Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917144892014592 |
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| author | Barequet, Gill Har-Peled, Sariel |
| author_facet | Barequet, Gill Har-Peled, Sariel |
| contents | $\renewcommand{\Re}{\mathbb{R}}$We present an efficient $O (n + 1/\varepsilon^{4.5})$-time algorithm for computing a $(1+\varepsilon$)-approximation of the minimum-volume bounding box of $n$ points in $\Re^3$. We also present a simpler algorithm (for the same purpose) whose running time is $O (n \log{n} + n / \varepsilon^3)$. We give some experimental results with implementations of various variants of the second algorithm. The implementation of the algorithm described in this paper is available online https://github.com/sarielhp/MVBB. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions Barequet, Gill Har-Peled, Sariel Computational Geometry $\renewcommand{\Re}{\mathbb{R}}$We present an efficient $O (n + 1/\varepsilon^{4.5})$-time algorithm for computing a $(1+\varepsilon$)-approximation of the minimum-volume bounding box of $n$ points in $\Re^3$. We also present a simpler algorithm (for the same purpose) whose running time is $O (n \log{n} + n / \varepsilon^3)$. We give some experimental results with implementations of various variants of the second algorithm. The implementation of the algorithm described in this paper is available online https://github.com/sarielhp/MVBB. |
| title | Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2512.12391 |