According to this textbook, the following superquadric equation describes the 3D surface of a unit sphere:
$$ S(\theta, \phi) = \begin{bmatrix} \cos(\theta) \cos(\phi); \\ \cos(\theta) \sin(\phi); \\ \sin(\theta) \end{bmatrix} $$
S(,) comes from the spherical product between two 2D surfaces h() and m():
$$ m(\theta) = [\cos(\theta); \sin(\theta)], \quad -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} $$
$$ h(\phi) = [\cos(\phi); \sin(\phi)], \quad -\pi \leq \phi \leq \pi $$
The textbook doesn't fully explain the detailed breakdown of $S(,)$. I would like to know how all the terms in $S(,)$ are found, specially if there is an actual "spherical product" formula.