jgt 2004

Observations on Silhouette SizesMorgan McGuire

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.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

sand the number of triangles in a model,f, is bounded above byand below by s = O(f)s = Ω(1), and that the expected value ofsover 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

fands. Measurements of the actual silhouettes of real-world 3D models with polygon counts varied across six orders of magnitude show them to follow the relationships ~ f. Furthermore, the expected value of^{0.8}sat infinity is a good approximation of the expected silhouette size for a viewer at a finite location.

Some images from the paper

@article{ mcguire04silhouette, author = "Morgan McGuire", title = "Observations on Silhouette Sizes", journal = "jgt", volume = {9}, number = {1}, pages = {1--12}, year = {2004}, URL = {http://www.cs.brown.edu/research/graphics/games/SilhouetteSize/index.html} }

HindsightsThe following previous work is relevant: Kettner and Welz Contour Edge Analysis for Polyhedron Projections. In: W. Strasser, R. Klein, R. Rau (Eds.), Geometric Modeling: Theory and Practice, Springer, pp. 379-394, 1997. (Thanks to Aaron Hertzman for pointing out this book chapter to me).

Kettner and Welz give a sphere proof and experimental results for polyhedral models in categories like "terrain" and "anatomy." My paper follows a similar theory/practice structure and extends their results. I begins with a simpler polygonal case derivation and proofs of the upper and lower bounds on silhouette (contour) size. For experimental analysis I benefitted from the incredible speedup of PCs over the last decade. I was able to perform a much more computationally intensive task than Kettner and Welz by working with a larger, albeit heterogeneous, data set and exhaustively measuring results for infinite (orthogonal) and finite viewpoints from many angles and distances.