Bézier curves with multiple shape parameters

First a set of polynomial function with three parameters is presented as an extension of Bernstein basis functions.The quality of the new basis is analyzed.Based on the new basis,the polynomial curve with three shape parameters is defined.The new curve not only holds many practical geometrical qualities of Bezier curve and the curve with shape parameters,but also its shape can be adjusted totally or locally through changing the value of λ,α,β.The geometrical meaning of the shape parameters is analyzed,and the continuity condition of the curve is also discussed.Finally some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.