摘要
给出了一组含有两个形状参数α,β的四次多项式基函数,是四次Bernstein基函数的扩展,分析了这组基的性质;基于这组基定义了带两个形状参数的多项式曲线,所定义的曲线不仅保留了四次Bézier曲线一些实用的几何特征,而且具有形状的可调性,在控制多边形不变的情况下,改变参数α,β的取值,可以生成不同的逼近控制多边形的曲线;通过分析该曲线与四次Bézier曲线之间的关系,给出了α和β的几何意义,并利用Bézier曲线递归分割算法给出了这种曲线的几何作图法,同时还讨论了曲线间的拼接问题.
A class of 4--degree polynomial basis functions containing two shape control parameters α,β is presented. It is the extention of quartic Bernstein basis functions. Properties of this new basis are analyzed and a polynomial curve with two shape parameters is defined based on it. The new curve not only holds many applied geometrical qualities of the quartic lezier curve, hut also can rectify the shape. When the control polygon is fixed, different curves approaching the control polygon with the changing of shape parameters are given. The geometrical meaning of α and β are discovered by analyzing the connection of the new curve and the quartic Bezier curve. Meanwhile,the geometrical drawing method of the curve is given with the recursion segmentation algorithm of Bezier curve and the continuity condition of the curve is discussed.
出处
《大学数学》
2016年第1期33-37,共5页
College Mathematics
