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Title: APLICATION OF ELLIPTIC INTEGRALS IN MATHEMATICAL CARTOGRAPHY CALCULATIONS
APLICATION OF ELLIPTIC INTEGRALS IN MATHEMATICAL CARTOGRAPHY CALCULATIONS

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Pawel Pedzich; Lukasz Wodzynski
10.5593/sgem2023/2.1/s11.40
10.5593/sgem2023/2.1
1314-2704
978-619-7603-57-6
English
23
2.1
•    Prof. DSc. Oleksandr Trofymchuk, UKRAINE 
•    Prof. Dr. hab. oec. Baiba Rivza, LATVIA
Cartography and GIS
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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conference
https://doi.org/10.5593/sgem2023/2.1/s11.40
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Proceedings of 23rd International Multidisciplinary Scientific GeoConference SGEM 2023
23rd International Multidisciplinary Scientific GeoConference SGEM 2023, 03 - 09 July, 2023
Proceedings Paper
STEF92 Technology
International Multidisciplinary Scientific GeoConference SGEM
SWS Scholarly Society; Acad Sci Czech Republ; Latvian Acad Sci; Polish Acad Sci; Russian Acad Sci; Serbian Acad Sci and Arts; Natl Acad Sci Ukraine; Natl Acad Sci Armenia; Sci Council Japan; European Acad Sci, Arts and Letters; Acad Fine Arts Zagreb Croatia; Croatian Acad Sci and Arts; Acad Sci Moldova; Montenegrin Acad Sci and Arts; Georgian Acad Sci; Acad Fine Arts and Design Bratislava; Russian Acad Arts; Turkish Acad Sci.
317-324
03 - 09 July, 2023
website
9120
mathematical cartography, geodesy, cartographic projection, meridian arc length