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On the Size of the 3D Visibility Skeleton: Experimental Results

  • Linqiao Zhang
  • Hazel Everett
  • Sylvain Lazard
  • Christophe Weibel
  • Sue Whitesides
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

Abstract

The 3D visibility skeleton is a data structure used to encode global visibility information about a set of objects. Previous theoretical results have shown that for k convex polytopes with n edges in total, the worst case size complexity of this data structure is Θ(n 2 k 2) [Brönnimann et al. 07]; whereas for k uniformly distributed unit spheres, the expected size is Θ(k) [Devillers et al. 03].

In this paper, we study the size of the visibility skeleton experimentally. Our results indicate that the size of the 3D visibility skeleton, in our setting, is \( C\,k\sqrt{n\,k}\), where C varies with the scene density but remains small. This is the first experimentally determined asymptotic estimate of the size of the 3D visibility skeleton for reasonably large n and expressed in terms of both n and k. We suggest theoretical explanations for the experimental results we obtained. Our experiments also indicate that the running time of our implementation is O(n 3/2 klogk), while its worst-case running time complexity is O(n 2 k 2 logk).

Keywords

Visibility Complex Input Scene Support Edge Sweep Plane Support Vertex 
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 2008

Authors and Affiliations

  • Linqiao Zhang
    • 1
  • Hazel Everett
    • 2
  • Sylvain Lazard
    • 2
  • Christophe Weibel
    • 3
  • Sue Whitesides
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada
  2. 2.INRIA Nancy Grand EstUniversité Nancy 2, LORIANancyFrance
  3. 3.Math DepartmentMcGill UniversityMontrealCanada

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