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LAMBERT AZIMUTHAL EQUAL-AREA PROJECTION

Year 2024, Volume: 25 Issue: 3, 380 - 389, 30.09.2024
https://doi.org/10.18038/estubtda.1410864

Abstract

In the present study, we give the proofs about important properties of Lambert azimuthal projection, like conformality, preserve area e.g. which characterizes it. While there are some kind of Lambert projection for instance standard, cylindrical in the literature, we utilize from the south polar aspect and in our proofs, we use this approach. Finally, we give some visualizations of the inverse of projection as an example.

References

  • [1] Marić M. A toolbox for visualizing Möbius transformations. IV Nordic GeoGebra Conference, Copenhagen, 2013.
  • [2] Wilson P. Curved Spaces: From Classical Geometries to Elementary Differential Geometry. Cambridge University Press, New York-United States of America, 2008. pp. 39-44.
  • [3] Marsland S, Mclachlan RI. Möbius invariants of shapes and images. Symmetry, Integrability and Geometry: Methods and Applications 2016; 12: 1-29.
  • [4] Mork LK, Ulness DJ. Visualization of Mandelbrot and Julia sets of Möbius transformations. Fractal and Fractional 2021; 5-73.
  • [5] Osborne P. The Mercator projections: The normal and transverse Mercator projections on the sphere and the ellipsoid with full derivations of all formulae. Edinburg Zenodo. https://doi.org/10.5281/zenodo.35392
  • [6] Fong C. An Indoor Alternative to Stereographic Spherical Panoramas. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture. pp. 103-110.
  • [7] Borradaile G. Statistics of Earth Science Data. Springer-Verlag Berlin Heidelberg New York, 2003.
  • [8] Snyder JP. Map Projections-A Working Manual. United States Goverment Printing Office, Washington, 1987.
  • [9] Pressley A. Elementary Differential Geometry, Springer Undergraduate Mathematics Series, London-England, 2010. pp. 391-398.
Year 2024, Volume: 25 Issue: 3, 380 - 389, 30.09.2024
https://doi.org/10.18038/estubtda.1410864

Abstract

References

  • [1] Marić M. A toolbox for visualizing Möbius transformations. IV Nordic GeoGebra Conference, Copenhagen, 2013.
  • [2] Wilson P. Curved Spaces: From Classical Geometries to Elementary Differential Geometry. Cambridge University Press, New York-United States of America, 2008. pp. 39-44.
  • [3] Marsland S, Mclachlan RI. Möbius invariants of shapes and images. Symmetry, Integrability and Geometry: Methods and Applications 2016; 12: 1-29.
  • [4] Mork LK, Ulness DJ. Visualization of Mandelbrot and Julia sets of Möbius transformations. Fractal and Fractional 2021; 5-73.
  • [5] Osborne P. The Mercator projections: The normal and transverse Mercator projections on the sphere and the ellipsoid with full derivations of all formulae. Edinburg Zenodo. https://doi.org/10.5281/zenodo.35392
  • [6] Fong C. An Indoor Alternative to Stereographic Spherical Panoramas. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture. pp. 103-110.
  • [7] Borradaile G. Statistics of Earth Science Data. Springer-Verlag Berlin Heidelberg New York, 2003.
  • [8] Snyder JP. Map Projections-A Working Manual. United States Goverment Printing Office, Washington, 1987.
  • [9] Pressley A. Elementary Differential Geometry, Springer Undergraduate Mathematics Series, London-England, 2010. pp. 391-398.
There are 9 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry, Cartography and Digital Mapping
Journal Section Articles
Authors

Emre Öztürk 0000-0001-6638-3233

Publication Date September 30, 2024
Submission Date December 27, 2023
Acceptance Date August 27, 2024
Published in Issue Year 2024 Volume: 25 Issue: 3

Cite

AMA Öztürk E. LAMBERT AZIMUTHAL EQUAL-AREA PROJECTION. Estuscience - Se. September 2024;25(3):380-389. doi:10.18038/estubtda.1410864