Andrea ÁBRAHÁMOVÁ, Margita VAJSÁBLOVÁ, Marek MACÁK

Modification of distortions in the conical cartographic projection of Slovakia using Laplace equation solved by the Finite Element Method

Ábrahámová, A., Vajsáblová, M., Macák, M.: Modification of distortions in the conical cartographic projection of Slovakia using Laplace equation solved by the Finite Element Method. Kartografické listy, 2022, 30 (1).

Abstract: The Finite Element Method (FEM) proves to be a very suitable computational method for solving the Laplace equation expressing a geodetic and other problem not only in engineering practice. Selecting an effective map projection for territory is probably the most important and challenging aspect of creating a cartographic projection in terms of the achieved scale distortions. The presented paper describes different methods to design conformal conic projections for the Slovakia territory and their optimizations based on solving the Laplace equation (LE) by the Finite Element Method (FEM). The modification was applied to four proposed cartographic projections, namely, Lambert’s conformal conic projection in a normal aspect (LCC_SK), Conformal conic projection in a normal aspect with minimizing Root Mean Square (RMS) of the scale distortion values, Conformal conic projection in an oblique aspect (different than the currently used Křovák’s projection) and Conformal conic projection in an oblique aspect with minimizing RMS of the scale distortion values. The results of the analysis of the proposed cartographic projections and their modifications using LE solved by FEM showed the suitability of the projections according to various criteria for the distortion of the elements of the displayed locality.

Keywords: Finite Element Method, Laplace equation, ANSYS, conformal conic projection, scale distortion, Root Mean Square