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.

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 = Ω(1)*, and that the
expected value of *s* over all observation points at infinity is proportional
to the sum of the dihedral angles.

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 ~ 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.