An Algorithm for Illuminating $n$ Nonoverlapping Circular Discs' Boundaries on the Plane with Application to Tree Stem Illumination Problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911131060142080 |
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| author | Sukkasem, Phapaengmuang Chaidee, Supanut Khokthong, Watit |
| author_facet | Sukkasem, Phapaengmuang Chaidee, Supanut Khokthong, Watit |
| contents | Given a set of $n$ nonoverlapping 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 LiDAR camera to determine the possible number and placement of cameras that can effectively illuminate trees within a forest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Algorithm for Illuminating $n$ Nonoverlapping Circular Discs' Boundaries on the Plane with Application to Tree Stem Illumination Problem Sukkasem, Phapaengmuang Chaidee, Supanut Khokthong, Watit Computational Geometry Given a set of $n$ nonoverlapping 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 LiDAR camera to determine the possible number and placement of cameras that can effectively illuminate trees within a forest. |
| title | An Algorithm for Illuminating $n$ Nonoverlapping Circular Discs' Boundaries on the Plane with Application to Tree Stem Illumination Problem |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2503.20440 |