Separating two simple polygons by a sequence of translations

Abstract

Let P and Q be two disjoint simple polygons having m and n sides, respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mnα(mn) log m log n) where α(k) is the extremely slowly growing inverse Ackermann's function. Since in the worst case Ω(mn) translations may be necessary to separate Q from P, our algorithm is close to optimal. © 1988 Springer-Verlag New York Inc.