There is another way that is both easier to understand and provides you with more insights into what rotation is really about. Instead of specifying a rotation by a series of canonical angles, we will specify an arbitrary axis of rotation and an angle. We will also first consider rotating vectors, and come back to points shortly.

The vector a specifies the axis of rotation. This axis vector must be normalized. The rotation angle is given by q.

You might ask "How am I going to remember this equation?". However, once you understand the geometry of rotation, the equation will seem obvious.

The basic idea is that any rotation can be decomposed into weighted contributions from three different vectors.