EPSG:9624

Affine parametric transformation

Attributes

Data source: EPSG

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

Revision date: 2013-06-12

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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
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