Validity of algorithm for creation of a non self-intersecting polygon

Question

As an extension and partial answer to my thread I wrote a simple algorithm that given a set of points(with xy coordinates) can form a non self-intersecting polygon.

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Answer 1

I'm not sure I understand correctly what you're trying to do. In the other thread, and in the corresponding thread at math.SE (which brought me here), you said you had a polygon and were trying to find its center of gravity. Here you say you have a set of points and you want to construct a non-intersecting polygon from it. Those are two quite different things. As I mentioned at math.SE, if the polygons are not known to be convex, a set of points doesn't uniquely define a polygon -- so the algorithm you propose here may construct some arbitrary non-self-intersecting polygon (I haven't checked whether it successfully does that) but that may or may not bear any relation to the polygon you were originally interested in. Or did I misunderstand your question at math.SE and you actually only have some points and want to construct just any non-self-intersecting polygon from them and don't care that there may be several inequivalent solutions for this?