Trigonometric extension of Bézier curve

One kind of curve with a shape control parameter is defined,which is an extension of the Bezier curve.Its base representation is presented.Meanwhile,the properties,application of the curve and its basis functions have been studied.The G and Gcontinuity conditions of two-piece of the curves is also discussed.This curve not only resolves the expand problem of the Bezier 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.