Minimum Illumination Range Voronoi Diagrams∗

The MIR Voronoi diagram appears with the notion of good illumination introduced in [3, 4]. This illumination concept generalizes well-covering [7] and triangle guarding [9]. The MIR Voronoi diagram merges the notions of proximity and convex dependency. Given a set S of planar light sources, for each point q in the plane we search for the subset Sq ⊂ S nearest to q and such that q is an interior point of the convex hull of Sq. The furthest point to q in Sq is called the Minimum Illumination Range point (MIR point) of q with respect to S. The MIR Voronoi diagram splits the interior of the convex hull of S into several regions, associating each point in S to its MIR point. This diagram is motivated by optimization problems on good illumination.