关键词: 四次Bézier曲线, 形状参数, 扩展, 近似合并

Abstract: A class of polynomial basis function of 5th degree with four shape control parameters is presented.It is an extension 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 inverse matrix and the error is given.Finally，the examples are presented，which show the effectiveness of the presented method.

Key words: quartic Bézier curve, shape parameter, extension, approximate merging