Definition: OGP XML
<div class="syntax"><pre><span class="cp"><?xml version="1.0" encoding="UTF-8"?></span>
<span class="nt"><gml:OperationMethod</span> <span class="na">xmlns:epsg=</span><span class="s">"urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset"</span> <span class="na">xmlns:gml=</span><span class="s">"http://www.opengis.net/gml/3.2"</span> <span class="na">xmlns:xlink=</span><span class="s">"http://www.w3.org/1999/xlink"</span> <span class="na">gml:id=</span><span class="s">"ogp-method-9621"</span><span class="nt">></span>
<span class="nt"><gml:metaDataProperty></span>
<span class="nt"><epsg:CommonMetaData></span>
<span class="nt"><epsg:informationSource></span>EPSG guidance note #7-2, http://www.epsg.org<span class="nt"></epsg:informationSource></span>
<span class="nt"><epsg:revisionDate></span>2010-06-29<span class="nt"></epsg:revisionDate></span>
<span class="nt"><epsg:changes></span>
<span class="nt"><epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:change-request:EPSG::2000.830"</span> <span class="nt">/></span>
<span class="nt"><epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:change-request:EPSG::2004.670"</span> <span class="nt">/></span>
<span class="nt"><epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:change-request:EPSG::2010.053"</span> <span class="nt">/></span>
<span class="nt"></epsg:changes></span>
<span class="nt"><epsg:show></span>true<span class="nt"></epsg:show></span>
<span class="nt"><epsg:isDeprecated></span>false<span class="nt"></epsg:isDeprecated></span>
<span class="nt"></epsg:CommonMetaData></span>
<span class="nt"></gml:metaDataProperty></span>
<span class="nt"><gml:metaDataProperty></span>
<span class="nt"><epsg:CoordinateOperationMethodMetaData></span>
<span class="nt"><epsg:isOperationReversible></span>true<span class="nt"></epsg:isOperationReversible></span>
<span class="nt"><epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">"false"</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8621"</span> <span class="nt">/></span>
<span class="nt"><epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">"false"</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8622"</span> <span class="nt">/></span>
<span class="nt"><epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">"false"</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8611"</span> <span class="nt">/></span>
<span class="nt"><epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">"false"</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8614"</span> <span class="nt">/></span>
<span class="nt"><epsg:example></span>ED50 / UTM zone 31N to ETRS89 / UTM zone 31N
Parameters of the Similarity Transformation:
XTO = -129.549 metres
YTO = -208.185 metres
M = 1.00000155
theta = 1.56504" = 0.000007588 rad
Forward computation for source coordinates 300000m E, 4500000m N:
E(ETRS89) = –129.549 + 300000.465 + 34.144
= 299905.060 m E
N(ETRS89) = –208.185 –2.276 + 4500006.977
= 4499796.515m N
Reverse computation of ETRS89 / UTM 31N coordinates 299905.060m E, 4499796.515m N:
E(ED50) = (300034.609 – 34.144) / 1.00000155
= 300000.000m E
N(ED50) = (2.276 + 4500004.700) / 1.00000155
= 4500000.000m N
Alternative reverse computation:
First calculate new parameter values:
XTO' = 129.5472 m
YTO' = 208.1857 m
M' = 0.99999845
theta' = –0.000007588 rad
Then apply these values to forward formula:
E(ED50) = 129.547 + 299904.595 + (–34.142)
= 300000.000 m
N(ED50) = 208.186 – (–2.276) + 4499789.539
= 4500000.000 m<span class="nt"></epsg:example></span>
<span class="nt"></epsg:CoordinateOperationMethodMetaData></span>
<span class="nt"></gml:metaDataProperty></span>
<span class="nt"><gml:identifier</span> <span class="na">codeSpace=</span><span class="s">"OGP"</span><span class="nt">></span>urn:ogc:def:method:EPSG::9621<span class="nt"></gml:identifier></span>
<span class="nt"><gml:name></span>Similarity transformation<span class="nt"></gml:name></span>
<span class="nt"><gml:remarks></span>Defined for two-dimensional coordinate systems.<span class="nt"></gml:remarks></span>
<span class="nt"><gml:formula></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.
The similarity transformation in algebraic form is:
XT = XT0 + XS * M * cos q + YS * M * sin q
YT = YT0 – XS * M * sin q + YS * M * cos q
where:
XT0 , YT0 = the coordinates of the origin point of the source coordinate reference system expressed in the target coordinate reference system;
M = the length of one unit in the source coordinate reference system expressed in units of the target coordinate reference system;
q = the angle about which the axes of the source coordinate reference system need to be rotated to coincide with the axes of the target coordinate reference system, counter-clockwise being positive. Alternatively, the bearing of the source coordinate reference system Y-axis measured relative to target coordinate reference system north.
The similarity transformation can also be described as a special case of the parametric affine transformation where coefficients A1 = B2 and A2 = - B1.
