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Mar 21, 2013 at 18:04 comment added Ben McKay In posing the question, Forrest pointed out that there are only two quaternions representing a given rotation, i.e. he already thought about the universal covering space of $SO(3)$ and noticed that it doesn't do what he wants.
Mar 21, 2013 at 3:41 history answered P Vanchinathan CC BY-SA 3.0