一类新的拟Bernstein-Bézier曲线

A Class of New Quasi-Bernstein-Bézier Curves

构造了一类新的带双参数形状可调的拟Bernstein基函数,它是在三次Bernstein多项式的基础上扩展而成的一组n次拟Bernstein基.在此基础上,定义了带双形状参数的拟Bernstein-Bézier曲线,它保留了Bézier曲线的几何特征,并具有形状可调的特性.在控制点给定的情况下,可通过改变形状参数的值整体或局部地调控曲线的形状,同时给出参数控制及曲线拼接应用的实例.

A class of new Quasi-Bernstein basis functions with two shape parameters is constructed,which is the recursive approach of cubic Bernstein basis functions.Based on these basis functions,a new type of Quasi-BernsteinBézier curve with two shape parameters is defined.The new curve contains some properties of the classical BernsteinBézier curve.We present that the shape of the Quasi-Bernstein-Bézier curves can be adjusted globally or locally by changing the values of the shape parameters when the control polygon is maintained.Meanwhile,the examples illustrate that the altered shape parameters make it a valuable method for the design of curves.