Reversibility
The reverse formula for the Similarity Transformation is:
XS = [(XT – XTO) * cos q – (YT – YTO) * sin q ] / [M ]
YS = [(XT – XTO) * sin q + (YT – YTO) * cos q] / [M ]
An alternative approach for the reverse operation is to use the same formula as for the forward computation but with different parameter values:
XT = XTO' + XS * M' * cos theta' + YS * M' * sin theta'
YT = YTO' – XS * M' * sin theta' + YS * M' * cos theta'
The reverse parameter values, indicated by a prime ('), can be calculated from those of the forward operation as follows:
XTO' = (YTO sin theta – XTO cos theta) / M
YTO' = –(YTO cos theta + XTO sin theta) / M
M' = 1/M
theta' = –theta<span class="nt"></gml:formula></span>
<span class="nt"><gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8621"</span> <span class="nt">/></span>
<span class="nt"><gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8622"</span> <span class="nt">/></span>
<span class="nt"><gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8611"</span> <span class="nt">/></span>
<span class="nt"><gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">"urn:ogc:def:parameter:EPSG::8614"</span> <span class="nt">/></span>
<span class="nt"></gml:OperationMethod></span>
</pre></div>
<?xml version="1.0" encoding="UTF-8"?>
<gml:OperationMethod xmlns:epsg="urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset" xmlns:gml="http://www.opengis.net/gml/3.2" xmlns:xlink="http://www.w3.org/1999/xlink" gml:id="ogp-method-9621">
<gml:metaDataProperty>
<epsg:CommonMetaData>
<epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
<epsg:revisionDate>2010-06-29</epsg:revisionDate>
<epsg:changes>
<epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2000.830" />
<epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2004.670" />
<epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2010.053" />
</epsg:changes>
<epsg:show>true</epsg:show>
<epsg:isDeprecated>false</epsg:isDeprecated>
</epsg:CommonMetaData>
</gml:metaDataProperty>
<gml:metaDataProperty>
<epsg:CoordinateOperationMethodMetaData>
<epsg:isOperationReversible>true</epsg:isOperationReversible>
<epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8621" />
<epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8622" />
<epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8611" />
<epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8614" />
<epsg:example>ED50 / UTM zone 31N to ETRS89 / UTM zone 31N
Parameters of the Similarity Transformation:
XTO = -129.549 metres
YTO = -208.185 metres
M = 1.00000155
theta = 1.56504" = 0.000007588 rad
Forward computation for source coordinates 300000m E, 4500000m N:
E(ETRS89) = –129.549 + 300000.465 + 34.144
= 299905.060 m E
N(ETRS89) = –208.185 –2.276 + 4500006.977
= 4499796.515m N
Reverse computation of ETRS89 / UTM 31N coordinates 299905.060m E, 4499796.515m N:
E(ED50) = (300034.609 – 34.144) / 1.00000155
= 300000.000m E
N(ED50) = (2.276 + 4500004.700) / 1.00000155
= 4500000.000m N
Alternative reverse computation:
First calculate new parameter values:
XTO' = 129.5472 m
YTO' = 208.1857 m
M' = 0.99999845
theta' = –0.000007588 rad
Then apply these values to forward formula:
E(ED50) = 129.547 + 299904.595 + (–34.142)
= 300000.000 m
N(ED50) = 208.186 – (–2.276) + 4499789.539
= 4500000.000 m</epsg:example>
</epsg:CoordinateOperationMethodMetaData>
</gml:metaDataProperty>
<gml:identifier codeSpace="OGP">urn:ogc:def:method:EPSG::9621</gml:identifier>
<gml:name>Similarity transformation</gml:name>
<gml:remarks>Defined for two-dimensional coordinate systems.</gml:remarks>
<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.
The similarity transformation in algebraic form is:
XT = XT0 + XS * M * cos q + YS * M * sin q
YT = YT0 – XS * M * sin q + YS * M * cos q
where:
XT0 , YT0 = the coordinates of the origin point of the source coordinate reference system expressed in the target coordinate reference system;
M = the length of one unit in the source coordinate reference system expressed in units of the target coordinate reference system;
q = the angle about which the axes of the source coordinate reference system need to be rotated to coincide with the axes of the target coordinate reference system, counter-clockwise being positive. Alternatively, the bearing of the source coordinate reference system Y-axis measured relative to target coordinate reference system north.
The similarity transformation can also be described as a special case of the parametric affine transformation where coefficients A1 = B2 and A2 = - B1.
Reversibility
The reverse formula for the Similarity Transformation is:
XS = [(XT – XTO) * cos q – (YT – YTO) * sin q ] / [M ]
YS = [(XT – XTO) * sin q + (YT – YTO) * cos q] / [M ]
An alternative approach for the reverse operation is to use the same formula as for the forward computation but with different parameter values:
XT = XTO' + XS * M' * cos theta' + YS * M' * sin theta'
YT = YTO' – XS * M' * sin theta' + YS * M' * cos theta'
The reverse parameter values, indicated by a prime ('), can be calculated from those of the forward operation as follows:
XTO' = (YTO sin theta – XTO cos theta) / M
YTO' = –(YTO cos theta + XTO sin theta) / M
M' = 1/M
theta' = –theta</gml:formula>
<gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8621" />
<gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8622" />
<gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8611" />
<gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8614" />
</gml:OperationMethod>