EPSG

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

2013-06-12

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

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