带两个形状参数的三次Bézier曲线的扩展

Extension of Cubic Bézier Curve with Two Shape Parameters

构造了一组带两个形状参数的四次调配函数，它是三次Bemstein基函数的扩展．基于该调配函数生成了带两个形状参数的四次参数曲线，并讨论了该曲线的性质和拼接条件．事实表明，该四次曲线是三次Bézier曲线的扩展，它不仅具有三次Bézier曲线的诸多特性，而且由于带有两个形状参数，使得曲线具有了更强的表现能力，在控制顶点保持不变时，可通过修改两个形状参数对曲线进行局部或全局调节．最后给出了应用实例，并给出了张量积曲面的定义．

A class of quartic polynomial basis functions with two shape parameters firstly is presented in this paper, whieh is an extension of cubic Bernstein basis. Then, a kind of quratie parametric curve is presented based on the basis functions, and discussing the properties and continuity condition of the eurve. The curve is an extension of cubic Bézier curve, it inherits the most properties of cubic Bézier curve, and its shape can be loeal or global modified by changing the value of two shape parameters when the control points are not changed. At last, some examples and the definition of surface are presented