EPSG:9822

Albers Equal Area

Attributes

Data source: OGP

Information source: USGS Professional Paper 1395, "Map Projections - A Working Manual" by John P. Snyder.

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-9822&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>USGS Professional Paper 1395, &quot;Map Projections - A Working Manual&quot; by John P. Snyder.<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::2006.200&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::2007.049&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::2015.022&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::8821&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::8822&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::8823&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::8824&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::8826&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::8827&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:example&gt;</span>See Information Source.<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::9822<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Albers Equal Area<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 coordinates of a point, geodetic latitude (lat) is converted to authalic latitude (ß). The formulas to convert geodetic latitude and longitude (lat, lon) to Easting (E) and Northing (N) are: Easting (E) = EF + (rho . sin(theta)) Northing (N) = NF + rhoO – (rho . cos(theta)) where theta = n . (lon - lonO) rho = [a . (C – n.alpha)^0.5] / n rhoO = [a . (C – n.alphaO)^0.5] / n and C = m1^2 + (n . alpha1) n = (m1^2 – m2^2) / (alpha2 - alpha1) m1 = cos lat1 / (1 – e^2 sin^2(lat1))^0.5 m2 = cos lat2 / (1 – e^2 sin^2(lat2))^0.5 alpha = (1 – e^2) . {[sin(lat) / (1 – e^2 sin^2(lat))] – [1/(2e)] . ln [(1 – e sin(lat)) / (1 + e sin(lat))]} alphaO = (1 – e^2) . {[sin(latO) / (1 – e^2 sin^2(latO))] – [1/(2e)] . ln [(1 – e sin(latO)) / (1 + e sin(latO))]} alpha1 = (1 – e^2) . {[sin(lat1) / (1 – e^2 sin^2(lat1))] – [1/(2e)] . ln [(1 – e sin(lat1)) / (1 + e sin(lat1))]} alpha2 = (1 – e^2) . {[sin(lat2) / (1 – e^2 sin^2(lat2))] – [1/(2e)] . ln [(1 – e sin(lat2)) / (1 + e sin(lat2))]} The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are: lat = ß&#39; + [(e^2/3 + 31e^4/180 + 517e^6/5040) . sin 2ß&#39;] + [(23e^4/360 + 251e^6/3780) . sin 4ß&#39;] + [(761e^6/45360) . sin 6ß&#39;] lon = lonO + (theta / n) where ß&#39; = asin(alpha&#39; / {1 – [(1 – e^2) / 2e] . ln [(1 – e) / (1 + e)]}) alpha&#39; = [C – (rho^2 . N^2 / a^2)] / n rho = {(E – EF)^2 + [rhoO – (N – NF)]^2 }^0.5 theta = atan2 {(E – EF) , [rhoO – (N – NF)]} and C, n and rhoO are as in the forward equations. (see implementation notes in GN7-2 preface for atan2 convention).<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::8821&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::8822&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::8823&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::8824&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::8826&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::8827&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/gml:OperationMethod&gt;</span> </pre></div>
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  <gml:identifier codeSpace="IOGP">urn:ogc:def:method:EPSG::9822</gml:identifier>
  <gml:name>Albers Equal Area</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 coordinates of a point, geodetic latitude (lat) is converted to authalic latitude (ß). The formulas to convert geodetic latitude and longitude (lat, lon) to Easting (E) and Northing (N) are: 
Easting (E)     =  EF + (rho . sin(theta)) 
Northing (N)  =  NF + rhoO – (rho . cos(theta))

where
theta  = n . (lon - lonO)
rho  = [a . (C – n.alpha)^0.5] / n
rhoO = [a . (C – n.alphaO)^0.5] / n
and
C  = m1^2 +  (n . alpha1)
n   = (m1^2 – m2^2) / (alpha2 - alpha1)
m1 = cos lat1 / (1 – e^2 sin^2(lat1))^0.5
m2 = cos lat2 / (1 – e^2 sin^2(lat2))^0.5
alpha  = (1 – e^2) . {[sin(lat) / (1 – e^2 sin^2(lat))] – [1/(2e)] . ln [(1 – e sin(lat)) / (1 + e sin(lat))]}
alphaO  = (1 – e^2) . {[sin(latO) / (1 – e^2 sin^2(latO))] – [1/(2e)] . ln [(1 – e sin(latO)) / (1 + e sin(latO))]}
alpha1  = (1 – e^2) . {[sin(lat1) / (1 – e^2 sin^2(lat1))] – [1/(2e)] . ln [(1 – e sin(lat1)) / (1 + e sin(lat1))]}
alpha2  = (1 – e^2) . {[sin(lat2) / (1 – e^2 sin^2(lat2))] – [1/(2e)] . ln [(1 – e sin(lat2)) / (1 + e sin(lat2))]}

The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are:
lat = ß' + [(e^2/3 + 31e^4/180 + 517e^6/5040) . sin 2ß'] + [(23e^4/360 + 251e^6/3780) . sin 4ß'] + [(761e^6/45360) . sin 6ß']

lon =   lonO + (theta / n)
where
ß' =  asin(alpha' / {1 – [(1 – e^2) / 2e] . ln [(1 – e) / (1 + e)]})
alpha' =  [C – (rho^2 . N^2 / a^2)] / n
rho =  {(E – EF)^2 + [rhoO – (N – NF)]^2 }^0.5
theta =  atan2 {(E – EF) , [rhoO – (N – NF)]}
and C, n and rhoO are as in the forward equations.
(see implementation notes in GN7-2 preface for atan2 convention).</gml:formula>
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