# Conformal mapping of images

1. Jul 11, 2011

### Avijeet

Hi everybody,

I was looking at the following link:
http://www.dimensions-math.org/Dim_CH5_E.htm

The section 6 deals with conformal mapping of the image for different kinds of transformations. I tried to reproduce them in mathematica for the transformation $z \rightarrow z^2$.
I followed the following algorithm:
1. Take an image and obtain the values for all pixels, say (x,y)=0.2.
2. Then I transformed the coordinates according to the transformation $(x,y)\rightarrow (x^2-y^2, 2xy)$.
3. The previously stored pixel values are now assigned to these new coordinates.
4. Get the new image.

The problem I am facing is that the dimension of the image changes from $m \times n \rightarrow m^2 \times n^2$ after the transformation. But I know the pixel values for only m n points. Thus I don't have enough points to generate the final image.

Can you suggest a way out of this difficulty or any other algorithm to generate the images.