How to automatically choose a camera viewing angle for any 3D model
blog.cubehero.com
blog.cubehero.com
However, it can oversimplify for objects which are significantly asymmetrical. A good place to go from here is statistical measures of object recognizability:
Betke & Makris, Information-Conserving Object Recognition.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.4...
For 3D models, you can use hierarchical space carving to simplify the mesh first. You don't need great resolution, you just need better resolution than a rectangular bounding box.
(Note: PCA can be used for recognizability, but is not ideal. Highish complexity & overly general.)
Maximizing the entropy of projected normals works well, for example, like this paper by Polonsky et al.: http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Oleg/Polon...
A related problem is automatically figuring out the "natural orientation" of a mesh, so your automatic renderings don't look upside down by accident. Fu et al. use pretty simple machine learning tools: http://www.cs.ubc.ca/nest/imager/tr/2008/upright_orientation...
PCA is often overused but for this specific use case it seems very well suited.