On the number of views of translates of a cube and related problems

Boris Aronov, Robert Schiffenbauer, Micha Sharir

    Research output: Contribution to journalArticle

    Abstract

    It is known that a general polyhedral scene of complexity n has at most O(n 6) combinatorially different orthographic views and at most O(n 9) combinatorially different perspective views, and that these bounds are tight in the worst case. In this paper we show that, for the special case of scenes consisting of a collection of n translates of a cube, these bounds improve to O(n 4+ε) and O(n 6+ε), for any ε>0, respectively. In addition, we present constructions inducing Ω(n 4) combinatorially different orthographic views and Ω(n 6) combinatorially different perspective views, thus showing that these bounds are nearly tight in the worst case. Finally, we show how to extend the upper and lower bounds to several classes of related scenes.

    Original languageEnglish (US)
    Pages (from-to)179-182
    Number of pages4
    JournalComputational Geometry: Theory and Applications
    Volume27
    Issue number2
    DOIs
    StatePublished - Feb 2004

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    Regular hexahedron
    Upper and Lower Bounds
    Class

    Keywords

    • Arrangements
    • Aspect graphs
    • Combinatorial geometry
    • Envelopes
    • Fat objects
    • Orthographic views
    • Perspective views
    • Polyhedral terrains
    • Visibility

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Science Applications
    • Computational Mathematics
    • Control and Optimization
    • Geometry and Topology

    Cite this

    On the number of views of translates of a cube and related problems. / Aronov, Boris; Schiffenbauer, Robert; Sharir, Micha.

    In: Computational Geometry: Theory and Applications, Vol. 27, No. 2, 02.2004, p. 179-182.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Schiffenbauer, Robert ; Sharir, Micha. / On the number of views of translates of a cube and related problems. In: Computational Geometry: Theory and Applications. 2004 ; Vol. 27, No. 2. pp. 179-182.
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