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arXiv · 1906.07919

Existence of a Convex Polyhedron with Respect to the Given Radii

Supanut Chaidee·Kokichi Sugihara
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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.

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Supanut Chaidee, Kokichi Sugihara. 2019-06-19. Existence of a Convex Polyhedron with Respect to the Given Radii. https://doi.org/10.3390/math8040645

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