An algorithm to find maximum area polygons circumscribed about a convex polygon

摘要

A convex polygon Q is circumscribed about a convex polygon P if every vertex of P lies on at least one side of Q. We present an algorithm for finding a maximum area convex polygon circumscribed about any given convex n-gon in O(n(3)) time. As an application, we disprove a conjecture of Farris. Moreover, for the special case of regular n-gons we find an explicit solution. (C) 2018 Elsevier B.V. All rights reserved.