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Conference Papers Year : 2006

An Upper Bound on the Average Size of Silhouettes


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.

Dates and versions

inria-00095282 , version 1 (15-09-2006)



Marc Glisse. An Upper Bound on the Average Size of Silhouettes. 22nd ACM Symposium on Computational Geometry 2006, Jun 2006, Sedona, Arizona, United States. pp.105-111, ⟨10.1145/1137856.1137874⟩. ⟨inria-00095282⟩
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