The Bezier Curve
The study of Bezier curves falls under the general topic of curve fitting, however, these curves really do not have much scientific purpose. That is, given some data points, a scientist would not use Bezier curves to approximate a function definition for the data. Rather, Bezier curves have more of an artistic purpose. Originally used by car designers to create pleasant looking curves, these methods are now used by graphics artists in many fields where the generation of curved shapes is a necessity.
What follows are some links to further your understanding of Bezier curves. By the way, you can change the above animation slightly by clicking somewhere in the middle of it.