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Geocentric conversions transcribed from Charles Karney's C++ classes Geocentric and LocalCartesian into pure Python classes EcefKarney respectively EcefCartesian, class EcefVeness transcribed from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian and class EcefYou implementing Rey-Jer You's transformations.
Convert between geodetic coordinates lat
-,
lon
gitude 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 origin of local cartesian coordinate system is at
lat0
, lon0
and height0
. The
z
axis is normal to the ellipsoid, the y
axis
points due North. The plane z = -height0
is tangent to the
ellipsoid.
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, 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, 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.
Version: 19.12.22
Classes | |
EcefError An ECEF issue. |
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_EcefBase (INTERNAL) Base class for EcefKarney, EcefVeness and EcefYou. |
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EcefKarney Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on Karney's Geocentric methods. |
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EcefCartesian Conversion between geodetic (lat, lon, height) and
local cartesian (x, y, z) coordinates with a local
cartesian origin at (lat0, lon0, height0) transcibed
from on Karney's C++ class LocalCartesian.
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EcefMatrix A rotation matrix. |
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Ecef9Tuple 9-Tuple (x, y, z, lat, lon, height, C, M, datum) with
geocentric coordinates x , y and
z , geodetic coordinates lat ,
lon and height , case C and
optionally, the EcefMatrix M and datum ,
with lat and lon in degrees
and x , y , z and
height in meter , usually.
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EcefVeness Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates transcribed from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian. |
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EcefYou Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates using Rey-Jer You's transformations. |
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