An Upper Bound on the Average Size of Silhouettes
Computational Geometry
2009-09-29 v1
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 be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size where the average is taken over all points of view and n is the complexity of the polyhedron.
Cite
@article{arxiv.cs/0702087,
title = {An Upper Bound on the Average Size of Silhouettes},
author = {Marc Glisse and Sylvain Lazard},
journal= {arXiv preprint arXiv:cs/0702087},
year = {2009}
}