[chombier]

From the documentation of the Eigen library [0]:

> If the quaternion is used to rotate several points (>1) then it is much more efficient to first convert it to a 3x3 Matrix. Comparison of the operation cost for n transformations:

> - Quaternion2: 30n

> - Via a Matrix3: 24 + 15n

So really it depends on what you're doing (admittedly here it is 3x3 not 4x4)

[0] https://eigen.tuxfamily.org/dox/classEigen_1_1QuaternionBase...

[banachtarski]

Right, as I said, composition is faster, not application.