The part that is less efficient is applying a rotation to a vector (you need to "sandwich multiply" by your quaternion which involves 3×4 + 4×4 = 28 multiplications, whereas with a matrix you only need 3x3 = 9 multiplications).
But composing, interpolating, exponentiating, etc. is a lot nicer with quaternions. (Easier to reason about, numerically better behaved, computationally cheaper.)
If you need to apply the same rotation to a large number of separate vectors, keep your rotation representation as a quaternion internally and convert to a matrix just before vector rotation.
But composing, interpolating, exponentiating, etc. is a lot nicer with quaternions. (Easier to reason about, numerically better behaved, computationally cheaper.)
If you need to apply the same rotation to a large number of separate vectors, keep your rotation representation as a quaternion internally and convert to a matrix just before vector rotation.