中文摘要：

给出了一组带三个形状参数的类四次Bernstein基函数,它是四次Bernstein基函数的扩展,讨论它的基本性质,基于这组基定义了带三个形状参数的类四次Bézier曲线,该曲线和四次Bézier曲线有类似的性质,并具体分析了形状参数的几何意义和曲线间的光滑拼接。实例表明,该方法在设计曲线曲面时十分有效。

英文摘要：

A class of quasi Bernstein basis function with three shape parameters is presented. It is the extension of quartic Bernstein basis function. Properties are analyzed and the quasi Bézier with three shape parameters is defined based on it.The curve inherits the outstanding properties of quartic Bézier curve. The geometric meaning of the shape parameters and smooth connection between curves are analyzed. Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.