Elevating Quadratic with Shape Parameter of Bézier Curve

This paper defines several new sixtic polynomial basis functions which are named the λQ—Bernstein basis function and they all have a shape parameter λ for quartic Bernstein basic function.These basis functions have a new feature and the function's degree is elevated secondary once.Above all,these new basis functinons contain all properties of quartic polynomial basis function and the quintic polynomial basis function with a shape parameter.Based on these basis functions,the paper defines λQ—Bezier curve which not only contains a shape parameter λ,but also could improve the adjustability of the new curve.An important property is that the curve could better approximate to control polygon which is given.