An Upper Bound on the Average Size of Silhouettes

Marc Glisse 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides for the first time theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may not be convex or differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size \(O(\sqrt{n})\) where the average is taken over all points of view and \(n\) is the complexity of the polyhedron.
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Submitted on : Friday, September 15, 2006 - 2:23:55 PM
Last modification on : Thursday, January 11, 2018 - 6:20:14 AM


  • HAL Id : inria-00095282, version 1



Marc Glisse. An Upper Bound on the Average Size of Silhouettes. 22nd ACM Symposium on Computational Geometry 2006, Jun 2006, Sedona, Arizona, USA. ⟨inria-00095282⟩



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