Composite Bézier curve

In geometric modelling and in computer graphics, a composite Bézier curve is a piecewise Bézier curve that is at least continuous. In other words, a composite Bézier curve is a series of Bézier curves joined end to end where the last point of one curve coincides with the starting point of the next curve. Depending on the application, additional smoothness requirements (such as C1 or C2 continuity) may be added.

A continuous composite Bézier is also called a polybezier, by similarity to polyline, but whereas in polylines the points are connected by straight lines, in a polybezier the points are connected by Bézier curves. A beziergon (also called bezigon) is a closed path composed of Bézier curves. It is similar to a polygon in that it connects a set of vertices by lines, but whereas in polygons the vertices are connected by straight lines, in a beziergon the vertices are connected by Bézier curves. Some authors even call a C0 composite Bézier curve a "Bézier spline"; the latter term is however used by other authors as a synonym for the (non-composite) Bézier curve, and they add "composite" in front of "Bézier spline" to denote the composite case.

Perhaps the most common use of composite Béziers is to describe the outline of each letter in a PostScript or PDF file. Such outlines are composed of one beziergon for open letters, or multiple beziergons for closed letters. Modern vector graphics and computer font systems like PostScript, Asymptote, Metafont, OpenType, and SVG use composite Bézier curves composed of cubic Bézier curves (3rd order curves) for drawing curved shapes.

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