Abstract: 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—Bézier 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.

Key words: Bernstein basic function, λQ—Bézier curve, elevating quadratic, shape parameter