Some problems related to good illumination

Abstract

A point p is 1-well illuminated by a set of n point lights if there is, at least, one light interior to each half-plane with p on its border. We consider the illumination range of the lights as a parameter to be optimized. So we minimize the lights' illumination range to 1-well illuminate a given point p. We also present two generalizations of 1-good illumination: the orthogonal good illumination and the good ⊖-illumination. For the first, we propose an optimal linear time algorithm to optimize the lights' illumination range to orthogonally well illuminate a point. We present the E-Voronoi Diagram for this variant and an algorithm to compute it that runs in σ(n4) time. For the second and given a fixed angle ⊖ ≤ π, we present a linear time algorithm to minimize the lights' illumination range to well ⊖-illuminate a point. © Springer-Verlag Berlin HeidelBerg 2007.