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Keywords = spherical Laguerre Voronoi diagram

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13 pages, 1704 KiB  
Article
The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms
by Supanut Chaidee and Kokichi Sugihara
Mathematics 2020, 8(4), 645; https://doi.org/10.3390/math8040645 - 22 Apr 2020
Cited by 2 | Viewed by 4152
Abstract
Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. [...] Read more.
Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, 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. Full article
(This article belongs to the Special Issue Modern Geometric Modeling: Theory and Applications)
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