In my current project, I am drawing Bézier curves in code rather than using MovieClip.curveTo(), thanks to the bug I wrote about back in May. Since I’m doing it in code myself, I thought I might as well use cubic Béziers (four control points) rather than Flash’s quadratic curves (only three control points). Plus, for the application in question, cubics just seemed to make more sense.
I found this helpful article, “Derivation of Incremental Forward-Difference Algorithm for Cubic Bezier Curves using the Taylor Series Expansion for Polynomial Approximation”. That title is quite a mouthful, but the upshot is it shows how to use only additions while drawing the curve, instead of a bunch of multiplications, for faster drawing time.