Parametrizing a 3D surface onto a 2D plane is a challenging task. I became interested in
it because it is the basis for many interesting mesh compression and reconstruction / remeshing
algorithms. The work of

Floater,

Hoppe and

Hormann is among the most impressive
in this field. I implemented a simple iterative approximation of

Tutte's barycentric mapping. I plan on
using this code as the basis for various projects like surface smoothing, compression, tesselation
and LOD generation.

This survey
by Floater / Hormann is a very good introduction to the field.