Elevating Secondary Extension with the Two Shape Parameters Bézier Curve

We difine several new quartic polynomial basis functions named the αβQ-Bernstein basis functions and they all have two shape parametersαandβfor the quadratic Bernsteins basic function.These basis functions have a new feature and the functions'degrees have been elevated secondary once.Above all,these new basis functinons contain all the properties of the quadratic polynomial basis function and the cubic polynomial basis function which have two shape parameters.Based on these basis functions,accordingly,we define theαβQ —Bezier curve which not only contains two shape parameters αandβ,but also have better ingenuity.Especially,the curves are C0-continuity in an endpoint and C4continuity whenαorβgets a certain value.Compared with the curve of elevating once,the new curve have an important property of wide modulatory area and good feasibility.