CGAL users discussion list

[Bob Bill <>]

I am given the vertices of a polygon, and I need to mesh it. I am following one of the first examples in the CDT package documentation. 

The code is the following:

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>

#include <CGAL/Constrained_Delaunay_triangulation_2.h>

#include <CGAL/Delaunay_mesher_2.h>

#include <CGAL/Delaunay_mesh_face_base_2.h>

#include <CGAL/Delaunay_mesh_size_criteria_2.h>

#include <CGAL/IO/write_VTU.h>

#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;

typedef CGAL::Triangulation_vertex_base_2<K> Vb;

typedef CGAL::Delaunay_mesh_face_base_2<K> Fb;

typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;

typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds> CDT;

typedef CGAL::Delaunay_mesh_size_criteria_2<CDT> Criteria;

typedef CDT::Vertex_handle Vertex_handle;

typedef CDT::Point Point;

int main()

{

  CDT cdt;

  Vertex_handle va = cdt.insert(Point(-1,-1));

  Vertex_handle vb = cdt.insert(Point(-1,-0.25714));

  Vertex_handle vc = cdt.insert(Point(-1.5,-1.4));

  Vertex_handle vd = cdt.insert(Point(1.3,-1.2));

  Vertex_handle ve = cdt.insert(Point(1.3,0.5));

  Vertex_handle vf = cdt.insert(Point(1, 0.45714));

  Vertex_handle vg = cdt.insert(Point(1, -1));

  cdt.insert_constraint(va, vb);

  cdt.insert_constraint(vb, vc);

  cdt.insert_constraint(vc, vd);

  cdt.insert_constraint(vd, ve);

  cdt.insert_constraint(ve,vf);

  cdt.insert_constraint(vf,vg);

  cdt.insert_constraint(vg,va);

  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;

  std::cout << "Meshing the triangulation..." << std::endl;

  // CGAL::refine_Delaunay_mesh_2(cdt, Criteria(0.125, 0.5));

  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;

  std::ofstream output("intersected_mesh.vtu");

  CGAL::write_vtu(output, cdt);

//Show the vertices of the triangulation

    for(auto it = cdt.finite_faces_begin();it!=cdt.finite_faces_end();++it){

    std::cout << cdt.triangle(it) <<'\n';

  }

}

If I look at the .vtu file, it seems to have the correct shape (see attached image). However, after I printed the vertices for each triangle, it appears that one element of the triangulation is also the one with vertices 

(-1, -0.25714)

(1, -1)

(1, 0.45714)

which should not be there since is not inside that polygon. Isn't this a bug? If not, how can I create a mesh for which this is avoided? I mean, I'd like to have all the triangles inside the domain.

Best regards,

Bob

Attachment: Screenshot 2022-03-13 at 02.41.52.png
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