I don't think there's any reason it needs to be completely convex, and I
don't think you should throw out points. But yes, I agree that he should
consider giving the user free reins.



that's a good algorithmic problem, and not a trivial  one:
http://en.wikipedia.org/wiki/Convex_hull

but if you draw the polygon based on the order in which the points were
clicked, (assuming the user will automatically generate a convex polygon)
then it will be a lot simpler.
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