Computing Visibility Information in an Inaccurate Simple Polygon

Abstract

This paper is concerned with the problem of capturing meaningful and useful visibility information inside a simple polygon given only an inaccurate representation of the vertices of the polygon. We introduce a notion of a visibility skeleton of an inaccurate representation of a simple polygon. We show that in most cases the visibility skeleton of a representation can be computed efficiently; furthermore, the visibility skeleton can be used to plan a collision-free path inside the polygon whose length approximates the length of a shortest such path to within a constant factor (independent of the number of vertices in the polygon).