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On the Number of Views of Polyhedral Scenes

  • Boris Aronov
  • Hervé Brönnimann
  • Dan Halperin
  • Robert Schiffenbauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2098)

Abstract

It is known that a scene consisting of k convex polyhedra of total complexity n has at most O(n 4 k 2) distinct orthographic views, and that the number of such views is Ω((nk 2+n 2)2) in the most case. The corresponding bounds for perspective views are O(n 6 k 3) and Ω((nk 2+n 2)3), respectively. In this papers, we close these gaps by improving the lower bounds. We construct an example of a scene θ(n 4 k 2) orthographic views, and another with θ(n 6 k 3) 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.

Keywords

Lower Bound Problem Complexity Computer Graphic Algorithm Analysis Discrete Mathematic 
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 Berlin Heidelberg 2001

Authors and Affiliations

  • Boris Aronov
    • 1
  • Hervé Brönnimann
    • 1
  • Dan Halperin
    • 2
  • Robert Schiffenbauer
    • 1
  1. 1.Polytechnic UniversityBrooklynUSA
  2. 2.Tel-Aviv UniversityTel-AvivIsrael

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