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

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.

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## 1 Answer

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

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It probably is the solution, but it is way beyond my math knowledge to understand it. I wonder if there is a simpler explanation. –  rwb Jan 28 '13 at 17:28
You do need to understand conformal mapping from Complex Analysis. But I know of no other solution in general. And it leads to nice integrals for the triangle. –  Ron Gordon Jan 28 '13 at 17:30
Also, I tried voting up your answer, but unfortunately I don't have enough points to do that yet. Sorry. –  rwb Jan 28 '13 at 17:46
@rwb: that's OK, try again later when you do. –  Ron Gordon Jan 28 '13 at 19:28