Can be written in the form
$$
\mathbf{q} = \left[ \begin{array}{c}
\cos\theta \ \mathbf{u} \sin\theta
\end{array} \right]
$$
with
$\mathbf{u}$ as a unit vector
$\theta$ is the angle between $\mathbf{q}$ and the
identity quaternion
$\mathbf{q}_I = \left[\begin{array}{cccc}1 & 0 & 0 & 0\end{array}\right]^\text{T}$
