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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 ...
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The geometry of a single bicubic patch is thus completely defined by a set of 16 control points. These are typically linked up to form a B-spline surface in a similar way as Bézier curves are linked up to form a B-spline curve. Simpler Bézier surfaces are formed from biquadratic patches (m = n = 2), or Bézier triangles.
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 ...
Approximation of sinc function constructed with Bezier splines Image title The sinc function (sin(x)/x) approximated with cubic bezier splines (and 1 line segment) for svg.
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English: Rational Bezier curve - polynomial curve defined in homogeneous coordinates (blue) and its projection on plane - rational curve (red) Polski: Wymierna krzywa beziera - na niebiesko zaznaczono krzywą wielomianową określoną we współrzędnych jednorodnych, na czerwono krzywą wymierną - rzut środkowy krzywej wielomianowej na ...
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