CGAL - Retrieve Vertex Index After Delaunay Triangulation

Question

I am computing the 2D delaunay triangulation of a few thousand points. Each point has more data associated with it beyond x and y coordinates. Therefore, I was wondering if it is possible to retrieve the index of each point so that I can access my own point struct in another vector.

Currently, as I access vertices from a Face_handle, it returns a point (i.e. x,y coordinates) How can I return each vertex by its ID (index) instead of its x,y coordinates? Thank you.

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

typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef CGAL::Delaunay_triangulation_2<Kernel> Delaunay;
typedef Kernel::Point_2 Point;

void example() {

  std::vector<Point> points;
  points.push_back(Point(1,1)); //index 0
  points.push_back(Point(1,2)); //index 1
  points.push_back(Point(1,3)); //index 2
  points.push_back(Point(2,1)); //index 3
  points.push_back(Point(2,2)); //index 4
  points.push_back(Point(2,3)); //index 5

  Delaunay triangulation;
  triangulation.insert(points.begin(),points.end());

  for(Delaunay::Finite_faces_iterator fit = triangulation.finite_faces_begin();
      fit != triangulation.finite_faces_end(); ++fit) {

    Delaunay::Face_handle face = fit;
    std::cout << "Triangle:\t" << triangulation.triangle(face) << std::endl;
    std::cout << "Vertex 0:\t" << triangulation.triangle(face)[0] << std::endl;
  }
}

Output (x,y coordinates):

Triangle:   1 3 1 2 2 2
Vertex 0:   1 3
Triangle:   1 2 1 1 2 1
Vertex 0:   1 2
Triangle:   1 3 2 2 2 3
Vertex 0:   1 3
Triangle:   1 2 2 1 2 2
Vertex 0:   1 2

Desired Output (indices):

Triangle:   2   1   4
Vertex 0:   2
Triangle:   1   0   3
Vertex 0:   1 
Triangle:   2   4   5
Vertex 0:   2
Triangle:   1   3   4
Vertex 0:   1

Sero

Answer 1

You can attach any information to vertices in a triangulation. For example to add indices (unsigned int) you could do the following:

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <vector>

typedef CGAL::Exact_predicates_inexact_constructions_kernel            Kernel;
typedef CGAL::Triangulation_vertex_base_with_info_2<unsigned int, Kernel> Vb;
typedef CGAL::Triangulation_data_structure_2<Vb>                       Tds;
typedef CGAL::Delaunay_triangulation_2<Kernel, Tds>                    Delaunay;
typedef Kernel::Point_2                                                Point;

int main() {

  std::vector< std::pair<Point,unsigned> > points;
  points.push_back( std::make_pair( Point(1,1), 0 ) );
  points.push_back( std::make_pair( Point(1,2), 1 ) );
  points.push_back( std::make_pair( Point(1,3), 2 ) );
  points.push_back( std::make_pair( Point(2,1), 3 ) );
  points.push_back( std::make_pair( Point(2,2), 4 ) );
  points.push_back( std::make_pair( Point(2,3), 5 ) );

  Delaunay triangulation;
  triangulation.insert(points.begin(),points.end());

  for(Delaunay::Finite_faces_iterator fit = triangulation.finite_faces_begin();
      fit != triangulation.finite_faces_end(); ++fit) {

    Delaunay::Face_handle face = fit;
    std::cout << "Triangle:\t" << triangulation.triangle(face) << std::endl;
    std::cout << "Vertex 0:\t" << triangulation.triangle(face)[0] << std::endl;
    std::cout << "Vertex 0:\t" << face->vertex(0)->info() << std::endl;
  }
}

Deprive

Thank you, this will solve my problem. I don't suppose it might be possible to assign more information to each vertex? e.g. using std::tuple? – Sero

I have never tried it, but I am almost sure you can assign whatever type you want (std::tuple or your own class etc.). Just use it as a template parameter for Vb and adjust the rest of the code as necessary. – Deprive

Let me confirm that you can add whatever you want to add to a vertex. And I would like to point out that all this is documented here: doc.cgal.org/latest/Triangulation_2/index.html#title40 – Backside

Can I embed the indices the same way for Surface_mesh? – Iva