CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 01/23/2012 12:37 AM, Juan Carlos Lopez Alfonso wrote:
> Hi There
>
> Again I want to ask about the coplanar test in 3D Delaunay
> triangulation, because after read the documentation I have not solved my
> problem. I have tested different Delaunay tirangulations and in
> different cases (different distributions of points) the resultant
> triangulations have several almost coplanar tetrahedras (very very small
> volume) and these are no very good triangulations. Before attempting to
> use another library to triangulate, I have some questions:
>
> - if Delaunay  triangulations are not uniques, Are there forms in Cgal
> to obtian different Delaunay triangulations for the same point
> distributions? in order to avoid this problem.
>
> - Are there forms in CGAL to impose a minimum volume for tetrahedras?
> something like a epsilon?
Again no.

> On the other hand, I still do not understand how in cgal when the
> jacobian using double precision is equal to zero, the triangulation give
> us coplanar tetrahedras (where the jacobians are about 1.0e-18). I will
> use this triangulation to optimizing a variational problem, and when the
> algorithm detect this tetrahedras the results are unexpected and erroneous.
>
> Could you give suggestions to obtain better triangulations?
Your points are in plane with axis aligned normal vectors right?
Make your points really coplanar and ALMOST coplanar tetrahedra will
disappear.

Sebastien.
> Sorry for these successive questions, but I dont know what I need to do
> to solve this problem, which is the only thing I need to complete the
> practical part of my model.
>
> Best Regards and thank you in advance
> Juan Carlos