Linear-time geometric algorithm for evaluating Bézier curves

Abstract: A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational complexity is linear with respect to the number of control points and its memory complexity is $O(1)$. Some remarks on similar methods for surfaces in rectangular and triangular B\'{e}zier form are also given.