We used quaternions in our engine back in 2005-2008. Compared to matrix multiplications, multiplying quaternions was cheaper so we could save a few instructions here and there. But I never used them since.
One reason being, I suppose, processors are now much more superscalar-friendly so a matrix multiplication doesn't take much more time than a quaternion multiplication does. And with matrices, you get the whole package: not only rotations, but translations, scalings, and even projections, - all in one go. So you have simpler code, simpler data structures, and you don't lose performance so... why bother?
I didn't even include quaternions in my book. Well, not that I didn't want to. We had a whole discussion with the publisher about whether we should keep the whole chapter (complex numbers, conformal transformations, non-commutative 3D rotations, and quaternions) and I lost.
One reason being, I suppose, processors are now much more superscalar-friendly so a matrix multiplication doesn't take much more time than a quaternion multiplication does. And with matrices, you get the whole package: not only rotations, but translations, scalings, and even projections, - all in one go. So you have simpler code, simpler data structures, and you don't lose performance so... why bother?
I didn't even include quaternions in my book. Well, not that I didn't want to. We had a whole discussion with the publisher about whether we should keep the whole chapter (complex numbers, conformal transformations, non-commutative 3D rotations, and quaternions) and I lost.