An Approximation Method of Bézier Curve

It is proved that the linear space constructed by power base is a banach space under 2-norm by using approximation method. For the Bezier curve--the elements in banach space, the linear combination of the low-order S power base is used to approximate optimal the high-order Bernstein base function. The original Bezier curve is instituted by the linear combination of low-order S power base and the optimal approximation element of the original Bezier curve is obtained.