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Alpha_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): Vincent Rouvreau
*
* Copyright (C) 2015 Inria
*
* Modification(s):
* - 2019/08 Vincent Rouvreau: Fix issue #10 for CGAL and Eigen3
* - 2024/10 Vincent Rouvreau: Add square root filtration values interface
* - YYYY/MM Author: Description of the modification
*/
#ifndef ALPHA_COMPLEX_H_
#define ALPHA_COMPLEX_H_
#include <gudhi/Alpha_complex/Alpha_kernel_d.h>
#include <gudhi/Debug_utils.h>
// to construct Alpha_complex from a OFF file of points
#include <gudhi/Points_off_io.h>
#include <CGAL/Delaunay_triangulation.h>
#include <CGAL/Regular_triangulation.h> // aka. Weighted Delaunay triangulation
#include <CGAL/Epeck_d.h> // For EXACT or SAFE version
#include <CGAL/Epick_d.h> // For FAST version
#include <CGAL/Spatial_sort_traits_adapter_d.h>
#include <CGAL/property_map.h> // for CGAL::Identity_property_map
#include <CGAL/version.h> // for CGAL_VERSION_NR
#include <CGAL/NT_converter.h>
#include <Eigen/src/Core/util/Macros.h> // for EIGEN_VERSION_AT_LEAST
#include <boost/range/size.hpp>
#include <boost/range/combine.hpp>
#include <boost/range/adaptor/transformed.hpp>
#include <iostream>
#include <vector>
#include <string>
#include <limits> // NaN
#include <map>
#include <utility> // std::pair
#include <stdexcept>
#include <numeric> // for std::iota
#include <algorithm> // for std::sort
#include <type_traits> // for std::is_same_v
#include <cmath> // isnan, fmax
#include <memory> // for std::unique_ptr
#include <cstddef> // for std::size_t
// Make compilation fail - required for external projects - https://github.com/GUDHI/gudhi-devel/issues/10
#if CGAL_VERSION_NR < 1041101000
# error Alpha_complex is only available for CGAL >= 4.11
#endif
#if !EIGEN_VERSION_AT_LEAST(3,1,0)
# error Alpha_complex is only available for Eigen3 >= 3.1.0 installed with CGAL
#endif
namespace Gudhi {
namespace alpha_complex {
template<typename D> struct Is_Epeck_D { static const bool value = false; };
template<typename D> struct Is_Epeck_D<CGAL::Epeck_d<D>> { static const bool value = true; };
template<class Kernel = CGAL::Epeck_d<CGAL::Dynamic_dimension_tag>, bool Weighted = false>
class Alpha_complex {
private:
// Vertex_handle internal type (required by triangulation_ and vertices_).
using Internal_vertex_handle = std::ptrdiff_t;
public:
using Geom_traits = std::conditional_t<Weighted, CGAL::Regular_triangulation_traits_adapter<Kernel>, Kernel>;
// CGAL::Triangulation_ds_full_cell<void, CGAL::TDS_full_cell_mirror_storage_policy> has been enhanced for CGAL >= 6.0
// But faster only with static dimensions
using Triangulation_full_cell = std::conditional_t<std::is_same_v<typename Kernel::Dimension, CGAL::Dynamic_dimension_tag>,
CGAL::Triangulation_ds_full_cell<>,
CGAL::Triangulation_ds_full_cell<void, CGAL::TDS_full_cell_mirror_storage_policy>>;
// Add an int in TDS to save point index in the structure
using TDS = CGAL::Triangulation_data_structure<typename Geom_traits::Dimension,
CGAL::Triangulation_vertex<Geom_traits, Internal_vertex_handle>,
Triangulation_full_cell >;
using Triangulation = std::conditional_t<Weighted, CGAL::Regular_triangulation<Kernel, TDS>,
CGAL::Delaunay_triangulation<Kernel, TDS>>;
using A_kernel_d = Alpha_kernel_d<Kernel, Weighted>;
// Numeric type of coordinates in the kernel
using FT = typename A_kernel_d::FT;
using Sphere = typename A_kernel_d::Sphere;
using Point_d = typename Geom_traits::Point_d;
private:
// Vertex_iterator type from CGAL.
