Subdivision Algorithm for Bézier Curves
This Demonstration illustrates the convergence of the de Casteljau-based subdivision algorithm for Bézier curves.
The subdivision algorithm follows from the de Casteljau algorithm that calculates a current point , for , of a polynomial Bézier curve , for , where are the control points, by applying the following recurrence formula:
For any value of between and , we have
The subdivision algorithm associates to the polygon the two polygons and . They constitute the control polygons of the two parts of the curve , respectively for in and :
When , varies over and varies over .
This Demonstration illustrates repeated application of the above procedure (the control "k" denotes the number of iterations). Obviously, the resulting polygon sequence converges very quickly to the curve .