I have to conformally map an image, from a disc to a rectangle.
Image - disc to rectangle transformation

The circle in the attached image can be considered as a disc with an inner radius of zero. The red line in the image marks the start, and the blue line marks the end.
I've tried using AffineTransform in Java, but it doesn't allow you to define custom transformations. Can someone help me tackle this problem?
You only need to transform from polar to cartesian coordinates.
Example code is provided on mindprod page.
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