# angle axis sequence

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Hey, folks. I'm working on a system that uses angle/axis pairs as its main rotation representation. I'm looking for a forumla that will give a final angle/axis pair that represents 2 applied in sequence: FinalRotation = Rotation1*Rotation2; Currently, I convert the angle/axis to quaternion form, do the multiplication there, then convert back angle/axis. This works, but it seems carry a bit more baggage than I was hoping for and am looking for a direct solution. Right now I'm in the process of combining all of the terms of the conversions and multiplications to see if I can reduce them or replace them with identities, but this is looking like it's not worth much. Has anyone solved this or seen the solution?

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You might find this article interesting; it's a discussion of the various ways of representing rotation and orientation, and their respective strengths and weaknesses.

In short, axis-angle pairs may not be the best fundamental representation to use. They are difficult to interpolate and concatenate, and (like quaternions) you usually have to convert them to matrices at some point anyway. Unless you have some really compelling reason to stick with axis-angle, I'd use quaternions or matrices instead.

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Now that is a very good article. Eberly is a good guy. I actually took the conversions between angle/axis and quaternions from his book. If he didn't document a way to compose two angle axis pairs, then I strongly doubt there is one at this time.

I don't have a lot of choice in the matter, as it's not my system. I'm on the client side. Internally it uses angle/axis, so I have to give them back to it.

Thanks, jyk.

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