It's just the 2D rotation matrix in complex number form ... into the W and X components of a quaternion we would get a rotation of 90 degrees around the X axis. If we did this same exercise with other ...

Knowing the axis and angle of a rotation $\left\langle \theta, x, y, z\right\rangle$, we can convert it to a ... e_3\right\rangle$ representing the orientation of a given solid, the 3x3 matrix ...