I'm starting to learn more about quaternions and its geometric meaning in the world of computer graphics.

From reading a borrowed book late in the night, I recall that one of its geometric meaning is that it can rotate a model once by an arbitrary axis spherically.

Can it allow affine transformation, so that a vertex V_{n} in an object space be rotated by a point (x + O_{1}, y + O_{2}, z + O_{3}), where (O_{1}, O_{2}, O_{3}) is the object space origin, and V_{n} is one of the vertices in a vertex buffer object?

Unless I have to re-borrow the book again...