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A Non-Zonal and Non-Singular Formulation of the Gauss-Krüger Projection for Polar Regions

Author

Listed:
  • Dongquan Zhou

    (School of Geography and Information Engineering, China University of Geosciences (Wuhan), Wuhan 430078, China)

  • Shaofeng Bian

    (School of Geography and Information Engineering, China University of Geosciences (Wuhan), Wuhan 430078, China)

  • Wenkui Li

    (College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China)

  • Zemin Wu

    (School of Geography and Information Engineering, China University of Geosciences (Wuhan), Wuhan 430078, China)

Abstract

The complex analytic continuation can be developed to enable the Gauss-Krüger projection to be non-zonal and non-singular in polar regions. The series expansion of the traditional Gauss-Krüger projection in terms of third flattening has been derived by using a computer algebra system, leading to a substantial simplification of the final formulas without compromising accuracy compared with the series expansion in terms of eccentricity. Therefore, the non-zonal formulas of the Gauss-Krüger projection in term of third flattening have been expressed, and the non-zonal and the non-singular formulas of the Gauss-Krüger projection has been derived by the conformal colatitude. With respect to the mapping of 4 high-latitude regions (Finland, Sweden, Norway and Alaska) and its isopleth map, it was verified that the non-zonal and the non-singular algorithm of the Gauss-Krüger projection had high precision and minimal distortion in polar regions. The method presented a meaningful supplement to the existing Gauss–Krüger projection family.

Suggested Citation

  • Dongquan Zhou & Shaofeng Bian & Wenkui Li & Zemin Wu, 2025. "A Non-Zonal and Non-Singular Formulation of the Gauss-Krüger Projection for Polar Regions," Mathematics, MDPI, vol. 14(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:14:y:2025:i:1:p:2-:d:1821861
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