EPSG:9801

Lambert Conic Conformal (1SP)

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Data source: OGP

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

Revision date: 2018-08-29

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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;iogp-method-9801&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>2018-08-29<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::2017.018&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::2017.024&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 JAD69 / Jamaica National Grid Parameters: Ellipsoid: Clarke 1866, a = 6378206.400 m., 1/f = 294.97870 then e = 0.08227185 and e^2 = 0.00676866 Latitude Natural Origin 18°00&#39;00&quot;N = 0.31415927 rad Longitude Natural Origin 77°00&#39;00&quot;W = -1.34390352 rad Scale factor at origin 1.000000 False Eastings FE 250000.00 m False Northings FN 150000.00 m Forward calculation for: Latitude: 17°55&#39;55.80&quot;N = 0.31297535 rad Longitude: 76°56&#39;37.26&quot;W = -1.34292061 rad first gives m0 = 0.95136402 t0 = 0.72806411 F = 3.39591092 n = 0.30901699 r = 19643955.26 r0 = 19636447.86 theta = 0.00030374 t = 0.728965259 Then Easting E = 255966.58 m Northing N = 142493.51 m Reverse calculation for the same easting and northing first gives theta&#39; = 0.000303736 t&#39; = 0.728965259 m0 = 0.95136402 r&#39; = 19643955.26 Then Latitude = 17°55&#39;55.800&quot;N Longitude = 76°56&#39;37.260&quot;W<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;IOGP&quot;</span><span class="nt">&gt;</span>urn:ogc:def:method:EPSG::9801<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Lambert Conic Conformal (1SP)<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. To derive the projected Easting and Northing coordinates of a point with geographical coordinates (lat,lon) the formulas for the one standard parallel case are: E = FE + r sin(theta) N = FN + r0 - r cos(theta) where n = sin lat0 r = a F t^n k0 for r0, and r m = cos(lat)/(1 - e^2 sin^2(lat))^0.5 for m0, lat0, and m2, lat2 where lat1 and lat2 are the latitudes of the standard parallels. t = tan(pi/4 - lat/2)/[(1 - e sin(lat))/(1 + e sin(lat))]^(e/2) for t0 and t using lat0 and lat respectively. F = m0/(n t1^n) theta = n(lon - lon0) The reverse formulas to derive the latitude and longitude of a point from its Easting and Northing values are: lat = pi/2 - 2arctan{t&#39;[(1 - esin(lat))/(1 + esin(lat))]^(e/2)} lon = theta&#39;/n +lon0 where theta&#39; = atan2[(E - FE),{r0 -(N - FN)}] (see implementation notes in GN7-2 preface for atan2 convention) r&#39; = +/-[(E - FE)^2 + {r0 - (N - FN)}^2]^0.5 taking the sign of n t&#39; = (r&#39;/(a k0 F))^(1/n) and n, F, and rF are derived as for the forward calculation.<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>
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      <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8807" />
      <epsg:example>For Projected Coordinate System JAD69 / Jamaica National Grid

Parameters:
Ellipsoid:  Clarke 1866, a = 6378206.400 m., 1/f = 294.97870
                                   then  e = 0.08227185 and e^2 = 0.00676866

Latitude Natural Origin         18°00'00"N  =  0.31415927 rad
Longitude Natural Origin     77°00'00"W = -1.34390352 rad
Scale factor at origin            1.000000
False Eastings  FE               250000.00 m
False Northings FN              150000.00 m

Forward calculation for: 
Latitude:     17°55'55.80"N  =  0.31297535 rad
Longitude:  76°56'37.26"W = -1.34292061 rad
first gives
m0    =  0.95136402        t0 =  0.72806411
F       =  3.39591092        n  =  0.30901699
r        =  19643955.26     r0  =  19636447.86
theta =  0.00030374        t   =  0.728965259

Then Easting E   =     255966.58 m
         Northing N =      142493.51 m

Reverse calculation for the same easting and northing first gives

theta' =  0.000303736
t'        =  0.728965259
m0     =  0.95136402
r'        =  19643955.26

Then Latitude     = 17°55'55.800"N
         Longitude  = 76°56'37.260"W</epsg:example>
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  <gml:identifier codeSpace="IOGP">urn:ogc:def:method:EPSG::9801</gml:identifier>
  <gml:name>Lambert Conic Conformal (1SP)</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.

To derive the projected Easting and Northing coordinates of a point with geographical coordinates (lat,lon) the formulas for the one standard parallel case are:

E = FE + r sin(theta)
N = FN + r0 - r cos(theta)
where
n = sin lat0
r = a F t^n k0     for r0, and r
m = cos(lat)/(1 - e^2 sin^2(lat))^0.5     for m0, lat0, and m2, lat2 where lat1 and lat2 are the latitudes of the standard parallels.
t  = tan(pi/4 - lat/2)/[(1 - e sin(lat))/(1 + e sin(lat))]^(e/2)   for t0 and t using lat0 and lat respectively.
F = m0/(n  t1^n)
theta = n(lon - lon0)

The reverse formulas to derive the latitude and longitude of a point from its Easting and Northing values are:

lat = pi/2 - 2arctan{t'[(1 - esin(lat))/(1 + esin(lat))]^(e/2)}
lon = theta'/n +lon0
where
theta' = atan2[(E - FE),{r0 -(N - FN)}]
(see implementation notes in GN7-2 preface for atan2 convention)
r' = +/-[(E - FE)^2 + {r0 - (N - FN)}^2]^0.5  taking the sign of n
t' = (r'/(a k0 F))^(1/n)
and n, F, and rF are derived as for the forward calculation.</gml:formula>
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