Alpha_complex.h

/*    This file is part of the Gudhi Library. The Gudhi library
 *    (Geometric Understanding in Higher Dimensions) is a generic C++
 *    library for computational topology.
 *
 *    Author(s):       Vincent Rouvreau
 *
 *    Copyright (C) 2015 Inria
 *
 *    This program is free software: you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation, either version 3 of the License, or
 *    (at your option) any later version.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#ifndef ALPHA_COMPLEX_H_
#define ALPHA_COMPLEX_H_

#include <gudhi/Debug_utils.h>
// to construct Alpha_complex from a OFF file of points
#include <gudhi/Points_off_io.h>

#include <stdlib.h>
#include <math.h>  // isnan, fmax

#include <CGAL/Delaunay_triangulation.h>
#include <CGAL/Epick_d.h>
#include <CGAL/Spatial_sort_traits_adapter_d.h>
#include <CGAL/property_map.h>  // for CGAL::Identity_property_map
#include <CGAL/NT_converter.h>

#include <iostream>
#include <vector>
#include <string>
#include <limits>  // NaN
#include <map>
#include <utility>  // std::pair
#include <stdexcept>
#include <numeric>  // for std::iota

namespace Gudhi {

namespace alpha_complex {

template<class Kernel = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>>
class Alpha_complex {
 public:
  // Add an int in TDS to save point index in the structure
  typedef CGAL::Triangulation_data_structure<typename Kernel::Dimension,
                              CGAL::Triangulation_vertex<Kernel, std::ptrdiff_t>,
                              CGAL::Triangulation_full_cell<Kernel> > TDS;
  typedef CGAL::Delaunay_triangulation<Kernel, TDS> Delaunay_triangulation;

  typedef typename Kernel::Point_d Point_d;
  typedef Kernel Geom_traits;

 private:
  typedef typename Kernel::Compute_squared_radius_d Squared_Radius;
  typedef typename Kernel::Side_of_bounded_sphere_d Is_Gabriel;
  typedef typename Kernel::Point_dimension_d        Point_Dimension;

  // Type required to compute squared radius, or side of bounded sphere on a vector of points.
  typedef typename std::vector<Point_d> Vector_of_CGAL_points;

  // Vertex_iterator type from CGAL.
  typedef typename Delaunay_triangulation::Vertex_iterator CGAL_vertex_iterator;

  // size_type type from CGAL.
  typedef typename Delaunay_triangulation::size_type size_type;

  // Map type to switch from simplex tree vertex handle to CGAL vertex iterator.
  typedef typename std::map< std::size_t, CGAL_vertex_iterator > Vector_vertex_iterator;

 private:
  Vector_vertex_iterator vertex_handle_to_iterator_;
  Delaunay_triangulation* triangulation_;
  Kernel kernel_;

 public:
  Alpha_complex(const std::string& off_file_name)
      : triangulation_(nullptr) {
    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)
      : triangulation_(nullptr) {
    init_from_range(points);
  }

  ~Alpha_complex() {
    delete triangulation_;
  }

  // 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;

  const Point_d& get_point(std::size_t vertex) const {
    return vertex_handle_to_iterator_.at(vertex)->point();
  }

  std::size_t number_of_vertices() const {
    return vertex_handle_to_iterator_.size();
  }

 private:
  template<typename InputPointRange >
  void init_from_range(const InputPointRange& points) {
    auto first = std::begin(points);
    auto last = std::end(points);

    if (first != last) {
      // point_dimension function initialization
      Point_Dimension point_dimension = kernel_.point_dimension_d_object();

      // Delaunay triangulation is point dimension.
      triangulation_ = new Delaunay_triangulation(point_dimension(*first));

      std::vector<Point_d> point_cloud(first, last);

      // Creates a vector {0, 1, ..., N-1}
      std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0),
                                          boost::counting_iterator<std::ptrdiff_t>(point_cloud.size()));

      typedef boost::iterator_property_map<typename std::vector<Point_d>::iterator,
                                           CGAL::Identity_property_map<std::ptrdiff_t>> Point_property_map;
      typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_property_map> Search_traits_d;

      CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud)));

      typename Delaunay_triangulation::Full_cell_handle hint;
      for (auto index : indices) {
        typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint);
        // Save index value as data to retrieve it after insertion
        pos->data() = index;
        hint = pos->full_cell();
      }
      // --------------------------------------------------------------------------------------------
      // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa
      // 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::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl;
#endif  // DEBUG_TRACES
          vertex_handle_to_iterator_.emplace(vit->data(), vit);
        }
      }
      // --------------------------------------------------------------------------------------------
    }
  }

 public:
  template <typename SimplicialComplexForAlpha>
  bool create_complex(SimplicialComplexForAlpha& complex) {
    typedef typename SimplicialComplexForAlpha::Filtration_value Filtration_value;
    return create_complex(complex, std::numeric_limits<Filtration_value>::infinity());
  }

  template <typename SimplicialComplexForAlpha, typename Filtration_value>
  bool create_complex(SimplicialComplexForAlpha& complex, Filtration_value max_alpha_square) {
    // From SimplicialComplexForAlpha type required to insert into a simplicial complex (with or without subfaces).
    typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle;
    typedef typename SimplicialComplexForAlpha::Simplex_handle Simplex_handle;
    typedef std::vector<Vertex_handle> Vector_vertex;

