CGAL users discussion list

[Sebastien Loriot <>]

The 3D triangulation of the points of a surface is a partition of the
convex-hull of the points into tetrahedra. It is not a 3D constrained
triangulation restricted to the inside of the volume bounded by your
input mesh. Such a triangulation is not yet available in CGAL.

Best,

Sebastien.

On 7/9/22 10:26, Bob Bill ( via cgal-discuss Mailing 
List) wrote:
> Okay, I discovered what is the problem.
>
> One of the faces of my original surface_mesh is *not* straight. So, when 
> I construct the triangulation giving only the set of points, this 
> feature is not present in the resulting triangulation. See the attached 
> image: in blue I have the original (triangulated) surface mesh, while 
> white line is coming from the Triangulation3 I created using the 
> vertices of the surface only. So, the question now is:
>
> How can I get a triangulation that is truly representing also the 
> boundary of the surface mesh? I think this should be possible, but I've 
> not been able to find an example about how to do this. This should be 
> possible. Also, my surface_mesh is a triangulated surface mesh, as it's 
> the result of a BooleanOperation.
>
>
> Best,
> Bob
>
> Il venerdì 8 luglio 2022, 13:37:52 CEST, Bob Bill" ( 
> via cgal-discuss Mailing List) <> ha scritto:
>
>
> Dear all,
>
> I notice that if I compute the volume bounded by a Surface_mesh with 
> CGAL::Polygon_mesh_processing::volume(surface_mesh)
>
>
>
> I have a result that is different w.r.t what I get if I first mesh the 
> inside and then sum the volume of each tetrahedron, i.e.
>
>
> using K = CGAL::Exact_predicates_inexact_constructions_kernel;
> using Triangulation_3 = CGAL::Triangulation_3<K>;
>
> double sum =0.;
> Triangulation_3 tria;
> tria.insert(sm.points().begin(), sm.points().end());
> for (const auto &c : tr_q.finite_cell_handles())
> {
> const auto &tet = tr_q.tetrahedron(c);
> sum += std::abs(tet.volume());
> }
>
>
>
> What is the reason for that? I spent a whole day but I really cannot 
> figure it out.
>
> Best, BoB
>
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