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Is there a way to verify whether a non-empty intersection exists between two simple polygons (not necessarily convex) using the Chazelle's simplicity test ?

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Perhaps connecting the two polygons together by a "bridge" to form one polygon might allow Chazelle's algorithm to answer the question. But: Are you interested in this for theoretical purposes, or for pragmatic reasons? If the latter, it would be far easier to use a plane-sweep algorithm than it would be to implement Chazelle's algorithm. – Joseph O'Rourke Dec 20 '10 at 15:43

Independent of Chazelle, a discussion of the case of intersecting convex polygons can be found at:

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Yes, although note that the convex-convex case is very special and will not help much for two simple polygons. – Joseph O'Rourke Dec 20 '10 at 15:36

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