Sharp bounds on the approximation of a Bezier polynomial by its quasi-control polygon

By connecting the points which are the kind of linear combinations of Bezier control points, a broken line polygon called quasi-control polygon is produced. Using it to approximate Bezier segment, this paper obtains two sharp, quantitative bounds, besides depending on the degree of the polynomial, the bounds depend only on the maximal absolute second differences or the sum of absolute second differences of the control point sequence respectively. The advantage of this method is hardly increasing calculation, the effect of using quasi-control polygon to approximate is better than that of using control polygon to approximate. (c) 2005 Elsevier B.V All rights reserved.