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Discrete & Computational Geometry

, Volume 12, Issue 2, pp 177–182 | Cite as

On the number of views of polyhedral terrains

  • P. K. Agarwal
  • M. Sharir
Article

Abstract

We show that the number of topologically different orthographic views of a polyhedral terrain withn edges isO(n 5+ɛ ), and that the number of topologically different perspective views of such a terrain isO(n 8+ɛ ), for any ɛ>0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in higher dimensions.

Keywords

Discrete Comput Geom Open Region Surface Patch Perspective View Critical Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • P. K. Agarwal
    • 1
  • M. Sharir
    • 2
    • 3
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.School of Mathematical SciencesTel Aviv UniversityRamat AvivIsrael
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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