Conformal Mapping

Conformal mapping generates different effects based on functions of a complex variable. Complex numbers have a real and imaginary part which may be thought of as x and y coordinates. A complex function maps one complex number to another. These mappings have interesting mathematical properties such as preserving the angles between intersecting lines, but mostly they are a way to achieve some unusual distortions. Each mathematical function has its own special character which is best discovered by experimentation.

                     Input Image                                         Mapped Using 1/z

When you start up the Conformal Mapping transformation, it displays an overlay over the input image window consisting of a control point to set the center of the image. You can drag this to a different location to offset the input coordinates to the complex function.

The output image created by this transformation is always the same size as the input image.

Type

This control lets you select the mathematical function to use for the mapping. Each function has its own unique look.

Tile

Tiling can be either on or off. When it is on, the input image is treated as though it covers the entire x-y plane by being replicated ad infinitum. This setting produces some very striking effects. If tiling is off, any coordinates that fall outside the input image simply show up as black.

Pre- and Post-Magnification

These sliders let you scale the coordinates entering the mapping and exiting the mapping. The results of the two are somewhat different and both are worth experimenting with.

Antialias

This control lets set the antialiasing level. The higher the value, the more accurate the result image but the longer it takes to compute.