Constrained Degree Reduction of Bézier Curve in L∞ Norm Using Basic Curve and Correction Curve

To avoid the complexity that arose from directly solving the constrained optimization in L ∞ norm,we present a new method,which decomposes the approximation curve into two parts：the basic curve and the correction curve.The basic curve can be explicitly obtained by using constrained Legendre polynomials ,and it satisfies the constrained conditions imposed on the approximation curve.The correction curve,whose control points are defined by the difference between the original curve and the approximation curve,is used to minimize the error in L ∞ norm.The new method performs mult-i degree reduction at one time in a steady and simple way,and achieves near optimal uniform approximation.Examples are included to show the performance of new method.