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Reconstruction of Map Projection, its Inverse and Re-Projection

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Abstract

This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections frequently used in early maps are involved and their inverse formulas are presented.

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Authors and Affiliations

  1. Faculty of Science, Charles University, Albertov 6, Praha 2, 120 78, Czech Republic

    Tomáš Bayer

  2. Faculty of Finance and Accounting, University of Economics, nám. W. Churchilla 1938/4, Praha 3, 130 67, Czech Republic

    Milada Kočandrlová

Authors
  1. Tomáš Bayer
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  2. Milada Kočandrlová
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Correspondence to Tomáš Bayer.

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Bayer, T., Kočandrlová, M. Reconstruction of Map Projection, its Inverse and Re-Projection. Appl Math 63, 455–481 (2018). https://doi.org/10.21136/AM.2018.0096-18

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  • DOI: https://doi.org/10.21136/AM.2018.0096-18

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