Modeling of asymptotically optimal piecewise linear interpolation of plane parametric curves

Abstract

An asymptotically optimal method of curves interpolation is satisfied to the condition of minimum number of approximation units. Algorithms for obtaining the values of the sequence of approximation nodes are suggested. This algorithm is based on numerical integration of the nodes regulator function with linear and spline interpolation of its values. The method of estimating the results of the curve approximation based on statistical processing of line segments sequence of relative errors is substantiated. Modeling of real curves approximation is carried out and influence of the sampling degree of integral function – the nodes regulator on distribution parameters of errors is studied. The influence is depending on a method of integral function interpolation.