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I have a set of points and I want to find all possible triangles which have empty circumcircle. I want to use Delaunay Triangulation.

I have read some papers on the subject but I am not sure whether Delaunay Triangulation finds all possible triangles or not. If yes, then how can I mathematically prove that?

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No, it does not. – studiosus Dec 14 '13 at 17:51
Is there any way to find all possible triangles which have the same properties as Delaunay? – Scorpionidas Dec 14 '13 at 18:36

To find all possible triangles you can make all the faces the same length:

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