Many techniques exist for the decomposition and simplification of 3D polygonal meshes. These ideas are useful for a number of applications, including levels-of-detail representations and geometry storage, transmission, and compression. Recently a paper by Stephan Bischoff and Leif Kobbelt was published about a technique of model decomposition using ellipsoids. I plan to look into this technique further and attempt to come up with heuristics for better decompositions using techniques other than those presented. Some ideas include using non-greedy randomized algorithms for decomposition.
S. Bischoff, L. Kobbelt. Ellipsoid decomposition of 3D-models, 3DPVT proceedings, 480-488, 2002.
Jianhua Wu, Leif Kobbelt. Fast Mesh Decimation by Multiple-Choice Techniques, to appear in Vision, Modeling, Visualization 2002 Proceedings.
D. Zorin, et al. Subdivision for Modeling and Animation, SIGGRAPH 00 Course Notes.