Existence of a Convex Polyhedron with Respect to the Given Radii
Computational Geometry
2025-08-22 v1
Abstract
Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the two-dimensional case is proved when radii are distinct or repeated at most four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.
Keywords
Cite
@article{arxiv.1906.07919,
title = {Existence of a Convex Polyhedron with Respect to the Given Radii},
author = {Supanut Chaidee and Kokichi Sugihara},
journal= {arXiv preprint arXiv:1906.07919},
year = {2025}
}
Comments
This paper is submitting to the journal 'Discrete and Computational Geometry'