A Staircase Illuminator for Simply Connected Orthogonal Polygons

Abstract

Let $S$ be an orthogonal polygon in the plane bounded by a simple closed curve. Assume that every two boundary points of $S$ have a common staircase illuminator whose edges are north and east. Then $S$ contains a staircase path ${\mu }_0$ whose edges are north and east such that ${\mu }_0$ illumines every point of $S$. Without the requirement that the illuminators share a common direction, the result fails.