用锯子雕刻 3D 多面体

arXiv - CS - Computational Geometry Pub Date : 2024-07-22 DOI:arxiv-2407.15981

Eliot W. Robson, Jack Spalding-Jamieson, Da Wei Zheng

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引用次数: 0

摘要

我们研究了利用一种工具来雕刻一个 $n$ 面的三角三维多面体的问题，该工具可以以半平面或无限射线扫描为模型进行切割。在半平面切割的情况下，我们提出了一种运行时间为 $O(n^2)$ 的确定性算法，以及一种运行时间为 $O(n^{3/2+\varepsilon})$ 的随机化算法，对于任意$\varepsilon>0$，预期时间均为 $O(n^{3/2+\varepsilon})$。对于由无限射线扫描定义的切割，我们提出了一种运行时间为 $O(n^5)$ 的算法。

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Carving Polytopes with Saws in 3D

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.

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arXiv - CS - Computational Geometry

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