Generalized Bézier Curves

In order to adjust effectively the shape of the Bézier curves,generalized Bézier curves with local shape parameters are given in this paper.Based on a kind of higher approximate polynomials of a function,satisfying curves can be generated by changing the given object derivative vectors.Taking the Bézier curve as a special case,the given curve is an effective modification for the Bézier curve of higher degree and curve segments can be joined up conveniently.