Ball曲线和曲面的扩展

本文构造了一组带有两个参数的四次多项式基函数,分析了这组基函数的性质,基于这组基函数定义了带有两个参数的多项式曲线;所定义的曲线不仅具有Ball曲线的特性,而且在控制顶点不变的情况下,随着参数的取值不同,可产生不同的逼近控制多边形的曲线。另外,三次Ball曲线和相关文献中的曲线均是该文所定义的曲线的特例。运用张量积的方法,将曲线推广到曲面;实例表明,定义的曲线和曲面为曲线曲面设计提供了一种有效地方法。

Expansion of Ball Curves and Surfaces

A class of quartic polynomial basis functions with two shape parameters is constructed in this paper, and the properties of the class of basis functions are analyzed and a polynomial curve with two parameters is defined based on it. The defined curve not only inherits the properties of Ball curves, but it is also adjustable in the shape with different parameters under the same controlling vertex and produces the different control polygons. In addition, the classical cubic Ball curve and the curves in the related literature are the special cases of the polynomial curve proposed in the paper. Moreover, the tensor product method is used to extend the curve to surface. Some examples show that the curve and surface defined in this paper provide an effective method for designing curves and surfaces.