How to generate delaunay by some 3D coplanar vertices By CGAL

Question

I'm new in developing with cgal library,I have tried the following code to generate delaunay in 2D.

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Delaunay_triangulation_2.h>

#include <cassert>
#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K> Triangulation;
typedef Triangulation::Point Point;


int main()
{
 std::vector<Point> PL;
 PL.push_back(Point(0, 0));
 PL.push_back(Point(1, 0));
 PL.push_back(Point(1, 1));
 PL.push_back(Point(0, 1));
 auto a = PL.begin();

 Triangulation T;
 T.insert(PL.begin(),PL.end());
 Triangulation::Finite_faces_iterator Finite_face_iterator;

 for (Finite_face_iterator = T.finite_faces_begin(); Finite_face_iterator != T.finite_faces_end(); ++Finite_face_iterator)
 {
  std::cerr << T.triangle(Finite_face_iterator) << std::endl;
 }

 return 0;
}

those code output two faces,and if the vertices change to 3D like Point(0,0,0), Point(1,0,0), Point(1,1,0), Point(0,1,0) those four vertices are in the same plane,how can I output two faces not intersected by CGAL?

Answer 1

You can use the Delaunay_triangulation_3 class for this purpose. It handles coplanar points as a special case of dimension 2. All your points must be exactly coplanar, then.

Another option is to use Delaunay_triangulation_2, by projecting your points to the plane they belong. This would handle points that are almost coplanar.