EPSG:9624

Affine parametric transformation

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Data source: OGP

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

Revision date: 2013-06-12

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<div class="syntax"><pre><span class="cp">&lt;?xml version=&quot;1.0&quot; encoding=&quot;UTF-8&quot;?&gt;</span> <span class="nt">&lt;gml:OperationMethod</span> <span class="na">xmlns:epsg=</span><span class="s">&quot;urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset&quot;</span> <span class="na">xmlns:gml=</span><span class="s">&quot;http://www.opengis.net/gml/3.2&quot;</span> <span class="na">xmlns:xlink=</span><span class="s">&quot;http://www.w3.org/1999/xlink&quot;</span> <span class="na">gml:id=</span><span class="s">&quot;ogp-method-9624&quot;</span><span class="nt">&gt;</span> <span class="nt">&lt;gml:metaDataProperty&gt;</span> <span class="nt">&lt;epsg:CommonMetaData&gt;</span> <span class="nt">&lt;epsg:informationSource&gt;</span>EPSG guidance note #7-2, http://www.epsg.org<span class="nt">&lt;/epsg:informationSource&gt;</span> <span class="nt">&lt;epsg:revisionDate&gt;</span>2013-06-12<span class="nt">&lt;/epsg:revisionDate&gt;</span> <span class="nt">&lt;epsg:changes&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2004.670&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2012.075&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/epsg:changes&gt;</span> <span class="nt">&lt;epsg:show&gt;</span>true<span class="nt">&lt;/epsg:show&gt;</span> <span class="nt">&lt;epsg:isDeprecated&gt;</span>false<span class="nt">&lt;/epsg:isDeprecated&gt;</span> <span class="nt">&lt;/epsg:CommonMetaData&gt;</span> <span class="nt">&lt;/gml:metaDataProperty&gt;</span> <span class="nt">&lt;gml:metaDataProperty&gt;</span> <span class="nt">&lt;epsg:CoordinateOperationMethodMetaData&gt;</span> <span class="nt">&lt;epsg:isOperationReversible&gt;</span>true<span class="nt">&lt;/epsg:isOperationReversible&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8623&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8624&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8625&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8639&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8640&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8641&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:example&gt;</span>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&#39; = -270201.960 Clarke&#39;s foot A1&#39; = 3.280900499 A2&#39; = -0.000165958 B0&#39; = -92178.507 Clarke&#39;s foot B1&#39; = 0.000165958 B2&#39; = 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<span class="nt">&lt;/epsg:example&gt;</span> <span class="nt">&lt;/epsg:CoordinateOperationMethodMetaData&gt;</span> <span class="nt">&lt;/gml:metaDataProperty&gt;</span> <span class="nt">&lt;gml:identifier</span> <span class="na">codeSpace=</span><span class="s">&quot;OGP&quot;</span><span class="nt">&gt;</span>urn:ogc:def:method:EPSG::9624<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Affine parametric transformation<span class="nt">&lt;/gml:name&gt;</span> <span class="nt">&lt;gml:formula&gt;</span>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&#39; + A1&#39; * XT + A2&#39; * YT YS = B0&#39; + B1&#39; * XT + B2&#39; * YT<span class="nt">&lt;/gml:formula&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8623&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8624&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8625&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8639&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8640&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8641&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/gml:OperationMethod&gt;</span> </pre></div>
<?xml version="1.0" encoding="UTF-8"?>
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         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8625" />
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         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8641" />
         <epsg: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</epsg:example>
      </epsg:CoordinateOperationMethodMetaData>
   </gml:metaDataProperty>
   <gml:identifier codeSpace="OGP">urn:ogc:def:method:EPSG::9624</gml:identifier>
   <gml:name>Affine parametric transformation</gml:name>
   <gml: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</gml:formula>
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8623" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8624" />
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   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8639" />
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   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8641" />
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