Bézier Curve by de Casteljau's Algorithm
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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
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 .