Abstract
The paper describes examples of applying elliptic integrals in mathematical cartography calculations, i.e. related with cartographic projections and reference surfaces. Selected equations and algorithms used in calculating the meridian arc length on an oblate spheroid, meridian arc length on a tri-axial ellipsoid, the equation and length of the geodesic, and coordinate transformation on an oblate spheroid, have been applied. Examples of elliptic integral application for the construction of cartographic projections of a sphere, oblate spheroid and tri-axial ellipsoid are also presented. Important elements of these equations are elliptic integrals of the first, second and third kind. Methods and tools for solving these integrals are presented, as well as calculations testing the described algorithms and methods. The results have allowed to test the precision of the performed calculations and the efficiency of the applied algorithms. The calculations were made using Octave and Matlab software. Conducted study reveals that obtained results are the same regardless of the method used but some methods are more efficient or convenient to use.
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