Existence of a Convex Polyhedron with Respect to the Given Radii
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866908497166204928 |
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| author | Chaidee, Supanut Sugihara, Kokichi |
| author_facet | Chaidee, Supanut Sugihara, Kokichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_07919 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Existence of a Convex Polyhedron with Respect to the Given Radii Chaidee, Supanut Sugihara, Kokichi Computational Geometry 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. |
| title | Existence of a Convex Polyhedron with Respect to the Given Radii |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/1906.07919 |