中文摘要：

给出了带有4个形状参数的5次多项式基函数,分析了这组基函数的性质,并由此基函数构造了带4个形状控制参数的四次扩展Bézier曲线（简称QE-Bézier曲线）。QE-Bézier曲线是对四次Bézier曲线的扩展,它不仅具有与四次Bézier曲线类似的性质,而且具有灵活的形状可调性和更好的逼近性。进一步研究了两相邻QE-Bézier曲线的合并问题,通过曲线拟合方法与广义逆矩阵理论相结合,直接得到了合并曲线控制顶点的显示表达式,并给出了误差分析,数值实例显示逼近效果较好。

英文摘要：

A class of polynomial basis function of 5th degree with four shape control parameters is presented.It is an exten- sion of cubic Bernstein basis functions.Properties of the basis function are analyzed and the corresponding polynomial curve with four sharp parameters is defined.QE-Bézier curve is extension of quartic Bézier curve,so the QE-Bézier curve not only inherits the outstanding properties of the quartic Bézier curve,but also is adjustable in sharp and fit close to the control polygon.The question about approximate merging a pair of QE-Bézier is researched.The explicit formula of control points of the merged QE-Bézier curve can be given directly by combining the fitting method of curves with the theory of general in- verse matrix and the error is given.Finally,the examples are presented,which show the effectiveness of the presented method