CGAL users discussion list

[Andreas Fabri <>]

Hello,

Note that write_VTU is documented in the  CGAL package 2D Conforming 
Triangulations and Meshes.

When you call a function like refine_Delaunay_mesh()  you define the 
domain (for example the interior
of your polygon, as a domain, otherwise the convex hull of the points is 
the domain.

When you follow the example Sebastien just gave you  must adapt it, as 
the Delaunay_mesh_face_base_2
class has a function to set the domain.

https://doc.cgal.org/latest/Mesh_2/classDelaunayMeshFaceBase__2.html#ac4a80317799961e7830b9690121d6bdc

Best,

Andreas


On 3/14/2022 8:40 AM, Sebastien Loriot ( via 
cgal-discuss Mailing List) wrote:
> A triangulation of a point set is a triangulation of the convex hull 
> of the points. If some constrain edges are added, you then have the 
> guarantee that those edges will be present in the triangulation of the
> convex hull of your points.
>
> If your constraints define a closed shape then you need a flooding like
> algorithm to only pick the triangles that are inside the shape, like in
> this example:
>
> https://doc.cgal.org/latest/Triangulation_2/Triangulation_2_2polygon_triangulation_8cpp-example.html 
>
>
> Best,
>
> Sebastien.
>
> On 3/13/22 02:46, Bob Bill ( via cgal-discuss 
> Mailing List) wrote:
> > 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
> >
> > --
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> > https://sympa.inria.fr/sympa/info/cgal-discuss
--
Andreas Fabri, PhD
Chief Officer, GeometryFactory
Editor, The CGAL Project