Table of Contents## Bézier Curves

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Arcs can be characterized as clean and functional, but one would rarely use the word “graceful” to describe them. If you want graceful, you need to use curves which are produced by graphing quadratic and cubic equations. Mathematicians have known about these curves for literally hundreds of years, but drawing them was always a computationally demanding task. This changed when Pierre Bézier, working for French car manufacturer Rénault and Paul de Casteljau, an engineer for Citroën, independently discovered a computationally convenient way to generate these curves.

If you have used graphics programs like Adobe Illustrator, you draw these Bézier curves by specifying two points and then moving a “handle” as shown in the following diagram. The end of this handle is called the control point, because it controls the shape of the curve. As you move the handle, the curve changes in a way that, to the uninitiated, is completely mystifying. Mike Woodburn, a graphic designer at Key Point Software, suggests Figure 6-6 as a way to visualize how the control point and the curve interact: imagine that the line is made of flexible metal. Inside the control point is a magnet; the closer a point is to the control point, the more strongly it is attracted.