Bézier curve
A Bézier curve is a parametric equation which describes a curve.
Contents
Description
Bézier curves are frequently used in computer graphics and related fields.
Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.
In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely.
Paths
"Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limits of rasterized images and are intuitive to modify.
Animation, user interface design
Bézier curves are also used in the time domain, particularly in animation and user interface design.
For example, a Bézier curve can be used to specify the velocity over time of an object such as an icon moving from A to B, rather than simply moving at a fixed number of pixels per step.
When animators or interface designers talk about the "physics" or "feel" of an operation, they may be referring to the particular Bézier curve used to control the velocity over time of the move in question.
This also applies to robotics where the motion of a welding arm, for example, should be smooth to avoid unnecessary wear.
History
The mathematical basis for Bézier curves -- the Bernstein polynomial -- has been known since 1912, but its applicability to graphics was understood half a century later.
Bézier curves were widely publicized in 1962 by the French engineer Pierre Bézier, who used them to design automobile bodies at Renault.
The study of these curves was however first developed in 1959 by mathematician Paul de Casteljau using de Casteljau's algorithm, a numerically stable method to evaluate Bézier curves at Citroën, another French automaker.
See also
- Animation
- Bernstein polynomial
- Pierre Bézier
- Bézier surface
- Bézier triangle
- Computer graphics
- Curve
- de Casteljau's algorithm
- Dimension
- Graphical user interface
- Mathematics
- Numerical stability
- Parametric equation
- Paul de Casteljau
- Rasterized image
- Spline (mathematics)
- User interface
- Vector graphics
External links
- Bézier curve @ Wikipedia
