Classification of the triaxial ellipsoid projections

Cartography

UDC:

528.9

DOI:

10.22389/0016-7126-2021-972-6-17-25

1 Nyrtsov M.V.

2 Fleis M.E.

Year:

2021

№:

972

Pages:

17-25

Lomonosov Moscow State University (MSU)

1,

Institute of Geography RAS

2,

Abstract:

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.

Keywords:

classification, map projection, mathematical cartography, triaxial ellipsoid

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).

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Citation:

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