The superformula can be turned into a 3d object (Supershape) using the spherical product of two superformulas.
When applying a toroidal rather than a spherical mapping, various kinds of donut-shaped forms result (Superdonuts). Things get even more twisted, if you add some torsion to the toroidal tube. Now you can create variations of the moebius strip and the umbilic torus.
If you gradually change the radius and the diameter of the toroidal tube, as well as the offset along the rotation axis, a variety of shell-like forms arise.
The superduperformula is a unified formula that allows for the creation of all kinds of 3d-objects described above. You can also chose the parameters to extrude a thin strip rather than a completely closed tube. By adding a twist and some additional rotations, you can obtain a closed torus covered by a moebius strip.
[h] help panel on/off
[i] info panel on/off
[p] param info: shape info / render info
[x] xchange help and info panels
[m] mode : lores/dynamic/hires
[c] color on/off
[l] lighting on/off
[g] grid view / surface view
[space] next shape
[u] undo (reset shape params)
[o] output mesh or image
Use the mouse while pressing one of the param keys to change shape parameters. The mapping of param keys to shape parameters is always displayed inside the help panel.
The mouse is used for navigation and for changing shape params. The effect of each mouse button is always displayed inside the help panel.
There is no supershape file format, but if you happen to find a supershape that you like, you can always reconstruct it by directly entering the supershape parameters.
Once you have obtained a shape you like, you can: