@techreport{Flemming2024,
  type      = {Working Paper},
  author    = {Flemming, Jens},
  title     = {A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere},
  publisher = {arXiv},
  doi       = {10.48550/arXiv.2407.19840},
  institution = {Physikalische Technik, Informatik},
  pages     = {13},
  year      = {2024},
  abstract  = {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.},
  language  = {en}
}