基于有理Bernstein函数类的一类有理Bezier曲线

A new class of rational Bezier curves based on rational Bernstein function class

从Bernstein多项式和参数有理变换出发,构造了一类新型的有理调配函数—有理Bernstein函数类,讨论了它的分析性质;运用该函数类给出了一类有理Bezier曲线的生成方法,研究了一类有理Bezier曲线的几何性质和几种实用的有理Bezier曲线并给出了数值例子。

In this paper, based on Bernstein polynomials and rational parameter transformation, a new class of rational composite functions ---- rational Bernstein function class is obtained and its analytical properties are discussed. Then, the method of a new class of rational Bezier curves design is introduced and the corresponding geometric properties of the curves are studied. At last, several applicable rational Bezier curves are studied and a numerical example is given.