numerical stable triangulation method?

Triangulations of regular polygons (in 2D?) are ambiguos. So for a square ABCD there are two possible triangulations -> ABC ACD or ABD DBC. My problems come from the fact/observation, that DelaunayTri gives me the different triangulation on different computers for the same input which breaks some of our regression tests for our SW...

1) Is there any possibility for force DelaunayTri to preserve something like an order?

2) What other MATLAB internals can be used/misused to create a triangulation

I was already wondering if i need to implement earclipping (which seems to have a internal ordering process) on our own?

Answer 1

[José-Luis]

1. No. Both are valid Delaunay triangulations.
2. None, unless you write it yourself. You could always try the file exchange, maybe someone has done this before. Matlab's triangulation is based on qHull. If you want other types of triangulations, I think you should look outside Matlab, for instance CGAL. CGAL has a very steep learning curve, and requires you to know C++. On the other hand, it can use exact arithmetic so numerical stability is less of a problem.

[Andreas Lobinger]

I'm not doubting the validity of the Delaunay triangulation. But if you look f.e. at the options of unique, there are the OCCURANCE and the 'stable' option. So even if the output is equal in the mathematical sense, ordering of the 'equal' outputs might be an issue.

[José-Luis]

Well, I think that what you could do instead is to check if the triangulation is valid, and not compare them directly.