I'm using a series of easing equations to make menus and transitions a little more interesting in my first game. That got me thinking about how game objects (enemies, NPCs, spaceships, whatever) are 'scripted' to move along complex paths. I'm no maths guy, but I've read that paths can be plotted using Bezier curves (define 2+ control points, interpolate to get position values using start, change and duration values). However I'm not exactly sure how to best go about this (in a structured way that works for a variety of different motions).
I already have a bunch of tweening functions, but these are relatively simple linear, quadratic and cubic curves.
An example - say I wanted enemies to appear at a certain point, then spin in an archimedes spiral until they were off-screen. How would this be best accomplished, and indeed, made generic enough so that another enemy of the same type could move along a sin wave-esque path instead?