For your viewing pleasure

https://vimeo.com/106757336

That's pretty well done.

I don't think it's mentioned anywhere but what he's describing is known as "de Casteljau's algorithm".  Interestingly Paul de Casteljau seems to have investigated these sorts of curves a few years before Pierre Bezier did but since he didn't publish his  work we'll never know.

For the (masochistically) mathematically inclined here's a *really* great page on what they are and how they work and how to do all manner of things with them

http://pomax.github.io/bezierinfo/

My brain hurts