    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 (triangulation_->number_of_vertices() > 0) {
      for (auto cit = triangulation_->finite_full_cells_begin(); cit != triangulation_->finite_full_cells_end(); ++cit) {
        Vector_vertex vertexVector;
#ifdef DEBUG_TRACES
        std::cout << "Simplex_tree insertion ";
#endif  // DEBUG_TRACES
        for (auto vit = cit->vertices_begin(); vit != cit->vertices_end(); ++vit) {
          if (*vit != nullptr) {
#ifdef DEBUG_TRACES
            std::cout << " " << (*vit)->data();
#endif  // DEBUG_TRACES
            // Vector of vertex construction for simplex_tree structure
            vertexVector.push_back((*vit)->data());
          }
        }
#ifdef DEBUG_TRACES
        std::cout << 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<double>::quiet_NaN());
      }
    }
    // --------------------------------------------------------------------------------------------

    // --------------------------------------------------------------------------------------------
    // Will be re-used many times
    Vector_of_CGAL_points pointVector;
    // ### 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) {
          pointVector.clear();
#ifdef DEBUG_TRACES
          std::cout << "Sigma of dim " << decr_dim << " is";
#endif  // DEBUG_TRACES
          for (auto vertex : complex.simplex_vertex_range(f_simplex)) {
            pointVector.push_back(get_point(vertex));
#ifdef DEBUG_TRACES
            std::cout << " " << vertex;
#endif  // DEBUG_TRACES
          }
#ifdef DEBUG_TRACES
          std::cout << std::endl;
#endif  // DEBUG_TRACES
          // ### If filt(Sigma) is NaN : filt(Sigma) = alpha(Sigma)
          if (std::isnan(complex.filtration(f_simplex))) {
            Filtration_value alpha_complex_filtration = 0.0;
            // No need to compute squared_radius on a single point - alpha is 0.0
            if (f_simplex_dim > 0) {
              // squared_radius function initialization
              Squared_Radius squared_radius = kernel_.compute_squared_radius_d_object();
              CGAL::NT_converter<typename Geom_traits::FT, Filtration_value> cv;

              alpha_complex_filtration = cv(squared_radius(pointVector.begin(), pointVector.end()));
            }
            complex.assign_filtration(f_simplex, alpha_complex_filtration);
#ifdef DEBUG_TRACES
            std::cout << "filt(Sigma) is NaN : filt(Sigma) =" << complex.filtration(f_simplex) << std::endl;
#endif  // DEBUG_TRACES
          }
          propagate_alpha_filtration(complex, f_simplex, decr_dim);
        }
      }
    }
    // --------------------------------------------------------------------------------------------

    // --------------------------------------------------------------------------------------------
    // As Alpha value is an approximation, we have to make filtration non decreasing while increasing the dimension
    complex.make_filtration_non_decreasing();
    // Remove all simplices that have a filtration value greater than max_alpha_square
    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, int decr_dim) {
    // From SimplicialComplexForAlpha type required to assign filtration values.
    typedef typename SimplicialComplexForAlpha::Filtration_value Filtration_value;
#ifdef DEBUG_TRACES
    typedef typename SimplicialComplexForAlpha::Vertex_handle Vertex_handle;
#endif  // DEBUG_TRACES

    // ### Foreach Tau face of Sigma
    for (auto f_boundary : complex.boundary_simplex_range(f_simplex)) {
#ifdef DEBUG_TRACES
      std::cout << " | --------------------------------------------------\n";
      std::cout << " | Tau ";
      for (auto vertex : complex.simplex_vertex_range(f_boundary)) {
        std::cout << vertex << " ";
      }
      std::cout << "is a face of Sigma\n";
      std::cout << " | isnan(complex.filtration(Tau)=" << std::isnan(complex.filtration(f_boundary)) << std::endl;
#endif  // DEBUG_TRACES
      // ### If filt(Tau) is not NaN
      if (!std::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::cout << " | filt(Tau) = fmin(filt(Tau), filt(Sigma)) = " << complex.filtration(f_boundary) << std::endl;
#endif  // DEBUG_TRACES
        // ### Else
      } else {
        // No need to compute is_gabriel for dimension <= 2
        // i.e. : Sigma = (3,1) => Tau = 1
        if (decr_dim > 1) {
          // insert the Tau points in a vector for is_gabriel function
          Vector_of_CGAL_points pointVector;
#ifdef DEBUG_TRACES
          Vertex_handle vertexForGabriel = Vertex_handle();
#endif  // DEBUG_TRACES
          for (auto vertex : complex.simplex_vertex_range(f_boundary)) {
            pointVector.push_back(get_point(vertex));
          }
          // Retrieve the Sigma point that is not part of Tau - parameter for is_gabriel function
          Point_d point_for_gabriel;
          for (auto vertex : complex.simplex_vertex_range(f_simplex)) {
            point_for_gabriel = get_point(vertex);
            if (std::find(pointVector.begin(), pointVector.end(), point_for_gabriel) == pointVector.end()) {
#ifdef DEBUG_TRACES
              // vertex is not found in Tau
              vertexForGabriel = vertex;
#endif  // DEBUG_TRACES
              // No need to continue loop
              break;
            }
          }
          // is_gabriel function initialization
          Is_Gabriel is_gabriel = kernel_.side_of_bounded_sphere_d_object();
          bool is_gab = is_gabriel(pointVector.begin(), pointVector.end(), point_for_gabriel)
              != CGAL::ON_BOUNDED_SIDE;
#ifdef DEBUG_TRACES
          std::cout << " | Tau is_gabriel(Sigma)=" << is_gab << " - vertexForGabriel=" << vertexForGabriel << 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::cout << " | 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_