The purpose of the nonlinear image resizing tool is to help with times when you need to resize an image between aspect ratios. I've been using this sample wonder woman graphic for some of my other examples, and so we'll use it again here. Below is a shot of the original graphic:

The size of the original image is 747x923. That yields an aspect ratio of approximately 0.81:1, which is unsuitable for use as a desktop wallpaper.

Let's try a simple resize of the image without applying any nonlinear effects:

The image has been resized to 1024x768, and aspect ratio of 1.33:1. Notice how our wonder woman has become noticably fatter. This is because the picture had to be stretched horizontally.

Now let's try some linear effects:

Horiz Warp = 110	Horiz Warp = 130	Horiz Warp = 150

When we increase the horizontal warp (nonlinear factor), the wonder woman in the center of the picture squeezes down, and the edges of the picture begin to stretch. This allows us to take our original graphic that had an aspect ratio of 0.81:1 and turn it into a graphic of aspect ratio 1.33:1. The important details, the figure in the center of the image, are preserved and the less important details, the background, are sacrificed.