gist_for_cgal_issue_3346

periodic_alpha_complex_3d.cpp

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_traits_3.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
#include <CGAL/Alpha_shape_3.h>
#include <CGAL/Alpha_shape_cell_base_3.h>
#include <CGAL/Alpha_shape_vertex_base_3.h>
#include <CGAL/iterator.h>

#include <CGAL/Random.h>
#include <CGAL/point_generators_3.h>

#include <fstream>
#include <cmath>
#include <string>
#include <tuple>
#include <map>
#include <utility>
#include <vector>
#include <cstdlib>

// Traits
using K = CGAL::Exact_predicates_inexact_constructions_kernel;
using PK = CGAL::Periodic_3_Delaunay_triangulation_traits_3<K>;
// Vertex type
using DsVb = CGAL::Periodic_3_triangulation_ds_vertex_base_3<>;
using Vb = CGAL::Triangulation_vertex_base_3<PK, DsVb>;
using AsVb = CGAL::Alpha_shape_vertex_base_3<PK, Vb>;
// Cell type
using DsCb = CGAL::Periodic_3_triangulation_ds_cell_base_3<>;
using Cb = CGAL::Triangulation_cell_base_3<PK, DsCb>;
using AsCb = CGAL::Alpha_shape_cell_base_3<PK, Cb>;
using Tds = CGAL::Triangulation_data_structure_3<AsVb, AsCb>;
using P3DT3 = CGAL::Periodic_3_Delaunay_triangulation_3<PK, Tds>;
using Alpha_shape_3 = CGAL::Alpha_shape_3<P3DT3>;
using Point = PK::Point_3;

// filtration with alpha values needed type definition
using Alpha_value_type = Alpha_shape_3::FT;
using Object = CGAL::Object;
using Dispatch =
    CGAL::Dispatch_output_iterator<CGAL::cpp11::tuple<Object, Alpha_value_type>,
                                   CGAL::cpp11::tuple<std::back_insert_iterator<std::vector<Object> >,
                                                      std::back_insert_iterator<std::vector<Alpha_value_type> > > >;
using Cell_handle = Alpha_shape_3::Cell_handle;
using Facet = Alpha_shape_3::Facet;
using Edge_3 = Alpha_shape_3::Edge;
using Vertex_handle = Alpha_shape_3::Vertex_handle;
using Vertex_list = std::vector<Alpha_shape_3::Vertex_handle>;

int main(int argc, char **argv) {
  typedef CGAL::Creator_uniform_3<double, Point> Creator;
  CGAL::Random random(7);
  CGAL::Random_points_in_cube_3<Point, Creator> in_cube(1, random);
  std::vector<Point> pts;
  // Generating 50 random points
  for (int i=0 ; i < 50 ; i++) {
    Point p = *in_cube++;
    pts.push_back(p);
  }

  for (int i=0 ; i < 5 ; i++) {
    std::ofstream out(std::to_string(i) + std::string(".txt"));
    // I maintain a map from Alpha_shape_3::Vertex_handle to my own vertex handles
    std::map<Alpha_shape_3::Vertex_handle, int> map_cgal_simplex_tree;

    // Define the periodic cube
    P3DT3 pdt(PK::Iso_cuboid_3(-1,-1,-1,1,1,1));
    // Heuristic for inserting large point sets (if pts is reasonably large)
    pdt.insert(pts.begin(), pts.end(), true);
    // As pdt won't be modified anymore switch to 1-sheeted cover if possible
    if (pdt.is_triangulation_in_1_sheet()) {
      pdt.convert_to_1_sheeted_covering();
    } else {
      std::cerr << "ERROR: we were not able to construct a triangulation within a single periodic domain." << std::endl;
      exit(-1);
    }
    std::cout << "============================ Periodic Delaunay computed." << std::endl;

    // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode
    // Maybe need to set it to GENERAL mode
    Alpha_shape_3 as(pdt, 0, Alpha_shape_3::GENERAL);

    // filtration with alpha values from alpha shape
    std::vector<Object> the_objects;
    std::vector<Alpha_value_type> the_alpha_values;

    Dispatch disp = CGAL::dispatch_output<Object, Alpha_value_type>(std::back_inserter(the_objects),
                                                                    std::back_inserter(the_alpha_values));

    as.filtration_with_alpha_values(disp);

    // Loop on objects vector
    for (auto object_iterator : the_objects) {
      Vertex_list vertex_list;
      // Retrieve Alpha shape vertex list from object
      if (const Cell_handle *ch = CGAL::object_cast<Cell_handle>(&object_iterator)) {
        for (auto i = 0; i < 4; i++) {
          vertex_list.push_back((*ch)->vertex(i));
        }
      } else if (const Facet *facet = CGAL::object_cast<Facet>(&object_iterator)) {
        for (auto i = 0; i < 4; i++) {
          if (facet->second != i) {
            vertex_list.push_back(facet->first->vertex(i));
          }
        }
      } else if (const Edge_3 *edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
        for (auto i : {edge->second, edge->third}) {
          vertex_list.push_back(edge->first->vertex(i));
        }
      } else if (const Vertex_handle *vh = CGAL::object_cast<Vertex_handle>(&object_iterator)) {
        vertex_list.push_back(*vh);
      }
      std::vector<int> the_simplex;
      // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
      for (auto the_alpha_shape_vertex : vertex_list) {
        std::map<Alpha_shape_3::Vertex_handle, int>::iterator the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex);
        if (the_map_iterator == map_cgal_simplex_tree.end()) {
          // alpha shape not found
          int vertex = map_cgal_simplex_tree.size();
#ifdef DEBUG_TRACES
          //std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl;
#endif  // DEBUG_TRACES
          map_cgal_simplex_tree.emplace(the_alpha_shape_vertex, vertex);
          the_simplex.push_back(vertex);
        } else {
          // alpha shape found
          int vertex = the_map_iterator->second;
#ifdef DEBUG_TRACES
          //std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl;
#endif  // DEBUG_TRACES
          the_simplex.push_back(vertex);
        }
      }
      for (auto vertex : the_simplex)
        out << vertex << ",";
      out << std::endl;
    }
    out.close();
  }
  return 0;
}