带双参数的四次Wang-Ball型曲线曲面

Quartic Wang-Ball type curves and surfaces with two parameters

文章构造了一组带有2个形状参数α、β的四次Wang-Ball型基函数,它是四次Wang-Ball基函数的扩展。基于Wang-Ball型基函数定义了带双参数的Wang-Ball型曲线和张量积曲面,这种曲线不仅具有四次Ball曲线的特性,还能够实现四次Wang-Ball曲线到Said-Ball曲线的过渡以及四次Said-Ball曲线到Bézier曲线的过渡,并且包含了Wang-Ball曲线与Bézier曲线之间的无数曲线。文中分析了基函数及曲线的性质和2个形状参数的几何意义;给出了2条Wang-Ball型曲线的G0、G1、G2连续拼接条件;最后以实例表明构造的新曲线为曲线曲面造型提供了一种有效方法。

A class of quartic Wang-Ball type blending functions with two shape parameters α,β is pres- ented in this paper, which is an extension of quartic Wang-Ball blending functions. Based on Wang- Ball type blending functions, the quartic Wang-Ball type curves and surfaces with two shape parame- ters are defined. This class of curves not only inherits the outstanding properties of the quartic Ball curve, but also realizes the transition from quartic Wang-Ball curve to Said-Ball curve and the transi- tion from quartic Said-Ball curve to Bezier curve, and it contains many curves locating between the quartic Wang-Ball curve and Bezier curve. The properties of the blending functions and curves, and the geometrical property of two shape parameters are analyzed. The G0 - continuity, G1- continuity and G2 - continuity conditions of two pieces of curves are also given. Some examples illustrate that this method of constructing curves and surfaces is useful for curves and surfaces design.