using CGAL_vertex_iterator = typename Triangulation::Vertex_iterator;
// Structure to switch from simplex tree vertex handle to CGAL vertex iterator.
using Vector_vertex_iterator = std::vector< CGAL_vertex_iterator >;
private:
Vector_vertex_iterator vertex_handle_to_iterator_;
std::unique_ptr<Triangulation> triangulation_;
A_kernel_d kernel_;
std::vector<Internal_vertex_handle> vertices_;
std::vector<Sphere> cache_, old_cache_;
public:
Alpha_complex(const std::string& off_file_name) {
Gudhi::Points_off_reader<Point_d> off_reader(off_file_name);
if (!off_reader.is_valid()) {
std::cerr << "Alpha_complex - Unable to read file " << off_file_name << "\n";
exit(-1); // ----- >>
}
init_from_range(off_reader.get_point_cloud());
}
template<typename InputPointRange >
Alpha_complex(const InputPointRange& points) {
init_from_range(points);
}
template <typename InputPointRange, typename WeightRange>
Alpha_complex(const InputPointRange& points, WeightRange weights) {
static_assert(Weighted, "This constructor is not available for non-weighted versions of Alpha_complex");
// FIXME: this test is only valid if we have a forward range
GUDHI_CHECK(boost::size(weights) == boost::size(points),
std::invalid_argument("Points number in range different from weights range number"));
auto weighted_points = boost::range::combine(points, weights)
| boost::adaptors::transformed([](auto const&t){return Point_d(boost::get<0>(t), boost::get<1>(t));});
init_from_range(weighted_points);
}
// Forbid copy/move constructor/assignment operator
Alpha_complex(const Alpha_complex& other) = delete;
Alpha_complex& operator= (const Alpha_complex& other) = delete;
Alpha_complex (Alpha_complex&& other) = delete;
Alpha_complex& operator= (Alpha_complex&& other) = delete;
std::size_t num_vertices() const {
if (triangulation_ == nullptr)
return 0;
else
return triangulation_->number_of_vertices();
}
const Point_d& get_point(std::size_t vertex) const {
auto it = vertex_handle_to_iterator_.at(vertex);
if (it == nullptr) throw std::out_of_range("This vertex is missing, maybe hidden by a duplicate or another heavier point.");
return it->point();
}
private:
template<typename InputPointRange >
void init_from_range(const InputPointRange& points) {
#if CGAL_VERSION_NR < 1050000000
if (Is_Epeck_D<Kernel>::value)
std::cerr << "It is strongly advised to use a CGAL version >= 5.0 with Epeck_d Kernel for performance reasons."
<< std::endl;
#endif
#if CGAL_VERSION_NR < 1050101000
// Make compilation fail if weighted and CGAL < 5.1.0
static_assert(!Weighted, "Weighted Alpha_complex is only available for CGAL >= 5.1.0");
#endif
auto first = std::begin(points);
auto last = std::end(points);
if (first != last) {
// Delaunay triangulation init with point dimension.
triangulation_ = std::make_unique<Triangulation>(kernel_.get_dimension(*first));
std::vector<Point_d> point_cloud(first, last);
// Creates a vector {0, 1, ..., N-1}
std::vector<Internal_vertex_handle> indices(boost::counting_iterator<Internal_vertex_handle>(0),
boost::counting_iterator<Internal_vertex_handle>(point_cloud.size()));
using Point_property_map = boost::iterator_property_map<typename std::vector<Point_d>::iterator,
CGAL::Identity_property_map<Internal_vertex_handle>>;
using Search_traits_d = CGAL::Spatial_sort_traits_adapter_d<Geom_traits, Point_property_map>;
CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud)));
typename Triangulation::Full_cell_handle hint;
for (auto index : indices) {
typename Triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint);
if (pos != nullptr) {
// Save index value as data to retrieve it after insertion
pos->data() = index;
hint = pos->full_cell();
}
}
// --------------------------------------------------------------------------------------------
// structure to retrieve CGAL points from vertex handle - one vertex handle per point.
