CGAL users discussion list

[Iosif Pinelis <>]

Iosif Pinelis wrote, in part:

> I think the CGAL polygon convexity test is pretty similar to the LEDA 
> test, whose proof can be found at http://arxiv.org/abs/cs.CG/0701045 
> .  So, I believe the CGAL test can be proved similarly to the LEDA 
> test and/or using the latter test.

Indeed, it turns out to be easily proved that an appropriate version of 
the CGAL polygon convexity test (as I understood it, with the bug 
observed by Camille Wormser fixed) is exactly equivalent to the 
``non-strict'' version of the LEDA test, with collinear vertices 
allowed. Quite similarly, the strict variant of the LEDA test is 
equivalent to a strict variant of the CGAL test. I am going to write up 
the proof of the equivalence of the two tests and then let you know.

Iosif Pinelis