EPSG Dataset :: v12.003

Position Vector transformation (geog2D domain)

Coordinate Operation Method Details [VALID]

Name:

Position Vector transformation (geog2D domain)

Code:

9606

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.

Transformation of coordinates from one geographic coordinate reference system into another is often carried out as a concatenation of the following operations:

(geographical to geocentric) + (geocentric to geocentric) + (geocentric to geographic)

The Position Vector transformation (geog2D domain) has 5 steps:

(i) geographic 2D coordinates are converted to 3D using EPSG coordinate operation method code 9659;

(ii) geographic 3D coordinates are converted to geocentric coordinates using EPSG coordinate operation method code 9602;

(iii) the middle step of the concatenated transformation, from geocentric coordinates to geocentric coordinates, uses the Position Vector(geocentric domain) method, EPSG method code 1033;

(iv) the geocentric coordinates are converted to geographic 3D using EPSG coordinate operation method code 9602;

(v) finally the geographic 3D coordinates are converted to geographic 2D using EPSG coordinate operation method code 9659.

Example:

Input point:
Coordinate reference system: WGS 72 (geographic 2D)
Latitude = 55 deg 00 min 00 sec N
Longitude = 4 deg 00 min 00 sec E

This is taken to be geographic 3D with an assumed Ellipsoidal height hS = 0 m

This transforms to Cartesian geocentric coords:
Xs = 3 657 660.66 (m)
Ys = 255 768.55 (m)
Zs = 5 201 382.11 (m)

Transformation parameters WGS 72 to WGS 84:
tX (m) = 0.000
tY (m) = 0.000
tZ (m) = 4.5
rX (") = 0.000 = 0.0 radians
rY (") = 0.000 = 0.0 radians
rZ (") = 0.554 = 0.000002685868 radians
dS (ppm) = 0.219

from which M = 1.000000219

Application of the 7 parameter Position Vector transformation results in WGS 84 coordinates of:
Xt = 3 657 660.78 (m)
Yt = 255 778.43 (m)
Zt = 5 201 387.75 (m)

This converts into:
Latitude = 55 deg 00 min 00.090 sec N
Longitude = 4 deg 00 min 00.554 sec E
Ellipsoidal height = +3.22 m
on the WGS 84 geographic 3D coordinate reference system. For the 2D equivalent the height is ignored.

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
X-axis translation	8605	Yes	The difference between the X values of a point in the target and source coordinate reference systems.
Y-axis translation	8606	Yes	The difference between the Y values of a point in the target and source coordinate reference systems.
Z-axis translation	8607	Yes	The difference between the Z values of a point in the target and source coordinate reference systems.
X-axis rotation	8608	Yes	The angular difference between the Y and Z axes directions of target and source coordinate reference systems. This is a rotation about the X axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Y-axis rotation	8609	Yes	The angular difference between the X and Z axes directions of target and source coordinate reference systems. This is a rotation about theY axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Z-axis rotation	8610	Yes	The angular difference between the X and Y axes directions of target and source coordinate reference systems. This is a rotation about the Z axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Scale difference	8611	Yes	Scale factor for source CRS axes minus one, where the scale factor is a multiplication factor to be applied to coordinates in the source CRS to obtain the correct scale in the target CRS. dS = (M – 1). If a distance of 100 km in the source CRS translates into a distance of 100.001 km in the target CRS, the scale difference is 1 ppm (the ratio being 1.000001). When the scale difference dS is expressed in parts per million (ppm), M = (1 + dS10-6). When the scale difference dS is expressed in parts per billion (ppb), M = (1 + dS10-9).

Meta Data

Remarks:

Note the analogy with the Coordinate Frame rotation (code 9607) but beware of the differences! The Position Vector convention is used by IAG and recommended by ISO 19111. See methods 1033 and 1037 for similar tfms operating between other CRS types.

Information Source:

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

Data Source:

EPSG

Revision Date:

February 21, 2019

Change ID:

[1998.16] [2009.083] [2013.021] [2018.001] [2019.006]

Alias:

Alias	Naming System	Remarks
Bursa-Wolf	EPSG alias	This names is ambiguous as it is also applied to the Coordinate Frame rotation method (code 9607).
Position Vector 7-param. transformation	EPSG alias	This name is ambiguous as it makes no distinction of the domain of the source and target CRSs to which it is applied. See also methods 1032 and 10xx.

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.