// Needs to be constructed before as vertex handles arrives in no particular order.
vertex_handle_to_iterator_.resize(point_cloud.size());
// List of sorted unique vertices in the triangulation. We take advantage of the existing loop to construct it
// Vertices list avoids quadratic complexity with the Simplex_tree. We should not fill it up with Toplex_map e.g.
vertices_.reserve(triangulation_->number_of_vertices());
// Loop on triangulation vertices list
for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
if (!triangulation_->is_infinite(*vit)) {
#ifdef DEBUG_TRACES
std::clog << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl;
#endif // DEBUG_TRACES
vertex_handle_to_iterator_[vit->data()] = vit;
vertices_.push_back(vit->data());
}
}
std::sort(vertices_.begin(), vertices_.end());
// --------------------------------------------------------------------------------------------
}
}
const Point_d& get_point_(std::size_t vertex) const {
return vertex_handle_to_iterator_[vertex]->point();
}
template<class SimplicialComplexForAlpha>
auto& get_cache(SimplicialComplexForAlpha& cplx, typename SimplicialComplexForAlpha::Simplex_handle s) {
auto k = cplx.key(s);
if(k==cplx.null_key()){
k = cache_.size();
cplx.assign_key(s, k);
// Using a transform_range is slower, currently.
thread_local std::vector<Point_d> v;
v.clear();
for (auto vertex : cplx.simplex_vertex_range(s))
v.push_back(get_point_(vertex));
cache_.emplace_back(kernel_.get_sphere(v.cbegin(), v.cend()));
}
return cache_[k];
}
template<class SimplicialComplexForAlpha>
auto radius(SimplicialComplexForAlpha& cplx, typename SimplicialComplexForAlpha::Simplex_handle s) {
auto k = cplx.key(s);
if(k!=cplx.null_key())
return kernel_.get_squared_radius(old_cache_[k]);
// Using a transform_range is slower, currently.
thread_local std::vector<Point_d> v;
v.clear();
for (auto vertex : cplx.simplex_vertex_range(s))
v.push_back(get_point_(vertex));
return kernel_.get_squared_radius(v.cbegin(), v.cend());
}
public:
template <bool Output_squared_values = true,
typename SimplicialComplexForAlpha,
typename Filtration_value = typename SimplicialComplexForAlpha::Filtration_value>
bool create_complex(SimplicialComplexForAlpha& complex,
Filtration_value max_alpha_square = std::numeric_limits<Filtration_value>::infinity(),
bool exact = false,
bool default_filtration_value = false) {
// Filtration_value must be capable to represent the special value "Not-A-Number"
static_assert(std::numeric_limits<Filtration_value>::has_quiet_NaN);
// Forbids weighted and output square root filtration values - cannot static_assert for python purpose
if constexpr(Weighted && !Output_squared_values)
throw std::invalid_argument("Weighted Alpha complex cannot output square root filtration values");
// To support more general types for Filtration_value
using std::isnan;
// From SimplicialComplexForAlpha type required to insert into a simplicial complex (with or without subfaces).
