Skip to main content
SpringerLink
Log in

An analytical method to transform geocentric into geodetic coordinates

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the polar axis, the equatorial plane and the Earth’s center. Comparison with the method of extrema with constraints to obtain this quartic equation is made.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ariel A, Ariel-Berger N (2006) Plotting the globe. Praeger, Wesport, Part 3

  • Borkowski KM (1987) Transformation of geocentric to geodetic coordinates without approximations. Astron Space Sci 139: 1–4

    Article  Google Scholar 

  • Borkowski KM (1989) Accurate algorithms to transform geocentric to geodetic coordinates. Bull Geod 63: 52–54

    Article  Google Scholar 

  • Cardanus H (1545) Artis magnae, sive de regulis algebraicis. Pavia, p 294

  • Descartes R (1637) Discours de la Méthode plus la Dioptrique, les Météores et la Géométrie. Ian Maire Leiden 3: 373

    Google Scholar 

  • Featherstone WE, Claessens SJ (2008) Closed-form transformation between geodetic and ellipsoidal coordinates. Stud Geophys Geod 52: 12

    Article  Google Scholar 

  • Fok HS, Iz HB (2003) A comparative analysis of the performance of iterative and non-iterative solutions to the Cartesian to geodetic coordinate transformation. J Geospat Eng 5: 61–74

    Google Scholar 

  • Fukushima T (1999) Fast transform from geocentric to geodetic coordinates. J Geod 73: 603–610

    Article  Google Scholar 

  • Fukushima T (2006) Transformation from Cartesian to geodetic coordinates accelerated by Halley’s method. J Geod 79((12): 689–693

    Article  Google Scholar 

  • Gonzalez-Vega L, Polo-Blanco I (2009) A symbolic analysis of Verm- eille and Borkowski polynomials for transforming 3D Cartesian to geodetic coordinates. J Geod 83: 1071–1081

    Article  Google Scholar 

  • IERS Conventions (1996) Technical note no. 21, pp 12–13

  • IERS Conventions (2003) Technical note no. 32, pp 30

  • Jones GC (2002) New solutions for the geodetic coordinate transformation. J Geod 76: 443

    Article  Google Scholar 

  • Merriman M (1892) The deduction of final formulas for the algebraic solution of quartic equation. Am J Math 14: 237–245

    Article  Google Scholar 

  • NIMA (2000) National Imagery and Mapping Agency (USA) Technical Report TR8350.2, 3

  • Taylor B (1715) Methodus incrementorum directa et inversa. Gul. Innys, London, pp 21–23

    Google Scholar 

  • Vermeille H (2002) Direct transformation from geocentric coordinates to geodetic coordinates. J Geod 76: 451–454

    Article  Google Scholar 

  • Vermeille H (2004) Computing geodetic coordinates from geocentric coordinates. J Geod 78: 94–95

    Article  Google Scholar 

  • Zhang CD et al (2005) An alternative algorithm to transform Cartesian to geodetic coordinates. J Geod 79: 413–420

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 2 Place Dr Léon Martin, 38000, Grenoble, France

    Hugues Vermeille

Authors
  1. Hugues Vermeille
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hugues Vermeille.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vermeille, H. An analytical method to transform geocentric into geodetic coordinates. J Geod 85, 105–117 (2011). https://doi.org/10.1007/s00190-010-0419-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00190-010-0419-x

Keywords

Search

Navigation