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 Θ-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 O(n) time. For the second and given a fixed angle Θ ≤ π, we present a linear time algorithm to minimize the lights’ illumination range to well Θ-illuminate a point.

DOI: 10.1007/978-3-540-74472-6_1

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Cite this paper

@inproceedings{Abellanas2007SomePR, title={Some Problems Related to Good Illumination}, author={Manuel Abellanas and Ant{\'o}nio Leslie Bajuelos and In{\^e}s Matos}, booktitle={ICCSA}, year={2007} }