New extension of cubic Bézier curve and its applications

In order to construct Bezier curves with shape control parameters,two classes of polynomial basis functions of 3th and 4th degree are presented in this paper.They are both extensions of cubic Bernstein basis functions.Properties of the proposed basis functions are analyzed and the corresponding polynomial curves with shape control parameters α,γ and α,β,γ are constructed accordingly.The constructed curves not only inherit the outstanding properties of the cubic Bezier curve,but also are adjustable in shape and fit close to the control polygon.In addition,the continuity condition and some applications in curve and surface design about the new curves are discussed,and two definition of Extension-surface are also presented.Some examples illustrate the new curves are very valuable for the design of curves and surfaces.