Carving Polytopes with Saws in 3D
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913441705361408 |
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| author | Robson, Eliot W. Spalding-Jamieson, Jack Zheng, Da Wei |
| author_facet | Robson, Eliot W. Spalding-Jamieson, Jack Zheng, Da Wei |
| contents | We investigate the problem of carving an $n$-face triangulated three-dimensional polytope using a tool to make cuts modelled by either a half-plane or sweeps from an infinite ray. In the case of half-planes cuts, we present a deterministic algorithm running in $O(n^2)$ time and a randomized algorithm running in $O(n^{3/2+\varepsilon})$ expected time for any $\varepsilon>0$. In the case of cuts defined by sweeps of infinite rays, we present an algorithm running in $O(n^5)$ time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Carving Polytopes with Saws in 3D Robson, Eliot W. Spalding-Jamieson, Jack Zheng, Da Wei Computational Geometry We investigate the problem of carving an $n$-face triangulated three-dimensional polytope using a tool to make cuts modelled by either a half-plane or sweeps from an infinite ray. In the case of half-planes cuts, we present a deterministic algorithm running in $O(n^2)$ time and a randomized algorithm running in $O(n^{3/2+\varepsilon})$ expected time for any $\varepsilon>0$. In the case of cuts defined by sweeps of infinite rays, we present an algorithm running in $O(n^5)$ time. |
| title | Carving Polytopes with Saws in 3D |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2407.15981 |