Bézier curve

plural Bézier curves

1. computer graphicsA 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.First known use 1960s.

   Bézier curves are applied, for example in computer graphics and animation, to produce smooth, infinitely scalable curves.

   3 more examples

   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

   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

   Synonyms: bezier