The Fairing of Cubic B-Spline Curves

Abstract

Cubic B-Spline curves are very important curves in the field of Computer Aided Geometric Design,which are widely used in practical applications.In this paper,which is based on the least bending energy for estimating the fairing of curves,the fairing of cubic B-Spline curves and bicubic B-Spline surfaces are discussed by the methods with control parameter.Through the methods and the examples in this paper,we can get the aim which is controlling the shapes of the curves and surfaces by modifying the value of parameter based on the fairing of curves and surfaces.What's more,the distance between the position of the modified data points and it's original position can be controlled by the parameter,so we can make the fairing in the control of the extent of the error in the surveying datas.