Bézier curve

Cubic Bézier curve with four control points The basis functions on the range t in [0,1] for cubic Bézier curves: blue: y = (1 − t), green: y = 3(1 − t)t, red: y = 3(1 − t)t, and cyan: y = t. A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay, French pronunciation: [bezje]) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape that otherwise has no mathematical representation or whose representation is unknown or too complicated. The Bézier curve is named after French engineer Pierre Bézier (1910–1999), who used it in the 1960s for designing curves for the bodywork of Renault cars. Other uses include the design of computer fonts and animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is a special case of the latter.

In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limits of rasterized images and are intuitive to modify.