ENERGY-AWARE STAGE ILLUMINATION

Abstract

Consider the following illumination problem: given a stage represented by a line segment L and a set of light sources represented by a set of points S in the plane, assign powers to the light sources such that every point on the stage receives a sufficient amount – e.g. one unit – of light while minimizing the overall power consumption. Under the assumption that the amount of light arriving from a fixed light source decreases rapidly with the distance from the light source, this becomes an interesting optimization problem. We propose to reconsider the classical illumination problems as known from computational geometry literature under this light attenuation model. This paper examines the simple problem introduced above and presents different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided.