UDC:
DOI:
10.22389/0016-7126-2023-994-4-50-59
Year:
№:
994
Pages:
50-59

### Omsk State Agrarian University named after P.A. Stolypin

###### 1,
Abstract:
At processing geodetic networks, it is necessary to transform the coordinates of points from one system to another. Two methods are most common: shifting and rotation of the coordinate system, or recalculation through a spatial geodetic one. In the first method, simple formulas are used, but for extended objects, the conformality of the coordinate transformation is violated. In the second one, the parameters of the systems are usually unknown, and a complex mathematical apparatus is used for converting coordinates. The complexity increases when the coordinate systems are built on different spheroids or projections. The transformation is proposed to be performed using the analytical function of a complex variable. The universality and simplicity of this method is proved. The errors do not depend on the projection type and the spheroids’ parameters. Coordinate transformations from Gaussian or UTM projections to another conformal projection or local coordinate system are performed using the same formulas.The accuracy is improved if the coefficients in the formulas are calculated using the smallest squares method.
References:
 1.   Afonin K. F. Vysshaya geodeziya. Sistemy koordinat i preobrazovaniya mezhdu nimi: Ucheb.-metod. posobie. Novosibirsk: SGGA, 2011, 56 p. 2.   Bol’shakov V.D. Teoriya oshibok nablyudenij [The theory of errors of observations]. M.: Nedra, 1983, 289 p. 3.   Gerasimov A. P. Mestnye sistemy koordinat. Geoprofi, 2009, no. 4, pp. 32–34. 4.   Gerasimov A.P., Nazarov V.G. Mestnye sistemy koordinat. M.: OOO «Izdatel'stvo «Prospekt», 2010, 64 p. 5.   Grinberg G.M. Matematicheskaya obrabotka gorodskih geodezicheskih setej. M.: Nedra, 1992, 192 p. 6.   Gorobets V.P. Dem’yanov G.V., Mayorov A.N., Pobedinskiy G.G. Sovremennoe sostoyanie i napravleniya razvitiya geodezicheskogo obespecheniya RF. Sistemy koordinat (nachalo). Geoprofi, 2013, no. 6, pp. 4–9. 7.   Dem'yanov G.V., Majorov A.N., Pobedinskij G.G. Mestnye sistemy koordinat, sushchestvuyushchie problemy i vozmozhnye puti ih resheniya. Geoprofi, 2008, no. 6, pp. 7–16. URL: http://www.geoprofi.ru/default.aspx?mode=binary&id=1065 8.   Morozov V. P. Kurs sferoidicheskoj geodezii. M.: Nedra, 1969, 304 p. 9.   Morozov V.P. Kurs sferoidicheskoj geodezii. Izd. 2-e, pererab. i dop. M.: Nedra, 1979, 295 p. 10.   Hristov V.K. Koordinaty Gaussa – Kryugera na ehllipsoide vrashcheniya. M.: Geodezizdat, 1957, 264 p. 11.   Adewale Adebayo, Emenari Udochukwu S., Amusuk Danboyi Joseph (2014) Coordinate Transformation of Birnin Kebbi. The International Journal of Engineering and Science, Volume 3, no. 11, pp. 62–70. 12.   Weiss G., Labant S., Weiss E., Mixtaj L., Schwarczová H. (2009) Establishment of Local Geodetic Nets. Acta Montanistica Slovaca, no. 14 (4), pp. 306–313.
Citation:
 Vinogradov A.V.,  (2023) Application of a complex variable’s analytical functions at converting the points’ coordinates from one system to another. Geodesy and cartography = Geodezia i Kartografia, 84(4), pp. 50-59. (In Russian). DOI: 10.22389/0016-7126-2023-994-4-50-59
Publication History
 Received: 30.06.2020 Accepted: 05.04.2023 Published: 20.05.2023

#### Content

 2023 April DOI: 10.22389/0016-7126-2023-994-4