Pierre Bézier worked as an engineer for the Renault car company. In the late 1960s he conceived a new curve formulation to represent 3D car body forms on computers.
Bézier curves, in their two-dimensional form, are now the basis of almost all common graphics programs (such as Adobe Illustrator and Corel Draw), following their adoption as the standard curve of the PostScript language. Most outline fonts, including TrueType and PostScript Type 1 (but not Ikarus) are stored as Bézier curves.
The standard Bézier curve, used throughout PostScript and in many drawing programs, is a parametric cubic (or third order) curve defined by its two end-points and two control-points, which in general are not on the curve. As well as other characteristics, the control-points define the tangents of the curve as it leaves the two end-points. A Bézier curve always remains inside a polygon drawn around all of its points (the “convex hull”).
The curves of TrueType are a quadratic (second order) version of Bézier curves, having two end-points but only one off-curve control-point. The single off-curve point then defines both tangent vectors, while the curve remains within the triangular convex hull.