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Good Illumination of Minimum Range

M. Abellanas·A. Bajuelos·G. Hernández·F. Hurtado·I. Matos·B. Palop
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Abstract

A point p is 1-well illuminated by a set F of n point lights if p lies in the interior of the convex hull of F. This concept corresponds to triangle-guarding or well-covering. In this paper we consider the illumination range of the light sources as a parameter to be optimized. First, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate a given point p. We also compute a minimal set of light sources that 1-well illuminates p with minimum illumination range. Second, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate all the points of a line segment with an O(n^2) algorithm. Finally, we give an O(n^2 log n) algorithm for preprocessing the data so that one can obtain the illumination range needed to 1-well illuminate a point of a line segment in O(log n) time. These results can be applied to solve problems of 1-well illuminating a trajectory by approaching it to a polygonal path.

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M. Abellanas, A. Bajuelos, G. Hernández, F. Hurtado, I. Matos, B. Palop. 2006-06-02. Good Illumination of Minimum Range. https://arxiv.org/abs/cs/0606013

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