3D Supershape

Over the last few years I was looking into the 3D Supershape formula described by Paul Bourke here and originally developed by Johan Gielis. I love the shape of the objects that are a result of those and therefore I always wanted to use it to create my own demos after I saw the one from Jetro Lauha (http://jet.ro/creations). Here is my first attempt to generate C source out of the equations:

Suitable C pseudo code could be:

float r = pow(pow(fabs(cos(m * o / 4)) / a, n2) + pow(fabs(sin(m * o / 4)) / b, n3), 1 / n1);

The result of this calculation is in polar coordinates. Please note the difference between the equation and the C code. The equation has a negative power value, the C doesn't. To extend this result into 3D, the spherical product of several superformulas is used. For example, the 3D parametric surface is obtained multiplying two superformulas S1and S2. The coordinates are defined by the relations:

The sphere mapping code uses two r values:

point->x = (float)(cosf(t) * cosf(p) / r1 / r2);
point->y = (float)(sinf(t) * cosf(p) / r1 / r2);
point->z = (float)(sinf(p) / r2);

Because r1 and r2 had a positive power value in the C code above we have to divide by those variables here. Here is a Mathematica render of this code: