Image Warping Using Conformal Mapping
This Demonstration shows how an image in the complex plane is transformed under a conformal mapping, using several simple complex functions. Use the "function" popup menu to select the complex function. Click the panel on the left or drag the locator to change the translation point.
The point in the initial image on the left corresponds to the complex number . The function converts to with and , which is plotted on the complex plane on the right.
Conformal mapping using an analytic function preserves angles locally, at any point where the function has a nonzero derivative.