A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere
<|reference_start|>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.<|reference_end|>
@article{flemming2024a,
    title={A simple linear time algorithm for smallest enclosing circles on the
  (hemi)sphere},
    author={Jens Flemming},
    journal={arXiv preprint arXiv:2407.19840},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.19840},
    primaryClass={cs.CG math.MG math.OC}
}