带双参数拟四次Wang-Ball曲线及在造型中的应用

Quasi Quartic Wang-Ball Curves with Two Parameters and the Application in the Modeling

针对四次Wang-Ball曲线不能改变曲线形状的不足,构造了一组带有2个形状参数α、β的拟四次Wang-Ball基函数,它是四次Wang-Ball基函数的扩展。基于拟四次Wang-Ball基函数定义了带双参数的拟四次Wang-Ball曲线,这种曲线拥有四次Wang-Ball曲线的特性,并且通过调整形状参数,可以改变曲线的形状。当α=0、β=0时,带双参数拟四次Wang-Ball曲线退化成四次Wang-Ball曲线。研究了基函数及曲线的性质,分析了2个形状参数的几何意义,探讨了2条拟四次Wang-Ball曲线拼接时应具备的条件。带双参数的拟四次Wang-Ball曲线缓解了四次Wang-Ball曲线不能改变曲线形状的不足,为曲线造型设计提供了一种实用的方法。

In order to solve the problem that the quartic Wang-Ball curve can not change the shape oI the curve,as an extension of the quartic Wang-Ball basis function,a set of quasi quartic Wang-Ball basis functions with double shape parameters is constructed.Based on the quasi quartic Wang-Ball basis functions,the quasi quartic Wang-Ball curves with two teristics of the quartic Wang-Ball curve and the shape parameters are defined,which have the charac of the curves can be changed by adjusting the shape parameters.When α=0 and β=O,the quasi quartic Wang-Ball curve with two parameters is de- generated into the quartic Wang-Ball curve.In this paper,the properties of the basic function and the curve are studied,the geometric meaning of the double shape parameters is analyzed,and the conditions of the two quasi Wang-Ball curves are discussed.The quasi quartic Wang-Ball curves with double shape parameters can alleviate the problem that the quartic Wang-Ball curve can not change the shape of the curve,and this will provide a practical method for curve modeling design.