CGAL users discussion list

[Sebastien Loriot <>]

As I said you need a 3D constrained triangulation like tetgen.

Best,

Sebastien.

On 7/11/22 17:07, Bob Bill ( via cgal-discuss Mailing 
List) wrote:
> Thanks Sebastien for the clarification. Is there any workaround/hack for 
> this?
> More precisely, since the blue surface mesh has triangulated faces, 
> isn't it possible to retrieve a minimal set of tetrahedra starting from 
> them?
>
> Best,
> Bob
>
> Il lunedì 11 luglio 2022, 08:45:43 CEST, Sebastien Loriot" 
> ( via cgal-discuss Mailing List) 
> <> ha scritto:
>
>
> 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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