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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05661 |
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| _version_ | 1866909068722962432 |
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| author | Espinoza, Jesús F. Esquer-Pérez, Cynthia G. |
| author_facet | Espinoza, Jesús F. Esquer-Pérez, Cynthia G. |
| contents | In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the Čech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection properties of finite disk collections Espinoza, Jesús F. Esquer-Pérez, Cynthia G. Computational Geometry 68U05, 65D17, 05E45 In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the Čech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system. |
| title | Intersection properties of finite disk collections |
| topic | Computational Geometry 68U05, 65D17, 05E45 |
| url | https://arxiv.org/abs/2401.05661 |