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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 ...
In computer graphics, free-form deformation (FFD) is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another hull object, and transforming the object within the hull as the hull is deformed.
The smooth portions of a curve are then approximated with a Bézier curve fitting procedure. Successive division may be used. Such a fitting procedure tries to fit the curve with a single cubic curve; if the fit is acceptable, then the procedure stops. Otherwise, it selects some advantageous point along the curve and breaks the curve into two ...
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value.
Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 February 2025. Computer graphics images defined by points, lines and curves This article is about computer illustration. For other uses, see Vector graphics (disambiguation). Example showing comparison of vector graphics and raster graphics upon magnification Vector graphics are a form of computer ...
For Bézier curves, it has become customary to refer to the -vectors in a parametric representation of a curve or surface in -space as control points, while the scalar-valued functions , defined over the relevant parameter domain, are the corresponding weight or blending functions.
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.