Carving Polytopes with Saws in 3D
<|reference_start|>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.<|reference_end|>
@article{robson2024carving,
    title={Carving Polytopes with Saws in 3D},
    author={Eliot W. Robson and Jack Spalding-Jamieson and Da Wei Zheng},
    journal={arXiv preprint arXiv:2407.15981},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.15981},
    primaryClass={cs.CG}
}