EPSG Dataset :: v12.053

Affine parametric transformation

Coordinate Operation Method Details [VALID]

Name:

Affine parametric transformation

Code:

9624

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.

XT = A0 + A1 * XS + A2 * YS
YT = B0 + B1 * XS + B2 * YS
where
XT , YT are the coordinates of a point P in the target coordinate reference system;
XS , YS are the coordinates of P in the source coordinate reference system.

Reversibility
The reverse transformation is another affine transformation using the same formulas but with different parameter values. The reverse parameter values, indicated by a prime (’), can be calculated from those of the forward transformation as follows:

D = A1 * B2 – A2 * B1
A0’ = (A2 * B0 – B2 * A0) / D
B0’ = (B1 * A0 – A1 * B0) / D
A1’ = +B2 / D
A2’ = – A2 / D
B1’ = – B1 / D
B2’ = +A1 / D

Then
XS = A0' + A1' * XT + A2' * YT
YS = B0' + B1' * XT + B2' * YT

Example:

Coordinate transformation: Jamaica 1875 / Jamaica (Old Grid) to JAD69 / Jamaica National Grid

Coordinate transformation parameter values:
A0 = 82357.457 metres
A1 = 0.304794369
A2 = 0.000015417425
B0 = 28091.324 metres
B1 = -0.000015417425
B2 = 0.304794369

The units for the Jamaica 1875 / Jamaica (Old Grid) are feet, those for the JAD69 / Jamaica National Grid are metres. The foot-metre conversion factor is embedded within the transformation, together with the scale and orientation differences between the two coordinate reference systems.

Jamaica 1875 / Jamaica (Old Grid) input point:
Easting E = XS = 553,900.00 feet
Northing N = YS = 482,500.00 feet

Then on JAD69 / Jamaica National Grid
Easting E = XT = 251,190.497 metres
Northing N = XT = 175,146.067 metres

For the reverse calculation, first calculate derived parameter values:

D = 0.092899608
A0' = -270201.960 Clarke's foot
A1' = 3.280900499
A2' = -0.000165958
B0' = -92178.507 Clarke's foot
B1' = 0.000165958
B2' = 3.280900499

Then for the same point
Easting E = XT = 251,190.497 metres
Northing N = XT = 175,146.067 metres
gives
Easting E = XS = 553,900.000 feet
Northing N = YS = 482,500.000 feet

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
A0	8623	No	Coefficient used in affine (general parametric) and polynomial transformations.
A1	8624	No	Coefficient used in affine (general parametric) and polynomial transformations.
A2	8625	No	Coefficient used in affine (general parametric) and polynomial transformations.
B0	8639	No	Coefficient used in affine (general parametric) and polynomial transformations.
B1	8640	No	Coefficient used in affine (general parametric) and polynomial transformations.
B2	8641	No	Coefficient used in affine (general parametric) and polynomial transformations.

Meta Data

Information Source:

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

Data Source:

EPSG

Revision Date:

June 12, 2013

Change ID:

[2004.67] [2012.075]

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.