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The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
from Wikimedia Commons plot-range: -25/12pi to 25/12pi plotted with three different cubic bezier-curves the bezier-controll-points are calculated to give a very accurate result. symbols in "Computer Modern" (TeX) font embedded created with a plain text editor using GNU/Linux
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English: Quadratic Bézier spline approximation (in red) overlayed on a black circle of radius 112 units, with tangent (on-curve) control points drawn as squares and off-curve control points drawn as circles. The spline's on-curve control points are placed at the circle's horizontal and vertical tangent points and at displacements (79, 79) from ...
English: Cubic Bézier spline approximation (in red) overlayed on a black circle of radius 112 units, with tangent (on-curve) control points drawn as squares and off-curve control points drawn as circles. The spline's on-curve control points are placed at the circle's horizontal and vertical tangent points.
English: Illustration of use of cubic Bezier splines to smooth a polyline, based on algorithm at . The different colours indicate different "curviness" values (black lowest and red highest). The different colours indicate different "curviness" values (black lowest and red highest).