Superquadrics

This app displays a set of geometric shapes called 'superquadrics'. Superquadrics are shapes that are defined by mathematical formulas.

Superquadrics can resemble a variety of simple geometric shapes. This app can generate circles, cones, cubes, cylinders, lozenges, octahedrons, rectangular prisms, spheres, and squares. These shapes appear when specific values for m and n are chosen in the app.

The shape can be morphed by swiping the borders of the app window or by entering values using the menus. The shape can be rotated and stretched by touch.

Concretely, this app graphs the following set of parametric equations:

pows(x, n) = sign(x) * abs(x) ^ n

Fx(u,v) = pows(cos(v), n) * pows(cos(u),m)

Fy(u,v) = pows(cos(v), n) * pows(sin(u), m)

Fz(u,v) = pows(sin(v), n)

Where u and v are parametric variables, and m and n are constants that you can adjust.

You can read a bit more about superquadrics on wikipedia:

http://en.wikipedia.org/wiki/Superquadrics