I want to construct the minimal convex hull of some n points such that the hull is a regular polygon of degree n. Math friends, pointers? :)
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"convex hull" is a misnomer, based on your description. It sounds like you actually want the minimal circumscribing n-gon.
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It's necessarily at least as big as the diameter of the set (which you can get by walking the vertices of the convex hull).
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Yep, I see that! Not sure how to construct the n-gon from there.