如何从 CGAL 中的坐标和拓扑列表创建Polyhedron_3数据结构

我有一个坐标列表（一个 n x 3 矩阵，其中 n 是点数）和一个拓扑连通性（一个 m x 3 矩阵，其中 m 是三角形的数量）。

我希望使用此信息在 CGAL 中创建一个CGAL::Polyhedron_3类。我该如何实现？

这是我当前的代码：

#include <cstdlib>
#include <iostream>
#include <fstream>
#include <iterator>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Random.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Polyhedron_items_with_id_3.h>
#include <CGAL/IO/Polyhedron_iostream.h>
#include <CGAL/Surface_mesh_shortest_path.h>
#include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
#include <CGAL/boost/graph/iterator.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel           Kernel;
typedef CGAL::Polyhedron_3<Kernel, CGAL::Polyhedron_items_with_id_3>  Polyhedron_3;
typedef Kernel::Point_3                                               Point_3;
typedef Polyhedron_3::HalfedgeDS                                      HalfedgeDS;
typedef Polyhedron_3::Vertex_iterator                                 Vertex_iterator;
typedef Polyhedron_3::Edge_iterator                                   Edge_iterator;
typedef Polyhedron_3::Facet_iterator                                  Facet_iterator;
typedef CGAL::Surface_mesh_shortest_path_traits<Kernel, Polyhedron_3> Traits;
typedef CGAL::Surface_mesh_shortest_path<Traits>                      Surface_mesh_shortest_path;
typedef boost::graph_traits<Polyhedron_3>                             Graph_traits;
typedef Graph_traits::vertex_iterator                                 vertex_iterator;
typedef Graph_traits::face_iterator                                   face_iterator;
typedef Polyhedron_3::Halfedge_around_facet_circulator                Halfedge_facet_circulator;
template <class HDS>
class Build_triangle : public CGAL::Modifier_base<HDS>
{
public:
    Build_triangle() {}
    void operator()(HDS & hds)
    {
        // Postcondition: hds is a valid polyhedral surface.
        CGAL::Polyhedron_incremental_builder_3<HDS> B(hds, true);
        B.begin_surface(5, 4, 16);
        typedef typename HDS::Vertex   Vertex;
        typedef typename Vertex::Point Point;
        B.add_vertex(Point(0.0, 0.0, 0.0));
        B.add_vertex(Point(1.0, 0.0, 0.0));
        B.add_vertex(Point(1.0, 1.0, 0.0));
        B.add_vertex(Point(0.0, 1.0, 0.0));
        B.add_vertex(Point(0.5, 0.5, 0.0));
        B.begin_facet();
        B.add_vertex_to_facet(0);
        B.add_vertex_to_facet(1);
        B.add_vertex_to_facet(4);
        B.end_facet();
        B.begin_facet();
        B.add_vertex_to_facet(1);
        B.add_vertex_to_facet(2);
        B.add_vertex_to_facet(4);
        B.end_facet();
        B.begin_facet();
        B.add_vertex_to_facet(2);
        B.add_vertex_to_facet(3);
        B.add_vertex_to_facet(4);
        B.end_facet();
        B.begin_facet();
        B.add_vertex_to_facet(3);
        B.add_vertex_to_facet(0);
        B.add_vertex_to_facet(4);
        B.end_facet();
        B.end_surface();
    }
};
int main(int argc, char *argv[])
{
    Polyhedron_3 P;
    Build_triangle<HalfedgeDS> triangle;
    P.delegate(triangle);
    CGAL_assertion(P.is_triangle(P.halfedges_begin()));
    return 0;
}

CGAL_assertion断言语句失败，这意味着我无法正确生成三角形。我需要更改 HalfedgeDS 数据结构吗？我无法找到有关如何正确执行此操作的好例子。