关键词: Bézier曲线, 曲线设计, 形状参数

Abstract: One kind of curve with a shape control parameter is defined，which is an extension of the Bézier curve.Its base representation is presented.Meanwhile，the properties，application of the curve and its basis functions have been studied.The G^₁ and G₂ continuity conditions of two-piece of the curves is also discussed.This curve not only resolves the expand problem of the Bézier curve，and can also precisely represent or approach quadric curves through changing the value of the shape parameters，such as circular arcs，ellipses etc.Some examples about how to precisely represent or approach a circular arc are given in this paper.This curve has high applied value in the curve design practice.

Key words: Bézier curve, curve design, shape control parameters