An upper bound on the average size of silhouettes

Authors:
Marc Glisse
Affiliations:
LORIA, Nancy, France
Venue:
Proceedings of the twenty-second annual symposium on Computational geometry
Year:
2006

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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(√n) where the average is taken over all points of view and n is the complexity of the polyhedron.