Treatment of non-equispaced two-dimensional data with a digital computer

Abstract Problems of acquisition and display of data with irregular control-point spacings are thoroughly discussed in this paper. Various methods are presented for computing values of the observed variable at equispaced points along two orthogonal directions with the help of irregularly distributed data. Only a few methods of interpolation are found accurate and reliable in maintaining broad as well as fine features of the original data without introducing undue distortion. One relatively simple method, the accuracy of which is considered adequate for studies of the broad features of the data, employs a quadratic, weighted average of the data points in the immediate vicinity of the grid point. However, the method best suited for accurate and detailed quantitative analysis uses least-squares fitting of the data with orthogonal polynomials generated by the Gram-Schmidt procedure.