Bézier曲线曲面的同次扩展

Extension of Bézier curves and surfaces of the same degree

在几何造型中,为了更加灵活地调控曲线曲面的形状,定义了一类带多形状参数的多项式基函数。同次Bernstein基函数是该基函数的特例,且二者具有类似的几何性质。利用该基函数构造了带形状参数的多项式参数曲线曲面,它们分别具有同次Bézier曲线曲面的形状特点。通过改变形状参数的取值可以整体或局部调控曲线曲面的形状。数值实例表明新方法在计算机辅助几何设计中是灵活有效的。

A class of Polynomial basis functions with multiple shape parameters is defined in order to adjust the shape ofcurves and surfaces more flexibly. Bemstein basis functions are special cases of them and they share the same properties. The basis functions are used to constructed polynomial curves and surfaces with shape parameters. Moreover, we studied that it is very convenient to adjust locally or entirely the shape of curves and surfaces by modifying the values of shape parameters. Some examples given in this paper show our method is effective in geometric modeling.