Three Different Extensions of Quintic Bézier Curve

Three classes of polynomial basis functions of 6th degree with shape control parameter λ are presented.They are extensions of quintic Bernstein basis functions.Properties of these three bases are analyzed and the corresponding polynomial curves with a shape parameterare λ are defined accordingly.These curves not only inherit the outstanding properties of quintic Bezier curve,but also are adjustable in shape and fit close to the control polygon.And a class of polynomial function of(n+1)th degree that containing an parameter is obtained by using de Casteljau algorithm Some examples illustrate the method of constructing curve is very useful for curve and surface design.