An Upper Bound on the Average Size of Silhouettes
<|reference_start|>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 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.<|reference_end|>
@article{glisse2007an,
    title={An Upper Bound on the Average Size of Silhouettes},
    author={Marc Glisse (INRIA Lorraine - LORIA), Sylvain Lazard (INRIA Lorraine -
  LORIA)},
    journal={arXiv preprint arXiv:cs/0702087},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702087},
    primaryClass={cs.CG}
}