Companion

Right-handed axis-angle rotation. The axis must be finite and nonzero; the angle is in radians.

Reject zero and non-finite quaternions; finite nonzero components are normalized.

Shortest rotation from one finite nonzero direction to another; magnitudes are ignored. Parallel directions return identity. Opposite directions use from crossed with the coordinate axis whose absolute component in from is smallest (ties prefer X, then Y, then Z). This antiparallel axis is deterministic, but no continuous choice exists around that case.