[Proj] Implementation of ECEF to geodetic coords (closed form solution)

Charles Karney ckarney at sarnoff.com
Thu Jan 29 22:14:53 EST 2009

I've updated GeographicLib to include ECEF and local Cartesian
coordinates.  Grab it at


This includes a utility ECEFConvert to convert between geodetic and ECEF
or local Cartesian coordinates.

The conversion from ECEF to geodetic coordinates follows

    H. Vermeille, Direct transformation from geocentric coordinates to
    geodetic coordinates, J. Geodesy 76, 451-454 (2002).

However, I have extended the method to ensure that it works close to the
center of the ellipsoid.  I believe that the accuracy is close to the
round-off limit for all inputs.

I also investigated

    T. Fukushima, Fast transform from geocentric to geodetic
    coordinates, J. Geodesy 73, 603-610 (2003)

which also works close to the center of the earth.  However, due to the
choice of independent variable, the accuracy is substantially poorer for
points close to the equatorial plane.

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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