http://www.algorithmist.net/composite.html

Essentially Jim describes a more general version of the algorithm I’m using. In particular, rather than having the 1/3 value hardcoded (lines 35, 36), it can be used as a parameter corresponding to the tension of the interpolated curve. You can even animate this parameter if you want, which can create some really cool animations. Also, Jim describes how you can do the work with a less trig calls, using dot products if I remember correctly. In my scenario, most of the work was being spent in the physics engine, so it didn’t really matter, but if the bottleneck shifts, it can make a big speed difference.

That algorithm can be expanded to work not only with one dimensional lines, but also with lines that have a definite thickness. You can vary that thickness along the way. You can see this effect in the background of the top banner (the moving lines) here:

http://mercurycloud.com/