stuff snipped > >Rotations in two dimensions are nicely represented by multiplication by >e^i(theta). But in three dimensions you need quarternions, and then the >object you are rotating is three dimensional, but the object representing the >rotation is four-dimensional. So things don't seem so nice. > >Does anyone have good ways to present or exploit the fact that rotations in >three dimensions are not commutative?
I've noticed over in comp.graphics.algorithms there has from time to time been a discussion of using quaterions for describing rotations as a great way of doing some of the 'magic' you see in the latest 3-d games, etc. Perhaps an ask over there or a check of the FAQ would be fruitful. I have been intrigued myself, but just haven't had the time to take on YAP (yet another project) :-).