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.

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 .