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 \(\mathcal{O}(n^4)\) 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.
When this paper was finished, the third author was supported by a FCT fellowship, grant SFRH/BD/28652/2006.
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Abellanas, M., Bajuelos, A., Matos, I. (2007). Some Problems Related to Good Illumination. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74472-6_1
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DOI: https://doi.org/10.1007/978-3-540-74472-6_1
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