Best bounds on the approximation of polynomials and splines by their control structure

We present best bounds on the deviation between univariate polynomials, ten sor product polynomials, Bezier triangles, univariate splines, and tensor p roduct splines and the corresponding control polygons and nets. Both pointw ise estimates and bounds on the L-p-norm are given in terms of the maximum of second differences of the control points. The given estimates are sharp for control points corresponding to arbitrary quadratic polynomials in the univariate case, and to special quadratic polynomials in the bivariate case . (C) 2000 Elsevier Science B.V. All rights reserved.