The arc is essentially a section of a great circle on a sphere.  http://en.wikipedia.org/wiki/Great_circle gives some information on it. In terms of actually drawing, consider doing a series of rotations such that the xy plane is aligned with the great circle, and then you can just use an arc() call. If I sound vague, it's intentional :)

Thanks for the tip! I watched the video again and it doesn't seem like the arcs are based on circles or spheres. They look like bezier curves.. I'm going to try and experiment with those. I'll post code if it works.

That's a good point; that's probably also much easier than what I was thinking.