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.

Eric Haines identified the following typographic errors in this paper after publication:

1. In the Figure 8 caption, f and s are swapped. The second sentence should read, "The dashed blue line is the s=f^1/2 trend for convex models and the thick red line is the s=0.7f^0.8 trend observed over all data."
2. In the Figure 9 caption, f and s are swapped. The second and third sentences should read, "The dashed blue lines are (from bottom to top): s=f^1/2, s =f^3/4, and s = f. The data (except for some outliers due to malformed meshes) lies between the outermost lines, clustered around the thick red trendline s = 0.7f^0.8."

@article{ mcguire04silhouette,
  author = "Morgan McGuire",
  title = "Observations on Silhouette Sizes",
  journal = "jgt",
  volume = {9},
  number = {1},
  pages = {1--12},
  year = {2004},
  URL = {http://graphics.cs.williams.edu/papers/SilhouetteJGT04/}
}