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The Number of Cylindrical Shells

Olivier Devillers 1
1 GEOMETRICA - Geometric computing
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 combinatorially different subsets of P has size Omega(n^3) and O(n^4) (previous known bound was O(n^5) ).
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Olivier Devillers. The Number of Cylindrical Shells. Discrete and Computational Geometry, Springer Verlag, 2003, 30 (3), pp.453-458. ⟨10.1007/s00454-003-2818-8⟩. ⟨inria-00090638⟩



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