
Partial specialization of get for Gudhi::persistence_matrix::Persistence_interval.
Definition persistence_interval.h:199
Gudhi
Gudhi namespace.
Definition SimplicialComplexForAlpha.h:14
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info
Type returned by Tangential_complex::fix_inconsistencies_using_perturbation.
Definition Tangential_complex.h:379
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info::final_num_inconsistent_stars
std::size_t final_num_inconsistent_stars
final number of inconsistent stars
Definition Tangential_complex.h:389
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info::success
bool success
true if all inconsistencies could be removed, false if the time limit has been reached before
Definition Tangential_complex.h:381
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info::num_steps
unsigned int num_steps
number of steps performed
Definition Tangential_complex.h:383
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info::best_num_inconsistent_stars
std::size_t best_num_inconsistent_stars
best number of inconsistent stars during the process
Definition Tangential_complex.h:387
Gudhi::tangential_complex::Tangential_complex::Fix_inconsistencies_info::initial_num_inconsistent_stars
std::size_t initial_num_inconsistent_stars
initial number of inconsistent stars
Definition Tangential_complex.h:385
Gudhi::tangential_complex::Tangential_complex::Num_inconsistencies
Type returned by Tangential_complex::number_of_inconsistent_simplices.
Definition Tangential_complex.h:547
Gudhi::tangential_complex::Tangential_complex::Num_inconsistencies::num_inconsistent_simplices
std::size_t num_inconsistent_simplices
Number of inconsistent simplices.
Definition Tangential_complex.h:551
Gudhi::tangential_complex::Tangential_complex::Num_inconsistencies::num_inconsistent_stars
std::size_t num_inconsistent_stars
Number of stars containing at least one inconsistent simplex.
Definition Tangential_complex.h:553
Gudhi::tangential_complex::Tangential_complex::Num_inconsistencies::num_simplices
std::size_t num_simplices
Total number of simplices in stars (including duplicates that appear in several stars).
Definition Tangential_complex.h:549