authors 
Gordon, William J. and Riesenfeld, Richard F. 
year 
1974 
title 
Bernstein Bezier Methods for the ComputerAided Design of FreeForm Curves and Surfaces 
source 
Journal of the ACM. April, 1974. vol. 21: pp. 293310 : ill. includes bibliography 
summary 
The mth degree Bernstein polynomial approximation to a function f defined over [0,1] is Emo f(u/m) Ou(s), where the weights Ou(s) are binomial density functions. The Bernstein approximations inherit many of the global characteristics of f, like monotonicity and convexity, and they always are at least as 'smooth' as f, where 'smooth' refers to the number of undulations, the total variation, and the differentiability class of f. Historically, their relatively slow convergence in the Loonorm has tended to discourage their use in practical applications. However, in a large class of problems the smoothness of an approximating function is of greater importance than closeness of fit. This is especially true in connection with problems of computeraided geometric design of curves and surfaces where aesthetic criteria and the intrinsic properties of shape are major considerations. For this latter class of problems, P. Bezier of Renault has successfully exploited the properties of parametric Bernstein polynomials. The purpose of this paper is to analyze the Bezier techniques and to explore various extensions and generalizations. In a sequel, the authors consider the extension of the results contained herein to freeform curve and surface design using polynomial splines. These Bspline methods have several advantages over the techniques described in the present paper 
keywords 
CAD, computer graphics, Bezier, curves, curved surfaces, representation, design, Bernstein, representation, B splines, user interface, approximation, interpolation 
series 
CADline 
references 
Contenttype: text/plain

last changed 
2003/06/02 11:58 
