I think that the "super-ellipse" has more generalized, elaborate mathematics, than the squircle script.
(The squircle is a subset of the super-ellipse...)
(I like Burr's method, for the Cab.)

The squircle shape for the outline of the gem is nice.
The lower portions of the Cab gem seem to vary, and are important for mounting...
Read that the bottom is often not polished, for light reasons, and can be flat or rounded.
It is difficult to cut, for perfect symmetry. Have not seen the special tool machine which could be used...

- Brian