Abstract : This paper presents an improved algebraic pruning method for point projection for Bézier curves. It first turns the point projection into a root finding problem, and provides a simple but easily overlooked method to avoid finding invalid roots which is obviously irrelative to the closest point. The continued fraction method and its expansion are utilized to strengthen its robustness. Since NURBS curves can be easily turned into Bézier form, the new method also works with NURBS curves. Examples are presented to illustrate the efficiency and robustness of the new method.