Skip to main content
SpringerLink
Log in

Inverse Transformation for Several Pseudo-cylindrical Map Projections Using Jacobian Matrix

  • Conference paper
Book cover Computational Science and Its Applications – ICCSA 2009 (ICCSA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5592))

Included in the following conference series:

Abstract

The normal practice in ‘mathematical cartography’ is transforming the graticule of meridians and parallels of a sphere onto a plane. The conversion from geographical to plane coordinates is called forward transformation. The inverse transformation, which yields geographical coordinates captured from paper maps, is a more recent development, due to the need for transformation between different map projections especially in Geographic Information Systems (GIS). Deriving the invers equations is sometimes not easy for the projections that have complicated forward functions including parametric variables. This paper describes an iteration algorithm using jacobian matrix for the inverse transformation of the pseudo-cylindrical map projections with non-linear forward projection equations. The method has been tested for ten pseudocylindrical world map projection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Canters, F., DeClair, H.: The World in Perspective: A Directory of World Map Projections. John Wiley and Sons, Chichester (1989)

    Google Scholar 

  2. Bugayevski, L., Snyder, J.P.: Map Projections: A Reference Manual, p. 328. Taylor and Francis, London (1995)

    Google Scholar 

  3. Richardus, P., Adler, R.K.: Map Projections: For Geodesists, Cartographers and Geographers, p. 174. North Holland Publishing Company, Amsterdam (1972)

    Google Scholar 

  4. Maling, D.H.: Coordinate Systems and Map Projections, p. 476. Pergamon Press, Oxford (1992)

    Google Scholar 

  5. Bildirici, İ.Ö., İpbüker, C., Yanalak, M.: Function matching for Soviet-era table-based modified polyconic projections. International Journal of Geographical Information Science 20(7), 769–795 (2006)

    Article  Google Scholar 

  6. Yang, Q., Snyder, J.P., Tobler, W.: Map Projection Transformation: Principles and Applications, p. 367. Taylor and Francis, London, England (2000)

    MATH  Google Scholar 

  7. Ipbuker, C., Bildirici, I.O.: Computer Program for the Inverse Transformation of the Winkel Projection. ASCE Journal of Surveying Eng. 131(4), 125–129 (2005)

    Article  Google Scholar 

  8. Bildirici, I.O.: Numerical inverse transformation for map projections. Computers & Geosciences 29, 1003–1011 (2003)

    Article  Google Scholar 

  9. Snyder, J.P.: Flattening the Earth, Two thousand years of map projections, p. 363. The University of Chicago Press (1993)

    Google Scholar 

  10. Delmelle, E.M.: Map Projection Properties: Considerations for small-scale GIS applications, Master of Arts, SUNY Department of Geography, p. 117 (2001)

    Google Scholar 

  11. Snyder, J.P., Voxland, P.M.: An Album of Map Projections, U.S. Geological Survey Bulletin 1453, U.S. Government Printing Office, Washington, p. 239 (1989)

    Google Scholar 

  12. Pipes, A.L., Harvill, R.L.: Applied Mathematics for Engineers and Physicists. McGraw Hill Book Company, New York (1970)

    Google Scholar 

  13. Strubecker, K.: Einführung in die höhere Matematik, Band II. R. Oldenberg Verlag, München, Wien (1967)

    Google Scholar 

  14. Ipbuker, C., Bildirici, I.O.: A General Algorithm for the Inverse Transformation of Map Projections using Jacobian Matrices. In: Proceedings of the Third International Conference on Mathematical & Computational Applications, Konya, Turkey, September 4-6, 2002, pp. 175–182 (2002)

    Google Scholar 

  15. Ruffhead, A.C.: Enhancement of Inverse Projection Algorithms with Particular Reference to the Syrian stereographic Projection. Survey Review 34(270), 501–508 (1998)

    Article  Google Scholar 

  16. Ipbuker, C.: An Inverse Solution to the Winkel Tripel Projection. Cartography and Geographical Information Science 29, 37–40 (2002)

    Article  Google Scholar 

  17. Oztan, O., Ipbuker, C., Ulugtekin, N.: A numerical Approach to Pseudo-projections on Example Franz Mayr Projection. Journal of General Command of Mapping 125, 37–50 (2001) (in turkish)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Geodesy and Photogrammetry Department, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Cengizhan Ipbuker

Authors
  1. Cengizhan Ipbuker
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

  2. School of Business Systems, Monash University, 3800, Clayton, Victoria, Australia

    David Taniar

  3. L.I.S.U.T. - D.A.P.I.T., University of Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Beniamino Murgante

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, 06123, Perugia, Italy

    Antonio Laganà

  5. School of Computing, Computer Communication Laboratory, SoongSil University, 1-1 Sang-do 5 Dong, Dong-jak Ku, 156-743, Seoul, Korea

    Youngsong Mun

  6. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ipbuker, C. (2009). Inverse Transformation for Several Pseudo-cylindrical Map Projections Using Jacobian Matrix. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2009. ICCSA 2009. Lecture Notes in Computer Science, vol 5592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02454-2_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02454-2_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02453-5

  • Online ISBN: 978-3-642-02454-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation