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In my situation, I have two completely different Quaternions and an arbitrary axis. What I need to find is the difference of rotation around that axis.

For example, if both quaternions had the axis (0, 0, 1) and different rotations, and my axis is (1, 0, 0), then there is no difference in rotation.

How can I do that with quaternions of different axis?

Thanks in advance.

Daniel Hurtado Ramirez
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    Can you clarify what what you mean by difference of rotation around that axis? What does this mean if they're not both rotations around that axis? – Kimball Jun 12 '16 at 09:34
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    My guess is by "axis" you are referring to the invariant (Euler) axis of the rotation (same as pure axis of the quaternion). Then you mention you have an "arbitrary" axis which I'm guessing is in 3-space. As @Kimball says, you need to explain what you mean by "difference of rotation" about the 3-space axis. Your example makes no sense to me. Explain what you mean by difference of rotation; perhaps you can include a better description of the application? – JMJ Jun 13 '16 at 18:42
  • The quaternions tag inspires more half-baked/incomprehensible questions than any other tag I pay attention to. I suppose that's a natural result of the quaternions both being an essential tool and being poorly understood at the same time. – rschwieb Jun 15 '16 at 15:55
  • Come to think of it though, most of the fogginess of these questions seem to come from geometry rather than the quaternions, so maybe $\Bbb H$ is really not the culprit. – rschwieb Jun 15 '16 at 15:58

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