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A Bézier curve is a curved line or path that is the result of a mathematical equation called a parametric function. It is commonly implemented in computer graphics, such as vector imaging, which uses quadratic and cubic Bézier curves. Graphics software programs often come with tools that generate and manipulate Bézier curves, typically with control handles that can control the shape, size and orientation of the curves.
Curve representation became necessary in graphics technology for the purposes of mechanical engineering largely during the 1950s and '60s. In 1962, an engineer by the name of Pierre Bézier (working for the Renault car company) published research that led to significant enhancements in computer-aided design (CAD), such as generating graphics through linear interpolation (the principal concept underlying Bézier curves).
A French physician and mathematician by the name of Paul De Casteljau worked on similar research concurrently with Bézier. However, Bézier’s research was published first, so he is often credited with the earliest implementations of this technology.