Bezier curves are really cool and fun to learn. I actually had built an Impact.js bezier tool plugin for a shmup I was working on a while ago: https://github.com/dclowd9901/impactjsBezier

I did different things like toy with caching movement on the curve, having constant speed on the path, etc. There's even a bit of calculus in there, in estimating the length of the curve.