EPSG Dataset :: v12.003

Coordinate Frame rotation (geocentric domain)

Coordinate Operation Method Details [VALID]

Name:

Coordinate Frame rotation (geocentric domain)

Code:

1032

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.

Although being common practice particularly in the European E&P industry, the Position Vector transformation sign convention is not universally accepted. A variation on this formula is also used, particularly in the USA E&P industry. That formula is based on the same definition of translation and scale parameters, but a different definition of the rotation parameters. The associated convention is known as the "Coordinate Frame rotation" convention.
The formula is:

(Xt) ( 1 +rZ -rY) (Xs) (tX)
(Yt) = M * ( -rZ 1 +rX) * (Ys) + (tY)
(Zt) ( +rY -rX 1 ) (Zs) (tZ)

and the parameters are defined as:

(tX, tY, tZ): Translation vector, to be added to the point's position vector in the source coordinate reference system in order to transform from source coordinate reference system to target coordinate reference system; also: the coordinates of the origin of source coordinate reference system in the target frame.

(rX, rY, rZ): Rotations to be applied to the coordinate reference frame. The sign convention is such that a positive rotation of the frame about an axis is defined as a clockwise rotation of the coordinate reference frame when viewed from the origin of the Cartesian coordinate reference system in the positive direction of that axis, that is a positive rotation about the Z-axis only from source coordinate reference system to target coordinate reference system will result in a smaller longitude value for the point in the target coordinate reference system. Although rotation angles may be quoted in any angular unit of measure, the formula as given here requires the angles to be provided in radians.

M: Multiplication factor to be applied to the position vector in the source coordinate reference system in order to obtain the correct scale of the target coordinate reference system. M = (1+dS) where dS is the scale difference. When dS is expressed in parts per million, M = (1+dS*10^-6). When dS is the scale difference expressed in parts per billion, M = (1+dS*10^-9).

In the absence of rotations the two formulas are identical; the difference is solely in the rotations. The name of the second method reflects this.

Note that the same rotation that is defined as positive in the first method is consequently negative in the second and vice versa. It is therefore crucial that the convention underlying the definition of the rotation parameters is clearly understood and is communicated when exchanging datum transformation parameters, so that the parameters may be associated with the correct coordinate transformation method (algorithm).

Example:

The same example as for the Position Vector transformation (coordinate operation method 1033) 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 for the 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

M = 1 + dS = 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:

This method is a specific case of the Molodensky-Badekas (CF) method (code 1034) in which the evaluation point is at the geocentre with coordinate values of zero. Note the analogy with the Position Vector method (code 1033) but beware of the differences!

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] [2014.039] [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 1033).
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 1038 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.