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Bezier curves are mathematical expressions used to describe curves in two or three dimensions. All fonts, excluding bitmap fonts, use bezier curves to describe the character shapes. Because the curves are mathematical they have the advantage of being infinitely scaleable. Therefore, a character described in bezier curves can be resized to any size without losing quality. Bezier curves are sometimes referred to a "vector graphics", contrasting with bitmaps which are called "raster graphics". Some software that authors vector graphics are the following: Adobe Illustrator, Macromedia Freehand, Macromedia Flash, Deneba Canvas, Corel Draw, Fontographer and FontLab.
Bezier curves consist of two anchor points and any number of control points. Curves with one control point are called quadratic curves because the forumla used to calculate them is based on a quadratic equation. Curves with two control points are referred to as cubic curves. TrueType fonts use quadratic curves, while Type 1 fonts use cubic curves. While curves may use more control points, they are not used commonly in type rendering technology. Because quadratic curves are more difficult to work with (mostly because it's harder to make circles), most vector authoring software uses cubic curves with two control points. What's more, it is a simple operation to convert cubic curves to quadratic. However, it is not possible to convert quadratic curves to cubic without some approximation.