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.
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