Abstract:

We difine several new quartic polynomial basis functions named the  αβQBernstein basis functions and they all have two shape parameters α and β for 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 the αβQ—Bézier curve which not only contains two shape parameters α and β,but also have  better ingenuity.Especially,the curves are  C0continuity in an endpoint and C4continuity when α or β gets a certain value.Compared with the curve of elevating once ,the new curve have an important property of wide modulatory area and good feasibility.

Key words: Bernstein basic functions;αβQ—Bézier curve;elevating secondary;C4continuity;shape parameter