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openglquaternionseuler-anglesrotational-matrices

How to obtain axis-angle from rotation matrix?

I need to obtain some data from an openGL rotation matrix. I need to obtain the equivalent euler angles (already did it), the equivalent quaternion (did it, but just copying it from the Internet) and the equivalent axis-angle.

I dont know if a rotation matrix can be expresed as a single rotation of a certain angle around an certain vector. Are these equivalent? If they are, how can I obtain one from the other?

Also, i would like to understand better the meaning of a quaternion, and the insides of a rotation matrix. Where should i go to learn about this?

Solution

  • Yes any rotation matrix/unit quaternion is equivalent to a rotation around a single axis. If we call this axis n and the angle theta then the quaternion for this rotation is:

    [n * sin(theta / 2) cos(theta / 2)]

    To reconstruct this use acos on the w element of the quaternion to get theta / 2. After you have theta you can divide x,y and z component with sin(theta / 2) to reconstruct the axis.