Here’s a class that will do that for you. It uses a “Catmull-Rom” spline (named after its inventors), which draws directly through any number of points.

It’s not a spectacular or pretty looking curve. It’s very “dowdy”, and somewhat ugly, but it doesn’t make wild swinging curves like many other equations. This humble quality makes it really good for situations where it’s important that the curve stays pretty close to the control points.

Example SWF (actionscript code)

CatmullRom curve actionscript class