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BibTeX entry
@Article{McGuire:2004:OSS,
author = "Morgan McGuire",
title = "Observations on Silhouette Sizes",
journal = j-J-GRAPHICS-TOOLS,
volume = "9",
number = "1",
pages = "1--12",
year = "2004",
CODEN = "JGTOFD",
ISSN = "1086-7651",
ISSN-L = "1086-7651",
bibdate = "Sat Dec 04 10:50:51 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
URL = "http://www.acm.org/jgt/papers/McGuire04/",
abstract = "Silhouettes have many applications in computer
graphics such as non-photorealistic edge rendering, fur
rendering, shadow volume creation, and anti-aliasing.
The number of edges, $s$, in the silhouette of a model
observed from a point is therefore useful in analyzing
such algorithms. \par
This paper examines, from a theoretical viewpoint, a
menagerie of objects with interesting silhouettes
(including those with minimal and maximal silhouettes).
It shows that the relationship between and $s$ and the
number of triangles in a model, $f$, is bounded above
by $s = O(f)$ and below by $s = \Omega(1)$, and that
the expected value of $s$ over all observation points
at infinity is proportional to the sum of the dihedral
angles. \par
In practice, the models used with silhouette-based
rendering algorithms are triangle meshes that are
manually constructed or result from scans of human-made
objects. They consist of only surface geometry with few
cracks; there is no internal detail like the engine
under a car's hood. Geometric and aesthetic constraints
on these models appear to create an inherent
relationship between $f$ and $s$. Measurements of the
actual silhouettes of real-world 3D models with polygon
counts varied across six orders of magnitude show them
to follow the relationship $s \sim f^{0.8}$.
Furthermore, the expected value of $s$ at infinity is a
good approximation of the expected silhouette size for
a viewer at a finite location.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
}
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