A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere
- Based on Welzl's algorithm for smallest circles and spheres we develop a simple linear time algorithm for finding the smallest circle enclosing a point cloud on a sphere. The algorithm yields correct results as long as the point cloud is contained in a hemisphere, but the hemisphere does not have to be known in advance and the algorithm automatically detects whether the hemisphere assumption is met. For the full-sphere case, that is, if the point cloud is not contained in a hemisphere, we provide hints on how to adapt existing linearithmic time algorithms for spherical Voronoi diagrams to find the smallest enclosing circle.
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| Author: | Jens Flemming |
|---|---|
| DOI: | https://doi.org/10.48550/arXiv.2407.19840 |
| Publisher: | arXiv |
| Document Type: | Working Paper |
| Language: | English |
| Year of first Publication: | 2024 |
| Page Number: | 13 |
| Note: | Referenz (Hochschulbibliographie), kein Volltext |
| Faculty: | Westsächsische Hochschule Zwickau / Physikalische Technik, Informatik |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| Open Access: | open_access |
| Release Date: | 2025/05/06 |
| Licence (German): |  Creative Commons 4.0 International - Namensnennung |
