> (*) Of course, he's speaking of quaternions as implemented in the software 
> library he's describing. I don't know how general this usage is.

They are used a lot in 3D animation for two main reasons.  One is that if 
you are realistically simulating forces on 3D bodies then it makes the 
rotation maths very simple, and avoids all the problems you get with using 
Euler angles or matrices.  The other is that it is much simpler to 
interpolate between two quaternions (than two rotation matrices or two sets 
of Euler angles) so that you get a correct and valid rotation at each point 
(eg rotating a camera or interpolating key frames).

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