Bézier curve

Bézier curves are also used in animation as a tool to control motion.

This is useful if software supports Bézier curves only of specific degree.

Bridges, string art and Bézier curves - mathematical analysis of the shape.

Bézier curves can be defined for any degree n.

The following picture shows this process for a cubic Bézier curve:

The interpretation given above is valid for a nonrational Bézier curve.

From the definition of the cubic Bézier curve, we have:

The points P are called control points for the Bézier curve.

In all cases, the edges of the triangle will be Bézier curves of the same degree.

Bézier curves are widely used in computer graphics to model smooth curves.

Consider a Bézier curve with control points .

Quadratic and cubic Bézier curves are most common.

A quadratic Bézier curve is also a parabolic segment.

Rational Bézier curves can, among other uses, be used to represent segments of conic sections exactly.

Given n + 1 control points P, the rational Bézier curve can be described by:

Moreover, the Bézier curve can be split at point into two curves with respective control points :

A designer need only draw on a computer screen the letter forms that he likes and the machine will convert them automatically into Bézier curves.

As with the Bézier curve, a Bézier surface is defined by a set of control points.

For examples which go near key points see nonuniform rational B-spline, or Bézier curve.

We may compose a circle of radius from an arbitrary number of cubic Bézier curves.

A Bézier curve is a parametric curve frequently used in computer graphics and related fields.

It is a generalization of the de Casteljau's algorithm for Bézier curves.

The formula for a Bézier curve.

Usually cubic Bézier curves are used, and additional control points (called handles) are added to define the shape of each curve.

The workflow of the application is based around drawing source and destination curves or shapes onto an image using bézier curve tools.