A New Algorithm for Contour-plotting

Abstract

A new algorithm for contour-plotting is introduced. The input function, tabulated or in a subroutine description, is approximated by an interpolation function. The contours of this approximating function are drawn piecewise on a subdivision of the given domain. The algorithm is based on the iterated solution of Initial Value Problems defined by applying the Implicit Function Theorem. Estimates on the dependence of the contourlines on the approximating function are presented using the method of gradient lines. Finally some examples are shown.