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

Boris Aronov*, Robert Schiffenbauer, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

It is known that a general polyhedral scene of complexity n has at most O(n6) combinatorially different orthographic views and at most O(n9) 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(n4+ε) and O(n6+ε), for any ε>0, respectively. In addition, we present constructions inducing Ω(n4) combinatorially different orthographic views and Ω(n6) 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
Pages (from-to)179-192
Number of pages14
JournalComputational Geometry: Theory and Applications
Volume27
Issue number2
DOIs
StatePublished - Feb 2004

Funding

FundersFunder number
Israel Science FundCCR-00-98246, CCR-97-32101
National Science FoundationITR CCR-00-81964, CCR-99-72568
United States-Israel Binational Science Foundation
Tel Aviv University

    Keywords

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

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