Zone theorem for arrangements in dimension three (Q2234787)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zone theorem for arrangements in dimension three |
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Zone theorem for arrangements in dimension three (English)
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19 October 2021
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The zone theorem is a statement about the complexity of regions of a real hyperplane arrangement, which is a fundamental tool in computational geometry. The author provides a proof of the zone theorem in dimensions two and three, which is essentially a simplified version of the proof given by \textit{H.\ Edelsbrunner} et al. [SIAM J.\ Comput. 22, No. 2, 418--429 (1993; Zbl 0778.52007)]. The proof in dimension three employs a deletion-restriction argument to use the zone theorem in dimension two.
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computational geometry
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zone theorem
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arrangements
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