Applications of Mathematics, Vol. 66, No. 6, pp. 887-927, 2021
On inversions of van der Grinten projections
Tomáš Bayer, Milada Kočandrlová
Received January 31, 2020. Published online May 14, 2021.
Abstract: Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I-IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement and are applicable to the coordinate transformations.
Keywords: mathematical cartography; inverse form; map; projection; van der Grinten; GIS
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Affiliations: Tomáš Bayer (corresponding author), Faculty of Science, Charles University, Albertov 6, 120 78 Praha 2, Czech Republic, e-mail: bayertom@natur.cuni.cz; Milada Kočandrlová, Faculty of Finance and Accounting, University of Economics, nám. W. Churchilla 1938/4, 130 67 Praha 3, Czech Republic, e-mail: kocandrlova@hotmail.cz
