EPSG Dataset :: v12.003

Coordinate Frame rotation (geog3D domain)

Coordinate Operation Method Details [VALID]

Name:

Coordinate Frame rotation (geog3D domain)

Code:

1038

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 Coordinate Frame rotation (geog3D domain) transformation has 3 steps:

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

(ii) the middle step of the concatenated transformation, from geocentric coordinates to geocentric coordinates, uses the Coordinate Frame rotation (geocentric domain) method, EPSG method code 1032;

(iii) finally the geocentric coordinates are converted to geographic 3D using EPSG coordinate operation method code 9602.

Example:

The same example as for the Position Vector transformation (coordinate operation method 1037) can be calculated, however the following transformation parameters have to be applied to achieve the same input and output in terms of coordinate values:

Transformation parameters Coordinate Frame rotation convention:
tX (m) = 0.000
tY (m) = 0.000
tZ (m) = 4.5
rX (") = 0.000
rY (") = 0.000
rZ (") = -0.554 = -0.000002685868 radians
dS (ppm) = 0.219

from which M = 1.000000219

Please note that only the rotation has changed sign as compared to the Position Vector transformation.

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 Position Vector tfm (code 1037) but beware of the differences! The Position Vector convention is used by IAG and recommended by ISO 19111. See methods 1032 and 9607 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:

[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 Position Vector transformation method (code 9606).
Coordinate Frame rotation	EPSG alias	This names is ambiguous as it makes no distinction between the domain of the source and target CRSs. See also methods 1032 and 9607.

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.