On the number of views of polyhedral scenes

Boris Aronov, Hervé Brönnimann, Dan Halperin, Robert Schiffenbauer

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

    Abstract

    It is known that a scene consisting of A- convex polyhedra of total complexity n has at most 0(n4 k2) distinct orthographic views, and that the number of such views is Ω((nk2 + n2)2) in the worst case. The corresponding bounds for perspective views are 0(n6 k3) and Ω((nk2+n2)3), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with Ө(n4 k2) orthographic views, and another with Ө(n6 k3) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.

    Original languageEnglish (US)
    Title of host publicationDiscrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers
    EditorsJin Akiyama, Mikio Kano, Masatsugu Urabe
    PublisherSpringer Verlag
    Pages81-90
    Number of pages10
    ISBN (Print)9783540477389
    DOIs
    StatePublished - 2001
    EventJapanese Conference on Discrete and Computational Geometry, JCDCG 2000 - Tokyo, Japan
    Duration: Nov 22 2000Nov 25 2000

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2098
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    OtherJapanese Conference on Discrete and Computational Geometry, JCDCG 2000
    CountryJapan
    CityTokyo
    Period11/22/0011/25/00

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Aronov, B., Brönnimann, H., Halperin, D., & Schiffenbauer, R. (2001). On the number of views of polyhedral scenes. In J. Akiyama, M. Kano, & M. Urabe (Eds.), Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers (pp. 81-90). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2098). Springer Verlag. https://doi.org/10.1007/3-540-47738-1_6