如何从CGAL凸包获得多边形面

Question

我使用CGAL中的3D凸包估计器实现来计算一组点的凸多面体。下面显示了代码：

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/algorithm.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/convex_hull_3.h>
#include <vector>
#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::Point_3 Point_3;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
typedef Polyhedron::Facet_iterator Facet_iterator;
typedef Polyhedron::Halfedge_around_facet_circulator Halfedge_facet_circulator;

int main()
{
  std::vector<Point_3> points;

  points.push_back(Point_3(2.0f, 3.535533905932738f, 3.535533905932737f));
  points.push_back(Point_3(4.0f, 2.0f, 0.0f));
  points.push_back(Point_3(0.0f, 2.0f, 0.0f));
  points.push_back(Point_3(1.0f, 0.0f, 0.0f));
  points.push_back(Point_3(4.0f, 1.414213562373095f, 1.414213562373095f));
  points.push_back(Point_3(0.0f, 1.414213562373095f, 1.414213562373095f));
  points.push_back(Point_3(3.0f, 0.0f, 0.0f));
  points.push_back(Point_3(2.0f, 5.0f, 0.0f));

  Polyhedron P;

  CGAL::convex_hull_3(points.begin(), points.end(), P);

  std::cout << "- Number of vertices  = " << P.size_of_vertices()    << std::endl;
  std::cout << "- Number of edges     = " << P.size_of_halfedges()/2 << std::endl;
  std::cout << "- Number of faces     = " << P.size_of_facets()      << std::endl;

  for ( Facet_iterator i = P.facets_begin(); i != P.facets_end(); ++i)
  {
    Halfedge_facet_circulator j = i->facet_begin();
    CGAL_assertion( CGAL::circulator_size(j) >= 3);
    std::cout << CGAL::circulator_size(j) << ' ';
    do{
      std::cout << ' ' << std::distance(P.vertices_begin(), j->vertex());
    }while ( ++j != i->facet_begin());

    std::cout << std::endl;
  }
  return 0;
}

但是，输出是多面体的三角形：

有没有办法强制CGAL用多边形表示一个面而不是一组三角形？

Answer 1

无法开箱即用。您需要测试每个边缘是否四个点是共面的。