# Bézier Curve by de Casteljau's Algorithm

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

As changes from 1 to 3 a sequence of linear interpolations shows how to construct a point on the cubic Bézier curve when there are four control points. The parameter controls the proportion of the distance along an interpolating line. As varies between 0 and 1 the entire curve is generated.

Contributed by: Bruce Atwood (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

For control points, , the Bézier curve can be constructed by the recurrence relation where is the linear interpolation between control points and . The recursion level goes from 1 to and runs from 0 to .

## Permanent Citation

"Bézier Curve by de Casteljau's Algorithm"

http://demonstrations.wolfram.com/BezierCurveByDeCasteljausAlgorithm/

Wolfram Demonstrations Project

Published: March 7 2011