is defined to operate on two 2D curves
In order to appreciate the formulae which represent a superquadric, it is
necessary to introduce the notion of a spherical product. The spherical
product is defined to operate on two 2D curves
and results in a 3D surface.
Each 2D curve has one degree of freedom, so the resultant surface has 2 degrees of freedom.
We can think of the function 
as a horizontal curve which is
swept vertically according to the function 
.
scales , while
defines the vertical sweeping
motion. In this way, we see that the parameter 
affects the
surface horizontally, while 
affects the surface vertically.
By adding a scaling term for each spatial direction, we achieve a form with 5 degrees of freedom.
A simple example of a spherical product is a unit sphere (from which the term spherical product derives its name). Thinking in terms of the description above, a unit sphere is just a spherical product of a circle (horizontally) and a half circle (vertically).
The following sphere has been rendered according to this equation:
