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_