六次广义Ball曲线的两种推广
Two Extensions of Sextic Generalized Ball Curves
摘要: 构造了两组含形状参数的多项式基函数，并以此构造了两组带形状参数的全新Ball曲线。一组囊括了六次Wang-Ball曲线与Said-Ball曲线以及二者之间的大量曲线；另一组则包含了六次Said-Ball曲线与Bézier曲线以及介于二者之间的大量曲线。通过对两组曲线与六次Bézier曲线关系的分析，得出了形状参数的几何意义，并通过Bézier方法中的递归分割算法求得到了两组新曲线的几何作图法。
Abstract:
Two classes of polynomial basis functions with shape parameter are constructed. Based on these two bases, two new Ball curves with shape parameter are defined. The former curve contained the sextic Wang-Ball and Said-Ball curve and a large number of curves between these two curves. The latter includes the sextic Said-Ball and Bézier curve and a large number of curves between these two curves. Through the analysis of the relationship between the two kinds of curves and the gen-eral sextic Bézier curve, the geometric meaning of the shape parameters is obtained, and the geo-metric drawing method of the two kinds of new curves are given out in virtue of the de Casteljau al-gorithm of the general Bézier curve.
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