Bézier curve en · NOUN
Pronunciation
- /ˈbɛz.i.eɪ/
Etymology
Probably a calque of French courbe de Bézier. Named after Renault engineer Pierre Bézier who popularized the curves developed earlier by Paul de Casteljau and used them to design curves for the bodywork of cars.
Meanings
-
A type of parametric curve defined by a set of control points, two of which are the ends of the curve, while the others determine its shape.
When an affine transformation is applied to the control points, the resulting Bézier curve with respect to the new control points coincides with the transformed Bézier curve. Therefore, Bézier curves are invariant under affine transformations like rotation, translation or scaling. Bézier curves are also symmetric with respect to their control points.
2012, Frank Klawonn, Introduction to Computer Graphics: Using Java 2D and 3D, 2nd edition, Springer, page 151:Bézier curves are applied, for example in computer graphics and animation, to produce smooth, infinitely scalable curves.
So, instead, it is often better to combine multiple Bézier curves to form a longer, more complicated curve called a piecewise Bézier curve. This section discusses how to join Bézier curves together – especially how to join them so as to preserve continuity and smoothness (i.e., continuity of the first derivative).
2003, Samuel R. Buss, 3D Computer Graphics: A Mathematical Introduction with OpenGL, Cambridge University Press, page 163:The initial points p₀, p₁, and p₂ are called control points of the Bézier curve.[…]The process outlined above for the generation of a quadratic Bézier curve from its three control points can be generalized for more control points in a straightforward manner.
2008, T. Theoharis, G. Papaioannou, N. Platis, N. M. Patrikalakis, Graphics & Visualization: Principles and Algorithms, Taylor & Francis (A K Peters / CRC Press), page 193:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Bézier curves | Number=Plur | lexicographic |
Relateds
composite Bézier curve · bezier · spline · Bernstein form · Bézier spline · Bézier surface · control point · Bézier triangle · Bézier coefficient
Synonyms
Translations (10)
fr courbe de Bézier (kind of parametric curve) · fi Bézier-käyrä (kind of parametric curve) · ja ベジェ曲線 (kind of parametric curve) · sv Bézier-kurva (kind of parametric curve) · cs Bézierova křivka (kind of parametric curve) · it curva di Bézier (kind of parametric curve) · cmn 貝茲曲線 /贝兹曲线 (kind of parametric curve) · es curva de Bézier (kind of parametric curve) · de Bézierkurve (kind of parametric curve) · ru крива́я Безье́ (kind of parametric curve)