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Given two frames, is it possible to compute any rotation of the form

$$R = R_xR_yR_z $$

that would tranform the frame $A$ into the frame $B$? the rotation will be described by Euler angles as I need to quantify the rotation on each axis.

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    Yes, this might be relevant for you: http://math.stackexchange.com/questions/66649/3-rotations-to-unit-vector-3d/67162#671622011-12-02

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