Line transversals of balls and smallest enclosing cylinders in three dimensions

P. K. Agarwal, Boris Aronov, M. Sharir

    Research output: Contribution to journalArticle

    Abstract

    We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions, and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

    Original languageEnglish (US)
    Pages (from-to)373-388
    Number of pages16
    JournalDiscrete and Computational Geometry
    Volume21
    Issue number3
    StatePublished - 1999

    Fingerprint

    Transversals
    Approximation algorithms
    Three-dimension
    Ball
    Computing
    Line
    Set of points
    Approximation Algorithms
    Upper bound

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Discrete Mathematics and Combinatorics
    • Geometry and Topology

    Cite this

    Line transversals of balls and smallest enclosing cylinders in three dimensions. / Agarwal, P. K.; Aronov, Boris; Sharir, M.

    In: Discrete and Computational Geometry, Vol. 21, No. 3, 1999, p. 373-388.

    Research output: Contribution to journalArticle

    Agarwal, P. K. ; Aronov, Boris ; Sharir, M. / Line transversals of balls and smallest enclosing cylinders in three dimensions. In: Discrete and Computational Geometry. 1999 ; Vol. 21, No. 3. pp. 373-388.
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