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Re: [cgal-discuss] triangulations with genus > 0


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  • Subject: Re: [cgal-discuss] triangulations with genus > 0
  • Date: Mon, 22 Oct 2007 13:51:37 +0200

Dear Matthijs,

I am not sure I understand what you need. Which kind of objects are you trying to triangulate?
The data structure is in fact able to store more than a triangulation of the sphere in 4D. We are re-using it for storing the triangulation of a torus in 4D (3D periodic space).
Do you need triangulations with boundaries? The CGAL triangulations have some properties, like for instance the fact that each facet is common to two tetrahedra. So, no boundaries.

Monique Teillaud

Matthijs Sypkens Smit wrote:
Hi all,

It seems that the CGAL Triangulation_3 does not support holes. When I build such a triangulation by manipulation the data_structure "by hand", then the validity check on the data structure fails with "Euler relation unsatisfied". I guess that could be expected since the manual mentions how the triangulation is actually a covering of the 4D sphere.

Can anyone comment on the problems of using the CGAL Triangulation for genus > 0 objects? It is at least possible to traverse the object. Could I disable the check for conformity to the Euler relation and have something workable, or would I be bound to run into troubles along the road?

If so, are there plans to support such triangulations in the future?





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