Inclusion of triaxial ellipsoid conical projections into geoinformation technologies

Cartography
UDC: 
528.9
DOI: 
10.22389/0016-7126-2026-1033-7-17-26
1 Nyrtsov M.V.
2 Sokolov A.I.
3 Fleis M.E.
4 Varushchenko A.S.
Year: 
2026
№: 
7
1033
Pages: 
17-26

Lomonosov Moscow State University (MSU)

1, 
2, 
4, 

Institute of Geography RAS

3, 
Abstract:
One of the conditions for including the triaxial ellipsoid map projections into geoinformation technologies is solving the problems of direct and reverse conversion between coordinate systems. The direct one is performed from the ellipsoid's reference surface to a plane, while the reverse means from the projection plane to the reference surface. Implementation of the conversion as software code is also required. Availability of conversion formulas makes it possible to solve a number of scientific problems related to transformation of celestial bodies' surfaces raster images using control points. Furthermore, using the rectangular coordinates of object points represented in vector format, one can calculate the area of the objects or estimate their shape distortions. The authors present a method for direct conversion for a conic projection that preserves lengths along meridians, an equal-area conic projection and a meridian section projection. It is implemented using a module in the GIS Axioma and an independent Javascript software. The method for inverse converting coordinates for conic projections, as well as for cylindrical, azimuthal, and Jacobi projection, described in previous studies, is based on the sequential calculation of one variable's functions arguments by bisecting the line segment using direct conversion formulas. However, working with conic projections has some unique features. The direct and inverse recalculation for the conic projection of the meridian section of the triaxial ellipsoid is shown on Casanova crater on the surface of the asteroid (433) Eros
The research was carried out within the framework of the state assignments: IG RAS FMWS-2024-0009 (M. E. Fleis) and MSU No. 121051400061-9 (M. V. Nyrtsov, A. I. Sokolov, A. S. Varushchenko)
References: 
1.   Zhuravskii A. M. Spravochnik po ellipticheskim funktsiyam. M.-L.: Izd-vo Akad. nauk SSSR, 1941, 236 p.
2.   Morozov V.P. Kurs sferoidicheskoj geodezii. Izd. 2-e, pererab. i dop. M.: Nedra, 1979, 295 p.
3.   Nyrtsov M.V., Fleis M.E., Sokolov A.I. (2021) Meridian section projections: a new class of the triaxial ellipsoid projections. Geodezia i Kartografia, 82(2), pp. 11-22. (In Russian). DOI: 10.22389/0016-7126-2021-968-2-11-22.
4.   Fleis M.E., Nyrtsov M.V., Sokolov A.I. (2025) Inverse task of recalculating coordinates from the projection plane onto a triaxial ellipsoid. Geodezia i Kartografia, 86(8), pp. 31-41. (In Russian). DOI: 10.22389/0016-7126-2025-1022-8-31-41.
5.   Fleis M.E., Nyrtsov M.V., Sokolov A.I. (2022) Cylindrical projections of triaxial ellipsoid: precise formulae and elliptical integrals. Geodezia i Kartografia, 83(4), pp. 26-38. (In Russian). DOI: 10.22389/0016-7126-2022-982-4-26-38.
6.   Archinal B.A., Acton C.H., A'Hearn M.F. et al. (2018) Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements 2015. Celestial Mechanics and Dynamical Astronomy, Volume 130, no. 22, DOI: 10.1007/s10569-017-9805-5.
Citation:
Nyrtsov M.V., 
Sokolov A.I., 
Fleis M.E., 
Varushchenko A.S., 
(2026) Inclusion of triaxial ellipsoid conical projections into geoinformation technologies. Geodesy and cartography = Geodeziya i Kartografiya, 87(7), pp. 17-26. (In Russian). DOI: 10.22389/0016-7126-2026-1033-7-17-26
Publication History
Received: 25.05.2026
Accepted: 08.07.2026
Published: 20.08.2026

Content

2026 July DOI:
10.22389/0016-7126-2026-1033-7