Directly Visible Pairs and Illumination by Reflections in Orthogonal Polygons

Abstract: We consider direct visibility in simple orthogonal polygons and derive tight lower and upper bounds on the number of strictly internal and external visibility edges. We also show a lower bound of ⌈ⁿ⁄₂⌉-1 on the number of diffuse reflections required for completely illuminating an orthogonal polygon from an arbitrary point inside it. Further, we derive lower bounds on the combinatorial complexity of the visibility polygon of a point S after k ≥ 1 specular reflections within special classes of polygons.