Amp simulating and I/O curves - a bit for the experts

[Stealth]

For all you gentlemen who are in the know about how amps work, here's a naïve question.

Due to my recent university final project (which dealt with real-time software sound processing - basically, effects simulation) I've become interested in simulating amplifiers along with other effects.

Considering pretty much all amplifiers have nonlinear input-output curves (which lead to overdrive, pun not intended), I was wondering if anyone had any amplifier I/O curves to show how hard it would be to simulate an amplifier, whether it could be modeled via segmented linear responses or some more extreme, nonlinear functions. The only time I used something similar in my final B.Sc. project was a very simple overdrive model - used a normalized arctan curve to drive the signal (and it even worked well for a bass signal).

[bongomania]

Interesting approach. I would think an amp would have so many stages that the overall model would look more like a random squiggle than a "curve". But I'm not saying that from any expert position.