Research articles
ScienceAsia 51S (2023): 1-11 |doi:
10.2306/scienceasia1513-1874.2023.s018
An algorithm for illuminating n non-overlapping circular
discs? boundaries on the plane with application to tree stem
illumination problem
Phapaengmuang Sukkasema, Supanut Chaideeb,*, Watit Khokthongc,d
ABSTRACT: Givenaset of nnon-overlapping circular discs on a plane, we aim to determine possible positions of points
(referred to as cameras) that could fully illuminate all the circular discs? boundaries. This work presents a geometric
approach for determining feasible camera positions that would provide total illumination of all circular discs. The
Laguerre Delaunay triangulation, coupled with the intersection of slabs formed by the boundaries of circular discs, is
employed to form the region that satisfies the given conditions. The experiment is conducted using a set of randomly
positioned circular discs on a plane. This study has the potential to address the issue of illumination in forests by
utilizing a terrestrial LiDAR to determine the possible number and placement of cameras that can effectively illuminate
tree stems within a forest.
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| a |
Program in Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University,
Chiang Mai 50200 Thailand |
| b |
Advanced Research Center for Computational Simulation (ARCCoS), Department of Mathematics, Faculty of
Science, Chiang Mai University, Chiang Mai 50200 Thailand |
| c |
Forest Restoration Research Unit, Department of Biology, Faculty of Science, Chiang Mai University,
Chiang Mai 50200 Thailand |
| d |
Environmental Science Research Centre, Faculty of Science, Chiang Mai University, Chiang Mai 50200 Thailand |
* Corresponding author, E-mail: supanut.c@cmu.ac.th
Received 1 Dec 2024, Accepted 0 0000
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