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七次广义Ball曲线的两种扩展
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Abstract:
构造了两组含形状参数的多项式基函数：第一组基既是七次Wang-Ball基的扩展，又是七次Said-Ball基的扩展；第二组基既是七次Said-Ball基的扩展，又是七次Bernstein基的扩展。并由此定义了两种新的七次广义Ball曲线：前者不仅包括了七次Wang-Ball和Said-Ball曲线，还涵盖了无数条处于这两种曲线之间的曲线；后者不仅包括了七次Said-Ball和Bézier曲线，还涵盖了无数条处于这两种曲线之间的曲线。依次分析了两种新的广义Ball曲线与七次Bézier曲线之间的关系后明确了每个形状参数的几何意义，并给出了其几何作图法。
Two classes of polynomial basis functions with shape parameter are constructed. The first class of basis is not only the extension of Wang-Ball basis of seventh degree, but also the extension of Said-Ball basis of seventh degree. The second class of basis is not only the extension of Said-Ball ba-sis of seventh degree, but also the extension of Bernstein basis of seventh degree. Based on these two new bases, two classes of new generalized Ball curves of seventh degree are defined. The former contained the Wang-Ball and Said-Ball curve of seventh degree and many curves between them. The latter contained the Said-Ball and Bézier curve of seventh degree and many curves between them. After analyzing the relationship between new generalized Ball curves and the Bezier curve of seventh degree, the geometric meaning of each shape parameter is clarified, and its geometric drawing method is given.
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