EPSG Dataset :: v12.003

Geocentric/topocentric conversions

Coordinate Operation Method Details [VALID]

Name:

Geocentric/topocentric conversions

Code:

9836

Operation is Reversible:

Yes

Formula:

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

First it is necessary to derive ellipsoidal values Po, Lo of the topocentric origin from their geocentric values Xo, Yo, Zo through the reverse formulas given in method 9602.

Then topocentric coordinates [U, V, W] are computed as follows:

U = – (X-Xo) sin Lo + (Y-Yo) cos Lo
V = – (X–Xo) sin Po cos Lo – (Y–Yo) sin Po sin Lo + (Z–Zo) cos Po
W = (X–Xo) cos Po cos Lo + (Y–Yo) cos Po sin Lo + (Z–Zo) sin Po

The reverse formulas to calculate geocentric coordinates from topocentric coordinates are:

X = Xo – U sin Lo – V sin Po cos Lo + W cos Po cos Lo
Y = Yo + U cos Lo – V sin Po sin Lo + W cos Po sin Lo
Z = Zo + V cos Po + W sin Po

Example:

For Geocentric CRS = WGS 84 (EPSG CRS code 4978)
and
Topocentric origin Xo = 3652 755.3058 m
Topocentric origin Yo = 319 574.6799 m
Topocentric origin Zo = 5201 547.3536 m

Ellipsoid parameters: a = 6378137m.0 1/f = 298.2572236

First calculate additional ellipsoid parameters:
e^2 = 0.006694380
eta = 0.006739497
b = 6356752.314

Next, derive Po, Lo from Xo,Yo,Zo by the formulas given in method 9602:
p = 3666708.2376
q = 0.9583523313
Po = 0.9599310885 rad
Lo = 0.0872664625 rad

Forward calculation for point with geocentric coordinates:
X= 3771 793.968
Y= 140 253.342
Z= 5124 304.349

gives topocentric coordinates
U= -189 013.869
V= -128 642.040
W= -4 220.171

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Geocentric X of topocentric origin	8837	No	For topocentric CSs, the geocentric Cartesian X coordinate of the topocentric origin.
Geocentric Y of topocentric origin	8838	No	For topocentric CSs, the geocentric Cartesian Y coordinate of the topocentric origin.
Geocentric Z of topocentric origin	8839	No	For topocentric CSs, the geocentric Cartesian Z coordinate of the topocentric origin.

Meta Data

Information Source:

EPSG guidance note #7-2, http://www.epsg.org

Data Source:

EPSG

Revision Date:

June 13, 2017

Change ID:

[2017.018]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.