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Re: Re: [cgal-discuss] good or bad triangulations?


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  • From: "Laurent Rineau (GeometryFactory)" <>
  • To:
  • Subject: Re: Re: [cgal-discuss] good or bad triangulations?
  • Date: Mon, 23 Jan 2012 11:38:43 +0100
  • Organization: GeometryFactory

Le lundi 23 janvier 2012 09:48:05 Monique Teillaud a écrit :
> Dear Juan Carlos,
>
> You can use another library, it will not change the Delaunay
> triangulation. The Delaunay triangulation is known to have slivers, i.e.
> tetrahedra whose vertices are almost coplanar and cocircular. As long as
> they have an empty circumscribing sphere, they are Delaunay tetrahedra.
> There is a huge literature on this topic.

In a Delaunay triangulation you can have every all types of almost degenerate
tetrahedra, not only slivers.

> You may want to use another triangulation. The regular triangulation, or
> weighted Delaunay triangulation, allows to avoid slivers. So, you can
> probably use the CGAL 3D Regular Triangulation, but you will need to
> choose the weights of your points in an appropriate way.
> There is in particular a paper by Dey, Edelsbrunner and others about
> this method (I don't have time right now to dig for the precise reference).
>
> In fact this method is already coded in the 3D CGAL mesh package as one
> of the optimization methods to improve dihedral angles, you might be
> able to reuse some code from this method.

Those optimization methods have been designed to work on regular
triangulations that are made by the mesh generator that does Delaunay
refinement. Those special triangulations are known to have no almost
degenerate tetrahedra but slivers. That is a special case of Delaunay
triangulations. I cannot certify that those optimization methods can do
anything useful on other triangulations.

--
Laurent Rineau, PhD
R&D Engineer at GeometryFactory http://www.geometryfactory.com/
Release Manager of the CGAL Project http://www.cgal.org/




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