Применение автоматических вычислительных машин при нахождении целесообразных вариантов картографических проекций

Summary

The paper points out the possibility of using automatic computers in solving projections by the difference grid method which, due to the influence of the development of computational techniques, has recently been paid considerable attention. The general theory of projections by Soviet authors is used for developing orthogonal equivalent projections under some limiting conditions, making it easier to perform direct integration and to obtain a concrete form of the basic projection equations (1).

Apart from the method indicated, it is possible to replace the continuous solution of the projection problem by a discontinuous solution, when the given region is covered by a sufficiently dense network of nodal points, and the values of the derivatives are then approximately replaced by expressions from the differences. When solving orthogonal equivalent representations it is possible to start out from Eq. (20); then the projection can be expanded numerically for a certain choice of coefficients in Eq. (22) without knowing the analytical expression of the projection equations (1) if it is required that thex-axis be the image of the central meridian. Such a procedure was programmed for a territorial rangeU<30^o, 80^o>,V<−50^o, +50^o> for a Ural 2 computer and the resultant projection, obtained for different choices of the coefficientsu _i in Eq. (22) and with the required values of the distortion, was deduced by the characteristic functional of maximum angular distortion (24). The results, obtained by the computer, were refined by taking the numerical derivatives of Eqs. (25) or (26). It is seen from the resultant values, expressed in the graphs and figures, that the solution is applicable, it can be carried out on a computer and the stability of the numerical process is sufficient. For a more exact solution, permitting the theoretical determination of the optimum boundary condition, relations with mean differences might be used for calculating the derivatives.