An Upper Bound on the Average Size of Silhouettes

Details An Upper Bound on the Average Size of Silhouettes An Upper Bound on the Average Size of Silhouettes

2007-02-14

arxiv.org/abs/cs/0702087v1

Computer Science

Computational Geometry

Scientific paper

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 be non-convex and non-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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