The orthogonal convex skull problem

Abstract

We give a combinatorial definition of the notion of a simple orthogonal polygon being k-concave, where k is a nonnegative integer. (A polygon is orthogonal if its edges are only horizontal or vertical.) Under this definition an orthogonal polygon which is 0-concave is convex, that is, it is a rectangle, and one that is 1-concave is orthoconvex in the usual sense, and vice versa. Then we consider the problem of computing an orthoconvex orthogonal polygon of maximal area contained in a simple orthogonal polygon. This is the orthogonal version of the potato peeling problem. An O(n2) algorithm is presented, which is a substantial improvement over the O(n7) time algorithm for the general problem. © 1988 Springer-Verlag New York Inc.