using Vertex_handle = typename SimplicialComplexForAlpha::Vertex_handle;
using Simplex_handle = typename SimplicialComplexForAlpha::Simplex_handle;
using Vector_vertex = std::vector<Vertex_handle>;
// For users to be able to define their own sqrt function on their desired Filtration_value type
using std::sqrt;
if (triangulation_ == nullptr) {
std::cerr << "Alpha_complex cannot create_complex from a NULL triangulation\n";
return false; // ----- >>
}
if (triangulation_->maximal_dimension() < 1) {
std::cerr << "Alpha_complex cannot create_complex from a zero-dimension triangulation\n";
return false; // ----- >>
}
if (complex.num_vertices() > 0) {
std::cerr << "Alpha_complex create_complex - complex is not empty\n";
return false; // ----- >>
}
// --------------------------------------------------------------------------------------------
// Simplex_tree construction from loop on triangulation finite full cells list
if (num_vertices() > 0) {
std::vector<Vertex_handle> one_vertex(1);
for (auto vertex : vertices_) {
#ifdef DEBUG_TRACES
std::clog << "SimplicialComplex insertion " << vertex << std::endl;
#endif // DEBUG_TRACES
one_vertex[0] = vertex;
complex.insert_simplex_and_subfaces(one_vertex, std::numeric_limits<Filtration_value>::quiet_NaN());
}
for (auto cit = triangulation_->finite_full_cells_begin();
cit != triangulation_->finite_full_cells_end();
++cit) {
Vector_vertex vertexVector;
#ifdef DEBUG_TRACES
std::clog << "SimplicialComplex insertion ";
#endif // DEBUG_TRACES
for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
if (*vit != nullptr) {
#ifdef DEBUG_TRACES
std::clog << " " << (*vit)->data();
#endif // DEBUG_TRACES
// Vector of vertex construction for simplex_tree structure
vertexVector.push_back((*vit)->data());
}
}
#ifdef DEBUG_TRACES
std::clog << std::endl;
#endif // DEBUG_TRACES
// Insert each simplex and its subfaces in the simplex tree - filtration is NaN
complex.insert_simplex_and_subfaces(vertexVector, std::numeric_limits<Filtration_value>::quiet_NaN());
}
}
// --------------------------------------------------------------------------------------------
if (!default_filtration_value) {
CGAL::NT_converter<FT, Filtration_value> cgal_converter;
// --------------------------------------------------------------------------------------------
// ### For i : d -> 0
for (int decr_dim = triangulation_->maximal_dimension(); decr_dim >= 0; decr_dim--) {
// ### Foreach Sigma of dim i
for (Simplex_handle f_simplex : complex.skeleton_simplex_range(decr_dim)) {
int f_simplex_dim = complex.dimension(f_simplex);
if (decr_dim == f_simplex_dim) {
// ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
if (isnan(complex.filtration(f_simplex))) {
Filtration_value alpha_complex_filtration = 0.0;
// No need to compute squared_radius on a non-weighted single point - alpha is 0.0
if (Weighted || f_simplex_dim > 0) {
auto const& sqrad = radius(complex, f_simplex);
#if CGAL_VERSION_NR >= 1050000000
if(exact) CGAL::exact(sqrad);
#endif
alpha_complex_filtration = cgal_converter(sqrad);
if constexpr (!Output_squared_values) {
alpha_complex_filtration = sqrt(alpha_complex_filtration);
}
}
complex.assign_filtration(f_simplex, alpha_complex_filtration);
#ifdef DEBUG_TRACES
std::clog << "filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl;
#endif // DEBUG_TRACES
}
// No need to propagate further, unweighted points all have value 0
if (decr_dim > !Weighted)
propagate_alpha_filtration(complex, f_simplex);
}
}
old_cache_ = std::move(cache_);
cache_.clear();
}
// --------------------------------------------------------------------------------------------
// --------------------------------------------------------------------------------------------
if (!exact)
// As Alpha value is an approximation, we have to make filtration non decreasing while increasing the dimension
// Only in not exact version, cf. https://github.com/GUDHI/gudhi-devel/issues/57
complex.make_filtration_non_decreasing();
// Remove all simplices that have a filtration value greater than max_alpha_square
if constexpr (!Output_squared_values) {
complex.prune_above_filtration(sqrt(max_alpha_square));
} else {
complex.prune_above_filtration(max_alpha_square);
}
// --------------------------------------------------------------------------------------------
}
return true;
}
private:
template <typename SimplicialComplexForAlpha, typename Simplex_handle>
void propagate_alpha_filtration(SimplicialComplexForAlpha& complex, Simplex_handle f_simplex) {
// From SimplicialComplexForAlpha type required to assign filtration values.
