Illuminating Rectangles and Triangles in the Plane

Abstract

A set S of light sources, idealized as points, illuminates a collection F of convex sets if each point in the boundary of the sets of F is visible from at least one point in S. For any n disjoint plane isothetic rectangles, └(4n + 4)/3┘ lights are sufficient to illuminate their boundaries. If, in addition, the rectangles have equal width, then n + 1 lights always suffice and n - 1 are occasionally necessary. For any family of n plane triangles, └(4n + 4)/3┘ light sources are sufficient and n - 1 are occasionally necessary. © 1993 by Academic Press, Inc.