Numerical Stability

This issue came up at work today, I thought ya /prog/ peeps might have some info.

So what do ya'll know about the numerical stability of rotations with, matrices, euler angles, and quaterions.

Also what do you know about the methods for interpolating rotations, and which method maintains numerical stability across the interpolation operation.

Wow stupidity is rampant here. Floating point numbers are real numbers but they can't represent all real numbers, they have huge inherent imprecision. We cannot represent with full accuracy an irrational number on the computer, the only numbers we can actually represent with full accuracy are a subset of the rational numbers.

There is no bijection between Math and CS, they just collide.

It's a waste of time explaining the obvious to /prog/