Minimum Area All-flush Triangles Circumscribing a Convex Polygon

12/14/2017

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by   Kai Jin, et al.

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In this paper, we consider the problem of computing the minimum area triangle that circumscribes a given n-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of n half-planes defined by a given convex polygon. Previously, O(n n) time algorithms were known which are based on the technique for computing the minimum weight k-link path given in kgon94,kgon95soda. By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygonal inclusion problems. Our algorithm actually computes all the local minimal area circumscribing triangles touching edge-to-edge.