An algorithm for recognizing palm polygons

Abstract

A polygon P is said to be a palm polygon if there exists a point x6P such that the Euclidean shortest path from x to any point y e P makes only left turns or only right turns. The set of all such points x is called the palm kernel. In this paper we propose an O(E) time algorithm for recognizing a palm polygon P, where E is the size of the visibility graph of P. The algorithm recognizes the given polygon P as a palm polygon by computing the palm kernel of P. If the palm kernel is not empty, P is a palm polygon.