The method of construction of cylindrical and azimuthal equal-area map projections of a tri-axial ellipsoid

• Autorzy: Pędzich P.

Identyfikatory

DOI

10.24425/gac.2018.125474

• Języki publikacji: EN

Abstrakty

EN

The paper presents a method of construction of cylindrical and azimuthal equalarea map projections of a triaxial ellipsoid. Equations of a triaxial ellipsoid are a function of reduced coordinates and functions of projections are expressed with use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows us to use standard methods of solving such integrals and functions. The article also presents functions for the calculation of distortion. The maps illustrate the basic properties of developed map projections. Distortion of areas and lengths are presented on isograms and by Tissot’s indicatrixes with garticules of reduced coordinates. In this paper the author continues his considerations of the application of reduced coordinates to the construction of map projections for equidistant map projections. The developed method can be used in planetary cartography for mapping irregular objects, for which tri-axial ellipsoids have been accepted as reference surfaces. It can also be used to calculate the surface areas of regions located on these objects. The calculations were carried out for a tri-axial ellipsoid with semi-axes a = 267:5 m, b = 147 m, c = 104:5 m accepted as a reference ellipsoid for the Itokawa asteroid.

Słowa kluczowe

EN

map projection; distortion in map projection; equal-area map projections; triaxial ellipsoid; reduced coordinates

PL

projekcja mapy; zniekształcenie mapy; współrzędne geodezyjne

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Geodesy and Cartography
• Rocznik: 2018
• Tom: Vol. 67, no. 2
• Strony: 271--294
• Opis fizyczny: Bibliogr. 13 poz., wykr.

Twórcy

autor

Pędzich P.

• Warsaw Technical University, Faculty of Geodesy and Cartography 1 Plac Politechniki, 00–661 Warsaw, Poland

Bibliografia

• [1] Balcerzak, J. and Panasiuk, J. (2005). Wprowadzenie do kartografii matematycznej. Oficyna Wydawnicza Politechniki Warszawskiej.
• [2] Berthoud, M.G. (2005). An equal-area map projection for irregular objects. Icarus, 175(2), 382–389.
• [3] Bugaevsky, L.M. (1987). K voprosu o poluchenii izometricheskikh koordinat i ravnougol’noy tsilindricheskoy proyektsii trekhosnogo ellipsoida. Izvestiya Vysshikh Uchebnykh Zavedeniy. Geodeziya i Aerofotosyemka, 4, 79–90.
• [4] Bugaevsky, L.M. (1991). Izometricheskiye koordinaty, ravnougol’noy tsilindricheskoy, konicheskoy i azimutal’noy proyektsii trekhosnogo ellipsoida. Izvestiya Vysshikh Uchebnykh Zavedeniy. Geodeziya i Aerofotosyemka, 3, 144–152.
• [5] Bugaevsky, L.M. (1999). Teoria kartograficheskikh proyektsiy riegularnykh povierkhnostiey. Zlatoust.
• [6] Byrd, P.F. and Friedmann, M.D. (1954). Handbook of elliptic integrals for engineers and phisicists. Springer-Verlag, Berlin-Gottingen-Heidelberg.
• [7] Fleis, M.E., Nyrtsov, M.V. and Borisov, M.M. (2013). Cylindrical Projection Conformality of Tri-axial Ellipsoid. Doklady Earth Sciences, 451, Part 1, 787–789. DOI: 10.1134/S1028334X13070234.
• [8] Nyrtsov, M.V., Fleis, M.E. and Borisov, M.M. (2012). Kartografirovaniye asteroida 433 Eros v ravnopromezhutochnykh vdol’ meridianov tsilindricheskoy i azimutal’noy proyektsiyakh trekhosnogo ellipsoida. Izvestiya Vysshikh Uchebnykh Zavedeniy. Geodeziya i Aerofotosyemka, 1, 54–61.
• [9] Nyrtsov,M. V., Fleis, M. E., Borisov, M. M. and Stooke, P. J. (2013). Equal-area projections of the tri-axial ellipsoid: first time derivation and implementation of cylindrical and azimuthal projections for small solar system bodies. The Cartographic Journal, 52(2), 114–124. 10.1080/00087041.2015.1119471.
• [10] Nyrtsov, M.V., Fleis, M.E., Borisov, M.M., Stooke, P.J. (2014). Jacobi Conformal Projection of the Triaxial Ellipsoid: New Projection for Mapping of Small Celestial Bodies. In: M. Buchroithner et al. (eds.). Cartography from Pole to Pole, Lecture Notes in Geoinformation and Cartography. Springer-Verlag Berlin Heidelberg. DOI: 10.1007/978-3-642-32618-9_17.
• [11] Pędzich, P. (2017). Equidistant map projections of a tri-axial ellipsoid with the use of reduced coordinates. Geodesy and Cartography, 66(2), 271–290. DOI: 10.1515/geocart-2017-0021.
• [12] Pędzich, P. (2014). Podstawy odwzorowań kartograficznych z aplikacjami komputerowymi. Oficyna Wydawnicza Politechniki Warszawskiej.
• [13] Snyder J.P. (1985). Conformal mapping of the tri-axial ellipsoid. Survey Review, 28(217), 130–148.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)