For the un-initiated, Bezier Curves are curves defined by a set of (at least 2) points in space (usually defined by x and y coordinates). By setting appropriate sets of points, complex curving paths can easily be defined. These could be simply drawn to the screen or used as paths for visual objects (eg a game character) to follow.

The simplest case is a curve defined by 2 points – which is just a straight line. As more points are added the curvature can become more complex. The curveTo method of the Graphics class uses a Bezier Curve of 3 points (1 point defined by the current drawing position and 2 points passed into the method).

So, if we want to draw a 2 or 3 point Bezier Curve, Flash can do the work for us, but for 4 points or more we need to handle it ourselves. Also, if we are using a Bezier Curve as a path for an object to follow, we need to know the coordinates at all positions along the path and the drawing methods of Flash wont help us with that.
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