1 Nyrtsov M.V.
2 Fleis M.E.

Lomonosov Moscow State University (MSU)


Institute of Geography RAS

There are generally accepted classifications of cartographic projections of a sphere and an ellipsoid of revolution according to various criteria. The projections of a triaxial ellipsoid have a number of differences from those of a sphere and an ellipsoid of revolution; therefore, the existing classifications need to be clarified. The definitions of the main classes of cartographic projections of a sphere and an ellipsoid of revolution by the type of cartographic grid cannot be extended to those of a triaxial ellipsoid. At the same time, the traditional approach with the auxiliary surface is maintained. To obtain projections of a triaxial ellipsoid in transverse orientation, there is no need to recalculate through polar spherical coordinates as is done for those of a sphere and an ellipsoid of revolution. The transition is carried out by rotating the ellipsoid around the axes, which is much easier. In the classification of the projections of a triaxial ellipsoid according to the distortions, it is necessary to distinguish conformal, quasiconformal, equal-area projections and the ones which preserve lengths along the meridians.
The materials used in the article were made according to state assignments No. АААА-А19-119022190168-8 (M. E. Fleis) and АААА-А16-116032810094-9 (M. V. Nyrtsov).
1.   Bespalov N. A. Metody resheniya zadach sferoidicheskoi geodezii. Moskva: Nedra, 1980, 287 p.
2.   Bugaevskii L. M. Teoriya kartograficheskikh proektsii regulyarnykh poverkhnostei. Moskva: Zlatoust, 1999, 144 p.
3.   Ginzburg G. A., Salmanova T. D. Posobie po matematicheskoi kartografii. Moskva: Nedra, 1964, 456 p.
4.   Graur A.V. Matematicheskaya kartografiya [Mathematical Cartography]. L.: Izd-vo Leningradskogo un-ta, 1956, 372 p.
5.   Solov'ev M. D. Matematicheskaya kartografiya. Moskva: Nedra, 1969, 287 p.
6.   Flejs M. Je., Nyrtsov M. V., Borisov M. M. Issledovanie svojstva ravnougol'nosti tsilindricheskih proektsij trjohosnogo jellipsoida. Doklady Akademii nauk, 2013, Vol. 451, no. 3, pp. 336–338.
7.   Archinal B. A., Acton C. H., A’Hearn M. F. et al. (2018) Report of the IAU Working Group on cartographic coordinates and rotational elements: 2015. Celestial Mechanics and Dynamical Astronomy, Volume 22, no. 130, DOI: 10.1007/s10569-017-9805-5.
8.   Bugayevskiy Lev M., Snyder John P. (1995) Map Projections. A Reference Manual. Taylor and Francis, London, 328 p.
9.   Grafarend E. W., You R.-J., Syffus R. (2014) Map Projections: Cartographic Information Systems, 2 ed. Springer, Berlin, 941 p. DOI: 10.1007/978-3-642-36494-5.
10.   Kessler Fritz, Battersby Sarah (2019) Working with Map Projections. A Guide to their Selection. CRC Press. 317 p. DOI: 10.1201/9780203731413.
11.   Nyrtsov M., Fleis M., Borisov M., Stooke P. (2014) Jacobi Conformal Projection of the Triaxial Ellipsoid: New Projection for Mapping of Small Celestial Bodies. Cartography from Pole to Pole. Lecture Notes in Geoinformation and Cartography. Berlin: Springer-Verlag. pp. 235–246. DOI: 10.1007/978-3-642-32618-9_17.
Nyrtsov M.V., 
Fleis M.E., 
(2021) Classification of the triaxial ellipsoid projections. Geodesy and cartography = Geodezia i Kartografia, 82(6), pp. 17-25. (In Russian). DOI: 10.22389/0016-7126-2021-972-6-17-25
Publication History
Received: 26.06.2020
Accepted: 30.03.2021
Published: 20.07.2021


2021 June DOI:

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