How to map points in a unit square to a regular polygon?

Question

I have a set of points in a unit square $x = [-1,1]$ and $y = [-1,1]$ and I want to remap them to their equivalent points in a regular polygon ($n \geq 3$; Triangle and so on).

I've found a really good article on mapping a unit square to a unit circle http://mathproofs.blogspot.com/2005/07/mapping-square-to-circle.html

But, I couldn't figure out mapping it to a polygon.

Answer 1

Maybe you've heard of the Schwarz-Christoffel mapping? It takes the upper half-plane in $\mathbb{C}$ to a polygon.