A Bézier curve is a type of parametric curve that is used in computer graphics and related applications. The curves, which are connected to Bernstein polynomials, are called for French engineer Pierre Bézier, who used it to develop curves for the bodywork of Renault vehicles in the 1960s. Other applications include the creation of computer typefaces and animation. Bézier curves can be coupled to create a Bézier spline, or they can be extended to higher dimensions to create Bézier surfaces. The Bézier triangle is a subset of the latter.
Bézier curves are used in vector graphics to describe smooth curves that may be scaled endlessly. Paths, as they are generally called to in picture editing software, are collections of connected Bézier curves. Paths are not constrained by the limitations of rasterized pictures and are simple to change.
This also applies to robotics where the motion of a welding arm, for example, should be smooth to avoid unnecessary wear.