Module ecef

Geocentric Earth-Centered, Earth-Fixed (ECEF) coordinates.

Geocentric conversions transcoded from Charles Karney's C++ class Geocentric into pure Python class EcefKarney, class EcefSudano based on John Sudano's paper, class EcefVeness transcoded from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian, class EcefYou implementing Rey-Jer You's transformations and classes EcefFarrell22 and EcefFarrell22 from Jay A. Farrell's Table 2.1 and 2.2, page 29-30.

Following is a copy of Karney's Detailed Description.

Convert between geodetic coordinates lat-, longitude and height h (measured vertically from the surface of the ellipsoid) to geocentric x, y and z coordinates, also known as Earth-Centered, Earth-Fixed (ECEF).

The origin of geocentric coordinates is at the center of the earth. The z axis goes thru the North pole, lat = 90°. The x axis goes thru lat = 0°, lon = 0°.

The local (cartesian) origin is at (lat0, lon0, height0). The local x axis points East, the local y axis points North and the local z axis is normal to the ellipsoid. The plane z = -height0 is tangent to the ellipsoid, hence the alternate name local tangent plane.

Forward conversion from geodetic to geocentric (ECEF) coordinates is straightforward.

For the reverse transformation we use Hugues Vermeille's Direct transformation from geocentric coordinates to geodetic coordinates, J. Geodesy (2002) 76, page 451-454.

Several changes have been made to ensure that the method returns accurate results for all finite inputs (even if h is infinite). The changes are described in Appendix B of C. F. F. Karney Geodesics on an ellipsoid of revolution, Feb. 2011, 85, 105-117 (preprint). Vermeille similarly updated his method in An analytical method to transform geocentric into geodetic coordinates, J. Geodesy (2011) 85, page 105-117. See Geocentric coordinates for more information.

The errors in these routines are close to round-off. Specifically, for points within 5,000 Km of the surface of the ellipsoid (either inside or outside the ellipsoid), the error is bounded by 7 nm (7 nanometers) for the WGS84 ellipsoid. See Geocentric coordinates for further information on the errors.