Triangles in space or Building (and analyzing) castles in the air

Boris Aronov, Micha Sharir

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

    Abstract

    We show that the combinatorial complexity of all non-convex cells in an arrangement of n (possibly intersecting) triangles in 3-space is O(n7/3+δ), for any δ>0, and that this bound is almost tight in the worst case. Our bound significantly improves a previous nearly cubic bound of Pach and Sharir. We also present a (nearly) worst-case optimal randomized algorithm for calculating a single cell of the arrangement, analyze some special cases of the problem where improved bounds (and better algorithms) can be obtained, and describe applications of our results to translational motion planning for polyhedra in 3-space.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988
    PublisherAssociation for Computing Machinery, Inc
    Pages381-391
    Number of pages11
    ISBN (Electronic)0897912705, 9780897912709
    DOIs
    StatePublished - Jan 6 1988
    Event4th Annual Symposium on Computational Geometry, SCG 1988 - Urbana-Champaign, United States
    Duration: Jun 6 1988Jun 8 1988

    Other

    Other4th Annual Symposium on Computational Geometry, SCG 1988
    CountryUnited States
    CityUrbana-Champaign
    Period6/6/886/8/88

    Fingerprint

    Triangle
    Arrangement
    Combinatorial Complexity
    Motion Planning
    Cell
    Randomized Algorithms
    Optimal Algorithm
    Polyhedron

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    Aronov, B., & Sharir, M. (1988). Triangles in space or Building (and analyzing) castles in the air. In Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988 (pp. 381-391). Association for Computing Machinery, Inc. https://doi.org/10.1145/73393.73432

    Triangles in space or Building (and analyzing) castles in the air. / Aronov, Boris; Sharir, Micha.

    Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988. Association for Computing Machinery, Inc, 1988. p. 381-391.

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

    Aronov, B & Sharir, M 1988, Triangles in space or Building (and analyzing) castles in the air. in Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988. Association for Computing Machinery, Inc, pp. 381-391, 4th Annual Symposium on Computational Geometry, SCG 1988, Urbana-Champaign, United States, 6/6/88. https://doi.org/10.1145/73393.73432
    Aronov B, Sharir M. Triangles in space or Building (and analyzing) castles in the air. In Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988. Association for Computing Machinery, Inc. 1988. p. 381-391 https://doi.org/10.1145/73393.73432
    Aronov, Boris ; Sharir, Micha. / Triangles in space or Building (and analyzing) castles in the air. Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988. Association for Computing Machinery, Inc, 1988. pp. 381-391
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