Another way of creating 3D models is by using parametric surfaces. A parametric surface is described by a function of two variables u and v that evaluates to a x,y,z coordinate. The function f(u,v) can then, by sweeping u and v over a range, generate points that can be connected to a mesh of small triangles.

An example is a flat plane given by:

x = u

y = v

z = 0

for u = [0,1] and v=[0,1]

This yields a small flat square (rather dull to look at).

More interesting are parametric surfaces that sweep through all three coordinates, x,y,z.

This formula is a the formula for a torus:

x = (0.7+0.3*cos(v))*cos(u)

y = (0.7+0.3*cos(v))*sin(u)

z = 0.3*sin(v)

for u = [0, 2*pi] and v = [0, 2*pi]

And the resulting image (using a glass material):