Maximal visibility and unions of orthogonally starshaped sets

Abstract

Let S be an orthogonal polygon in the plane. For each point x in S,let denote the set of points which x sees via staircase paths and let (Error rendering LaTeX formula) . For S simply connected, S is starshaped via staircase paths (i.e., orthogonally starshaped) if and only if S contains exactly one such closed set , and when this occurs is the staircase kernel of S. In general, if S contains exactly k such distinct closed set , then S is a union of k (or possibly fewer) orthogonally starshaped sets chosen from .