A new O(n·log n) algorithm for computing the intersection of convex polygons

摘要

We present a new O(n·log n) algorithm for computing the intersection of a set of arbitrary (possibly unbounded) polygons, where n is the total number of edges in the polygons. An interesting property of this algorithm is that if the intersection is empty, then the algorithm finds a minimal set of at most three polygons whose intersection is empty. The algorithm is based on a simple technique for detecting a redundant inequality among a set of inequalities of two variables.