On Feb 24, 10:57 am, Volker Braun <vbraun.n...@gmail.com> wrote:
> On Thursday, February 24, 2011 6:29:11 PM UTC, Dmitri wrote:
>
> > I think my problem is actually doing the comparison. So I have this
> > chosen set of points which I don't know is convex. I compute its
> > convex hull. Now how do I compare these two objects?
>
> Assuming that we are still talking about lattice polytopes: check that
> LatticePolytope(points).npoints() is the same as the number of points you
> started with.

This won't always work.

Suppose you have a lattice polygon P with vertices (-1, 1), (-1,0),
(0,0), and (1,1), and another lattice polygon Q with vertices (-1,0),
(-1,-1), (1,-1), and (1,0).  Let R be the union of P and Q.  Then R is
not convex: it looks like a square with a triangle cut out of it.  But
R and its convex hull contain the same lattice points.

UAW

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