On lines avoiding unit balls in three dimensions

Pankaj K. Agarwal, Boris Aronov, Vladlen Koltun, Micha Sharir

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Let B be a set of n unit balls in ℝ3. We show that the combinatorial complexity of the space of lines in ℝ3 that avoid all the balls of B is O(n3+ε), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning and geometric optimization.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
    Pages36-45
    Number of pages10
    StatePublished - 2004
    EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
    Duration: Jun 9 2004Jun 11 2004

    Other

    OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
    CountryUnited States
    CityBrooklyn, NY
    Period6/9/046/11/04

    Fingerprint

    Ray Shooting
    Geometric Optimization
    Combinatorial Complexity
    Motion Planning
    Motion planning
    Visibility
    Unit ball
    Three-dimension
    Ball
    Line

    Keywords

    • Combinatorial complexity
    • Lines in space
    • Visibility

    ASJC Scopus subject areas

    • Software
    • Geometry and Topology
    • Safety, Risk, Reliability and Quality
    • Chemical Health and Safety

    Cite this

    Agarwal, P. K., Aronov, B., Koltun, V., & Sharir, M. (2004). On lines avoiding unit balls in three dimensions. In Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) (pp. 36-45)

    On lines avoiding unit balls in three dimensions. / Agarwal, Pankaj K.; Aronov, Boris; Koltun, Vladlen; Sharir, Micha.

    Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. p. 36-45.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Agarwal, PK, Aronov, B, Koltun, V & Sharir, M 2004, On lines avoiding unit balls in three dimensions. in Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). pp. 36-45, Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States, 6/9/04.
    Agarwal PK, Aronov B, Koltun V, Sharir M. On lines avoiding unit balls in three dimensions. In Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. p. 36-45
    Agarwal, Pankaj K. ; Aronov, Boris ; Koltun, Vladlen ; Sharir, Micha. / On lines avoiding unit balls in three dimensions. Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04). 2004. pp. 36-45
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