带形状参数控制的三次B样条曲线曲面的光顺

The Fairing of Cubic B-Spline Curves

三次B样条曲线是一种广泛应用于计算机辅助几何设计中的非常重要的曲线.本文在以曲线的最小应变能作为衡量曲线光顺性的基础上,采用带调节控制参数的方法分别对三次B样条曲线和双三次B样条曲面进行了光顺处理.由所提供的方法以及实例可以看出,本方法可在曲线曲面光顺的基础上通过修改参数大小以达到控制曲线曲面形状的目的,且修改后的点的位置与原坏点的距离是由参数的大小控制决定的,这样就使得我们的光顺处理可以控制在数据测量的误差范围内.

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 PrSpline 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 surveving datas.