Taking 3D rotations into log space gets tricky. 3D rotation is not commutative, so if you have two quaternions Q and R, you can’t in general say that QR = exp(l

Taking 3D rotations into log space gets tricky. 3D rotation is not commutative, so if you have two quaternions Q and R, you can’t in general say that QR = exp(log(Q))exp(log(R)) = exp(log(Q) + log(R)). That identity only holds if the bivector (“imaginary”) parts of Q and R are oriented the same way in space, i.e. are scalar multiples of each-other. Otherwise in general exp(log(Q))exp(log(R)) ≠ exp(log(R))exp(log(Q)). The log space version is still useful though if you want to e.g. take the nth root of a spatial rotation.