New Extension of Bézier Curves

Two classes of polynomial basis functions of the 4th and the 5th degree with two shape control parameters α,β are presented.They are extensions of cubic and quartic Bernstein basis functions.Properties of these two bases are analyzed and the corresponding polynomial curves called cubic E-Bezier curve and quartic E-Bezier curve with α,β are defined.These curves inherit the outstanding properties of cubic and quartic Bezier curve,and are better adjustable in shape and fit closer to the control polygon.These curves converge to cubic and quartic Bezier curve when α=β=0.Two definition of extension-surface are presented.Some examples illustrate the variation curve offers a sort of new effective means for design of curve/surface.