Degree reduction of Bezier curves by L(1)-approximation with endpoint interpolation

Abstract

We consider the one-degree reduction problem with endpoint interpolation in the L(1)-norm. We obtain the best one-degree reduction of Bezier curve of the degree n less than or equal to 5 with endpoint interpolation by using perfect splines. For the general degree n, we propose a 'good' one-degree reduction by use of an appropriate transform of the Tchebycheff polynomials U-n(x) of the second kind of degree n. By use of the good one-degree reduction, subdivision algorithm is given to get one-degree reduced Bezier curve within a given tolerance E. Some numerical experiments are also given.