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On the Number of Cylindrical Shells

Olivier Devillers 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Given a set $P$ of $n$ points in three dimensions, a cylindrical shell or zone cylinder is formed by two cylindrical cylinders with the same axis such that all points of $P$ are between the two cylinders. We prove that the number of cylindrical shells enclosing $P$ passing through combinator- ially different subsets of $P$ has size $\Omega(n^3)$ and $O(n^4)$ (previous known bound was $O(n^5)$).
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Submitted on : Tuesday, May 23, 2006 - 8:30:13 PM
Last modification on : Friday, February 4, 2022 - 3:18:47 AM
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  • HAL Id : inria-00072353, version 1

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Olivier Devillers. On the Number of Cylindrical Shells. RR-4234, INRIA. 2001. ⟨inria-00072353⟩

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