Thin plate spline

A thin plate spline is a way to "bend" a flat surface into the shape of something else. It works like this: First, you draw a flat surface (like a piece of paper). Then, you put a bunch of points on that surface. Finally, you draw curves connecting all of the points. The way the curves are drawn is determined by a special equation that makes sure that the bends are smooth and even. The end result is a curved surface that looks like whatever you wanted it to look like originally.