Good Illumination of Minimum Range
M. Abellanas, A. Bajuelos, G. Hern\'andez, F. Hurtado, I. Matos, B., Palop

TL;DR
This paper investigates optimizing the illumination range of point lights to ensure a point or line segment is 1-well illuminated, providing algorithms for minimal range and efficient querying.
Contribution
It introduces algorithms for minimizing light source range for 1-well illumination of points and segments, including preprocessing for fast range queries.
Findings
O(n^2) algorithm for segment illumination
Minimal illumination range computation for a point
Preprocessing enables O(log n) query time
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…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Computer Graphics and Visualization Techniques · Remote Sensing and LiDAR Applications
