Abstract: In order to be rendered or analyzed, a B-spline curve is often approximated by its control polygon after subdivision.In this approximating process, the distance between the curve and its control polygon is critical to determine the depth of subdivision.In order to achieve lower bound of the distance and reduce the segment needed for approximation, this paper proposes an upper bound only related to the norm of second order forward difference of the control polygon and the angle between the first and second order forward differences, by bounding the accumulating position changes of the control polygon through the subdivision process.Thus more compact bound can be achieved when this angle is small.Experimental results shows when the curve is smooth, this estimation could yield better result compared to previous methods.