using Filtration_value = typename SimplicialComplexForAlpha::Filtration_value;
// To support more general types for Filtration_value
using std::isnan;
// ### Foreach Tau face of Sigma
for (auto face_opposite_vertex : complex.boundary_opposite_vertex_simplex_range(f_simplex)) {
auto f_boundary = face_opposite_vertex.first;
#ifdef DEBUG_TRACES
std::clog << " | --------------------------------------------------\n";
std::clog << " | Tau ";
for (auto vertex : complex.simplex_vertex_range(f_boundary)) {
std::clog << vertex << " ";
}
std::clog << "is a face of Sigma\n";
std::clog << " | isnan(complex.filtration(Tau)=" << isnan(complex.filtration(f_boundary)) << std::endl;
#endif // DEBUG_TRACES
// ### If filt(Tau) is not NaN
if (!isnan(complex.filtration(f_boundary))) {
// ### filt(Tau) = fmin(filt(Tau), filt(Sigma))
Filtration_value alpha_complex_filtration = fmin(complex.filtration(f_boundary),
complex.filtration(f_simplex));
complex.assign_filtration(f_boundary, alpha_complex_filtration);
#ifdef DEBUG_TRACES
std::clog << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl;
#endif // DEBUG_TRACES
// ### Else
} else {
auto const& cache=get_cache(complex, f_boundary);
bool is_gab = kernel_.is_gabriel(cache, get_point_(face_opposite_vertex.second));
#ifdef DEBUG_TRACES
std::clog << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << face_opposite_vertex.second << std::endl;
#endif // DEBUG_TRACES
// ### If Tau is not Gabriel of Sigma
if (false == is_gab) {
// ### filt(Tau) = filt(Sigma)
Filtration_value alpha_complex_filtration = complex.filtration(f_simplex);
complex.assign_filtration(f_boundary, alpha_complex_filtration);
#ifdef DEBUG_TRACES
std::clog << " | filt(Tau) = filt(Sigma) = " << complex.filtration(f_boundary) << std::endl;
#endif // DEBUG_TRACES
}
}
}
}
};
} // namespace alpha_complex
namespace alphacomplex = alpha_complex;
} // namespace Gudhi
#endif // ALPHA_COMPLEX_H_
Gudhi::Points_off_reader
OFF file reader implementation in order to read points from an OFF file.
Definition Points_off_io.h:122
Gudhi::Points_off_reader::get_point_cloud
const std::vector< Point_d > & get_point_cloud() const
Point cloud getter.
Definition Points_off_io.h:158
Gudhi::Points_off_reader::is_valid
bool is_valid() const
Returns if the OFF file read operation was successful or not.
Definition Points_off_io.h:150
Gudhi::alpha_complex::Alpha_complex
Alpha complex data structure.
Definition Alpha_complex.h:103
Gudhi::alpha_complex::Alpha_complex< Kernel >::Triangulation
std::conditional_t< false, CGAL::Regular_triangulation< Kernel, TDS >, CGAL::Delaunay_triangulation< Kernel, TDS > > Triangulation
Definition Alpha_complex.h:123
Gudhi::alpha_complex::Alpha_complex< Kernel >::Sphere
typename A_kernel_d::Sphere Sphere
Definition Alpha_complex.h:135
Gudhi::alpha_complex::Alpha_complex::Alpha_complex
Alpha_complex(const InputPointRange &points, WeightRange weights)
Alpha_complex constructor from a list of points and weights.
Definition Alpha_complex.h:211
Gudhi::alpha_complex::Alpha_complex< Kernel >::Geom_traits
std::conditional_t< false, CGAL::Regular_triangulation_traits_adapter< Kernel >, Kernel > Geom_traits
Definition Alpha_complex.h:110
Gudhi::alpha_complex::Alpha_complex::create_complex
bool create_complex(SimplicialComplexForAlpha &complex, Filtration_value max_alpha_square=std::numeric_limits< Filtration_value >::infinity(), bool exact=false, bool default_filtration_value=false)
Inserts all Delaunay triangulation into the simplicial complex. It also computes the filtration value...
