Degree reduction of Bézier curves by L1-Approximation with endpoint interpolation

AbstractWe consider the one-degree reduction problem with endpoint interpolation in the L1-norm. We obtain the best one-degree reduction of Bézier curve of the degree n ≤ 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 Un(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 Bézier curve within a given tolerance ϵ. Some numerical experiments are also given