On the approximation of curves with polylines

Abstract

The exact values of the estimation of the approximation error of parametrically defined curves by inscribed polylines in them-dimensional space Rm for classes of functions defined by moduli of continuity are presented. The result is a sort of generalization of the results of B.N. Malozemov on the approximation of continuous functions with polylines. Also, the problem of finding the upper bounds of deviations of parametrically defined curves for this class is solved based on the assumption that these curves intersect at N (N ≥ 2) points of the partition of [0, L]. In the case of m = 2, from the obtained results follow the previous results on the approximation of plane curves with polylines in Euclidean, Hausdorff, and Hamming metrices.