Definition Alpha_complex.h:386
Gudhi::alpha_complex::Alpha_complex::get_point
const Point_d & get_point(std::size_t vertex) const
get_point returns the point corresponding to the vertex given as parameter.
Definition Alpha_complex.h:242
Gudhi::alpha_complex::Alpha_complex::Alpha_complex
Alpha_complex(const std::string &off_file_name)
Alpha_complex constructor from an OFF file name.
Definition Alpha_complex.h:173
Gudhi::alpha_complex::Alpha_complex< Kernel >::A_kernel_d
Alpha_kernel_d< Kernel, false > A_kernel_d
Definition Alpha_complex.h:127
Gudhi::alpha_complex::Alpha_complex< Kernel >::Point_d
typename Geom_traits::Point_d Point_d
Definition Alpha_complex.h:138
Gudhi::alpha_complex::Alpha_complex::num_vertices
std::size_t num_vertices() const
Returns the number of finite vertices in the triangulation.
Definition Alpha_complex.h:229
Gudhi::alpha_complex::Alpha_complex::Alpha_complex
Alpha_complex(const InputPointRange &points)
Alpha_complex constructor from a list of points.
Definition Alpha_complex.h:194
Gudhi::alpha_complex::Alpha_kernel_d
Alpha complex kernel container.
Definition Alpha_kernel_d.h:42
Gudhi
Gudhi namespace.
Definition SimplicialComplexForAlpha.h:14
Gudhi::alpha_complex::SimplicialComplexForAlpha
The concept SimplicialComplexForAlpha describes the requirements for a type to implement a simplicial...
Definition SimplicialComplexForAlpha.h:21
Gudhi::alpha_complex::SimplicialComplexForAlpha::skeleton_simplex_range
Skeleton_simplex_range skeleton_simplex_range
Returns a range over the simplices of the skeleton of the simplicial complex, for a given dimension.
Definition SimplicialComplexForAlpha.h:72
Gudhi::alpha_complex::SimplicialComplexForAlpha::assign_filtration
int assign_filtration(Simplex_handle simplex, Filtration_value filtration)
Gudhi::alpha_complex::SimplicialComplexForAlpha::num_vertices
std::size_t num_vertices()
Gudhi::alpha_complex::SimplicialComplexForAlpha::dimension
int dimension(Simplex_handle simplex)
Gudhi::alpha_complex::SimplicialComplexForAlpha::prune_above_filtration
void prune_above_filtration(Filtration_value filtration)
Gudhi::alpha_complex::SimplicialComplexForAlpha::make_filtration_non_decreasing
void make_filtration_non_decreasing()
Gudhi::alpha_complex::SimplicialComplexForAlpha::simplex_vertex_range
Simplex_vertex_range simplex_vertex_range(Simplex_handle const &simplex)
Returns a range over vertices of a given simplex.
Gudhi::alpha_complex::SimplicialComplexForAlpha::insert_simplex_and_subfaces
void insert_simplex_and_subfaces(std::vector< Vertex_handle > const &vertex_range, Filtration_value filtration)
Inserts a simplex with vertices from a given simplex (represented by a vector of Vertex_handle) in th...
Gudhi::alpha_complex::SimplicialComplexForAlpha::Simplex_handle
unspecified Simplex_handle
Definition SimplicialComplexForAlpha.h:23
Gudhi::alpha_complex::SimplicialComplexForAlpha::Vertex_handle
unspecified Vertex_handle
Definition SimplicialComplexForAlpha.h:25
Gudhi::alpha_complex::SimplicialComplexForAlpha::Filtration_value
unspecified Filtration_value
Definition SimplicialComplexForAlpha.h:29