EPSG:9804

Mercator (variant A)

Attributes

Data source: OGP

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

Revision date: 2010-11-02

Remarks: Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for completeness in CRS labelling.

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Definition: OGP XML

<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-9804&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:alias</span> <span class="na">alias=</span><span class="s">&quot;Mercator (1SP)&quot;</span> <span class="na">code=</span><span class="s">&quot;14437&quot;</span> <span class="na">codeSpace=</span><span class="s">&quot;urn:ogc:def:naming-system:EPSG::7301&quot;</span><span class="nt">&gt;</span> <span class="nt">&lt;epsg:remarks&gt;</span>This was the method name used prior to October 2010.<span class="nt">&lt;/epsg:remarks&gt;</span> <span class="nt">&lt;/epsg:alias&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>2010-11-02<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::2001.080&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::2004.430&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::2008.000&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::2010.058&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::8801&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::8802&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::8805&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::8806&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::8807&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:example&gt;</span>For Projected Coordinate System Makassar / NEIEZ Parameters: Ellipsoid Bessel 1841 a = 6377397.155 m 1/f = 299.15281 then e = 0.08169683 Latitude of natural origin = 00°00&#39;00&quot;N = 0.0000000 rad Longitude of natural origin = 110°00&#39;00&quot;E = 1.91986218 rad Scale factor at natural origin ko = 0.997 False Eastings FE = 3900000.00 m False Northings FN = 900000.00 m Forward calculation for: Latitude = 3°00&#39;00.00&quot;S = -0.05235988 rad Longitude = 120°00&#39;00.00&quot;E = 2.09439510 rad gives Easting E = 5009726.58 m Northing N = 569150.82 m Reverse calculation for same easting and northing first gives : t = 1.0534121 chi = -0.0520110 Latitude = 3°00&#39;00.000&quot;S Longitude = 120°00&#39;00.000&quot;E<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::9804<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Mercator (variant A)<span class="nt">&lt;/gml:name&gt;</span> <span class="nt">&lt;gml:remarks&gt;</span>Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for completeness in CRS labelling.<span class="nt">&lt;/gml:remarks&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. The formulas to derive projected Easting and Northing coordinates are: E = FE + a*ko(lon - lonO) N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where symbols are as listed above and logarithms are natural. The reverse formulas to derive latitude and longitude from E and N values are: lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi) + (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi) + (7e^6/120 + 81e^8/1120) sin(6chi) + (4279e^8/161280) sin(8chi) where chi = pi/2 - 2 arctan t t = B^((FN-N)/(a*ko)) B = base of the natural logarithm, 2.7182818... and for the 2 SP Case, ko is calculated as for the forward transformation above. lon = ((E - FE)/(a*ko)) + lonO<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::8801&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::8802&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::8805&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::8806&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::8807&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/gml:OperationMethod&gt;</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-9804">
   <gml:metaDataProperty>
      <epsg:CommonMetaData>
         <epsg:alias alias="Mercator (1SP)" code="14437" codeSpace="urn:ogc:def:naming-system:EPSG::7301">
            <epsg:remarks>This was the method name used prior to October 2010.</epsg:remarks>
         </epsg:alias>
         <epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
         <epsg:revisionDate>2010-11-02</epsg:revisionDate>
         <epsg:changes>
            <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2001.080" />
            <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2004.430" />
            <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2008.000" />
            <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2010.058" />
         </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::8801" />
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8802" />
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8805" />
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8806" />
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8807" />
         <epsg:example>For Projected Coordinate System Makassar / NEIEZ

Parameters:
Ellipsoid   Bessel 1841  a = 6377397.155 m   1/f = 299.15281
then e = 0.08169683

Latitude of natural origin = 00°00'00"N  = 0.0000000 rad
Longitude of natural origin = 110°00'00"E  = 1.91986218 rad
Scale factor at natural origin ko = 0.997
False Eastings FE = 3900000.00 m
False Northings FN = 900000.00 m

Forward calculation for: 
Latitude = 3°00'00.00"S   = -0.05235988 rad
Longitude = 120°00'00.00"E   =  2.09439510 rad
gives
Easting  E  =  5009726.58 m
Northing N  =   569150.82 m

Reverse calculation for same easting and northing first gives :
t    = 1.0534121
chi = -0.0520110

Latitude   =   3°00'00.000"S
Longitude  = 120°00'00.000"E</epsg:example>
      </epsg:CoordinateOperationMethodMetaData>
   </gml:metaDataProperty>
   <gml:identifier codeSpace="OGP">urn:ogc:def:method:EPSG::9804</gml:identifier>
   <gml:name>Mercator (variant A)</gml:name>
   <gml:remarks>Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for completeness in CRS labelling.</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 formulas to derive projected Easting and Northing coordinates are:

E = FE + a*ko(lon - lonO)              
N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where symbols are as listed above and logarithms are natural.

The reverse formulas to derive latitude and longitude from E and N values are:

lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi) 
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi)
+ (7e^6/120 +  81e^8/1120) sin(6chi)  + (4279e^8/161280) sin(8chi)

where chi = pi/2 - 2 arctan t
t = B^((FN-N)/(a*ko)) 
B = base of the natural logarithm, 2.7182818...
and  for the 2 SP Case, ko is calculated as for the forward transformation above.
lon  =  ((E - FE)/(a*ko))  + lonO</gml:formula>
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8801" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8802" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8805" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8806" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8807" />
</gml:OperationMethod>