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Hello, I have an orientation P1 in a 3D space, represented as a quaternion [w x y z]. Then P1 is rotated using another quaternion (q1) with the formula

P2=q1*P1*q1'


Is there any formula in order to get q1 from P2 and P1?

Thank you.

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closed as too localized by Igor Rivin, Anton Petrunin, Qiaochu Yuan, Deane Yang, Will Jagy Apr 15 '11 at 17:38

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What is an "orientation"? –  Igor Rivin Apr 15 '11 at 15:20
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1 Answer 1

I am not sure what the OP means by "orinentation", but if the question is about the rotation of one (unit) vector into another, the axis of such a rotation is the cross product of the two vectors (assumed unit) and the angle is the arccos of the scalar product. You can then read off the quaternion. See:

http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

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