Extension of the Quintic Bézier Curve with Two Shape Parameters

A class of 6-degree polynomial basis functions containing two shape control parameters α,β is presented.It is the extention of quintic Berstein basis functions.Properties of this new basis are analyzed and a polynomial curve with two shape parameters is defined based on it.The curve inherits the outstanding properties of the quintic Bezier curve,its shape can adjusted flexibility through changing the value of α,β and approach to the given polygon up or from both sides.The classical quintic Bezier curve and the curves with a parameter in related literatures are especial examples of this paper.Some examples illustrate that the curve defined in this paper provides an effective method for designing curves and surfaces.