262
Views
2
CrossRef citations to date
0
Altmetric
Articles

A statistical reinterpretation and assessment of criteria used for measuring map projection distortion

ORCID Icon
Pages 481-491 | Received 21 Oct 2019, Accepted 09 May 2020, Published online: 16 Jun 2020

References

  • Airy, G. B. (1861). Explanation of a projection by balance of errors for maps applying to a very large extent of the earth’s surface; and comparison of this projection with other projections. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 22(149), 409–421. https://doi.org/10.1080/14786446108643179
  • Baranyi, J. (1968). The problems of the representation of the globe on a plane with special reference to the preservation of the forms of continents. In S. Radó (Eds.), Hungarian Cartographical Studies (pp. 19–43). Foldmeresi Intezet.
  • Basaraner, M., & Cetinkaya, S. (2019). New measures for analysis and comparison of shape distortion in world map projections. Cartography and Geographic Information Science, 46(6), 518–531. https://doi.org/10.1080/15230406.2019.1567394
  • Bayeva, Y. (1987). Kriterii otsenki dostoinstva kartograficheskikh proyektsiy, ispolzuyemykh dlya sostavleniya kart mira. Geodeziya i Aerofotosyomka, (3), 109–112.
  • Behrmann, W. (1910). Die beste bekannte flächentreue Projektion der ganzen Erde. Petermanns Mitteilungen, 56(3), 141–144.
  • Canters, F. (2002). Small-scale map projection design. Taylor & Francis.
  • Frančula, N. (1971). Die vorteilhaftesten Abbildungen in der Atlaskartographie (Doctoral dissertation). Reinischen Friedrich Wilhelms Universität, Hohen Landwirtschaftlichen Fakultät.
  • Frančula, N. (1980). Über die Verzerrungen in den kartographischen Abbildungen. Kartographische Nachrichten, 30(6), 214–216.
  • Galton, F. (1879). The geometric mean, in vital and social statistics. Proceedings of the Royal Society of London, 29(196–199), 365–367. https://doi.org/10.1098/rspl.1879.0060
  • Gede, M. (2011). Optimising the distortions of sinusoidal- elliptical composite projections. In A. Ruas (Ed.), Advances in cartography and giscience (Vol. 2, pp. 209–225). Springer.
  • Goldberg, D. M., & Gott, J. R. (2007). Flexion and skewness in map projections of the Earth. Cartographica: The International Journal for Geographic Information and Geovisualization, 42(4), 297–318. https://doi.org/10.3138/carto.42.4.297
  • Gott, R. J., Mugnolo, C., & Colley, W. N. (2007). Map projections minimizing distance errors. Cartographica: The International Journal for Geographic Information and Geovisualization, 42(3), 219–234. https://doi.org/10.3138/carto.42.3.219
  • Grafarend, E. W., & Krumm, F. W. (2006). Map projections: Cartographic information systems. Springer. https://doi.org/10.1007/978-3-540-36702-4
  • Grafarend, E. W., & Niermann, A. (1984). Beste echte Zylinderabbildungen. Kartographische Nachrichten, 34(3), 103–107.
  • Györffy, J. (1990). Anmerkungen zur Frage der besten echten Zylinderabbildungen. Kartographische Nachrichten, 40(4), 140–146.
  • Györffy, J. (2016). Some remarks on the question of pseudocylindrical projections with minimum distortions for world maps. In G. Gartner, M. Jobst, & H. Huang (Eds.), Progress in cartography: Eurocarto 2015 (pp. 253–265). Springer. https://doi.org/10.1007/978-3-319-19602-2_16
  • Györffy, J., & Klinghammer, I. (2004). Die kleinmaßstäbige Darstellung von Europa in Projektionen geringster Verzerrung – Die Basis für einen Europa-Atlas. Kartographische Nachrichten, 54(6), 262–268. https://doi.org/10.1007/BF03545455
  • Jenny, B., Patterson, T., & Hurni, L. (2008). Flex projector–interactive software for designing world map projections. Cartographic Perspectives, (59), 12–27. https://doi.org/10.14714/CP59.245
  • Kavrayskiy, V. V. (1934). Matematicheskaya kartografiya. Redbaza Goskartotresta.
  • Kerkovits, K. (2017). Legjobb valódi hengervetület nagy területek ábrázolására. Geodézia és Kartográfia, 69(3), 29–32.
  • Kerkovits, K. (2018). Calculation and visualization of flexion and skewness. Kartografija i Geoinformacije, 17(29), 32–45. https://doi.org/10.32909/kg.17.29.3
  • Kerkovits, K. (2019). Comparing finite and infinitesimal map distortion measures. International Journal of Cartography, 5(1), 3–22. https://doi.org/10.1080/23729333.2018.1500255
  • Kerkovits, K. (2020). Quadrature rules to calculate distortions of map projections. The Cartographic Journal. Advance online publication. https://doi.org/10.1080/00087041.2020.1714278
  • Kirkwood, T. B. L. (1979). Biometrics. Geometric Means and Measures of Dispersion, 35 (4), 908–909. Retrieved from http://www.jstor.org/stable/2530139
  • Laskowski, P. (1997a). Part 2: Distortion-spectrum applications projection cross-breeding. Cartographica: The International Journal for Geographic Information and Geovisualization, 34(3), 19–40. https://doi.org/10.3138/08N6-T847-U740-7458
  • Laskowski, P. (1997b). Part 1: Distortion-spectrum fundamentals a new tool for analyzing and visualizing map distortions. Cartographica: The International Journal for Geographic Information and Geovisualization, 34(3), 3–18. https://doi.org/10.3138/Y51X-1590-PV21-136G
  • Limpert, E., Stahel, W. A., & Abbt, M. (2001). Log-normal distributions across the sciences: Keys and clues: On the charms of statistics, and how mechanical models resembling gambling machines offer a link to a handy way to characterize log-normal distributions, which can provide deeper insight into variability and probability—normal or log-normal: That is the question. BioScience, 51(5), 341–352. https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2
  • Meshcheryakov, G. A. (1968). Teoreticheskie osnovy matematicheskoj kartografii. Nedra.
  • Peters, A. B. (1975). Wie man unsere Weltkarten der Erde ähnlicher machen kann. Kartographische Nachrichten, 25(5), 173–183.
  • Peters, A. B. (1979). Die Winkelsche Abbildung geringster Verzerrung: Anmerkung zum Gutachten von A. Heupel und J. Schoppmeyer. Kartographische Nachrichten, 29(5), 179–182.
  • Snyder, J. P. (1987). Map projections — A working manual. Vol. 1395 US Government Printing Office. http://pubs.er.usgs.gov/publication/pp1395
  • Tissot, A. (1878). Mémoire sur la représentation des surfaces et les projections des cartes géographiques. Nouvelles annales de mathématiques, journal des candidats aux écoles polytechnique et normale, 2(18), 385–397. http://www.numdam.org/item/NAM_1879_2_18__385_0/

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.