EPSG:9839

Vertical Perspective (Orthographic case)

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Data source: OGP

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

Revision date: 2007-11-01

Remarks: This is a special case of the general Vertical Perspective (method code 9838) in which the viewing point at infinity.

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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;epsg-method-9839&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>2007-11-01<span class="nt">&lt;/epsg:revisionDate&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>false<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::8834&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::8835&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:example&gt;</span>See EPSG Guidance Note 7-2.<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::9839<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Vertical Perspective (Orthographic case)<span class="nt">&lt;/gml:name&gt;</span> <span class="nt">&lt;gml:remarks&gt;</span>This is a special case of the general Vertical Perspective (method code 9838) in which the viewing point at infinity.<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 orthographic vertical perspective is a special case of the vertical perspective with the viewing point (hv) at infinity. Therefore, all projection &quot;rays&quot; are parallel to one another and all are perpendicular to the tangent plane. Since the rays are parallel, coordinates in the tangent-plane are the same in any other parallel mapping plane, i.e. are consistent for any value of ho, which therefore becomes irrelevant to the forward formulas. The orthographic vertical perspective forward conversion from 3D geographic coordinates latitude, longitude and ellipsoidal height (lat, lon, h) to Easting (E) and Northing (N) is given by: E = U = limit (U hv / (hv – W), hv -<span class="ni">&amp;gt;</span> infinity) N = V = limit (V hv / (hv – W), hv -<span class="ni">&amp;gt;</span> infinity) where, as in Sections 2.2.3 and 1.3.17.2: U = (* + h) cos * sin (* – *O) V = (* + h) [sin * cos *O – cos * sin *O cos (* – *O)] + e2 (*O sin *O – * sin * ) cos *O The reverse calculation from E,N to U,V,W and *,*,h is indeterminate.<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::8834&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::8835&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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   <gml:metaDataProperty>
      <epsg:CommonMetaData>
         <epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
         <epsg:revisionDate>2007-11-01</epsg:revisionDate>
         <epsg:isDeprecated>false</epsg:isDeprecated>
      </epsg:CommonMetaData>
   </gml:metaDataProperty>
   <gml:metaDataProperty>
      <epsg:CoordinateOperationMethodMetaData>
         <epsg:isOperationReversible>false</epsg:isOperationReversible>
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8834" />
         <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8835" />
         <epsg:example>See EPSG Guidance Note 7-2.</epsg:example>
      </epsg:CoordinateOperationMethodMetaData>
   </gml:metaDataProperty>
   <gml:identifier codeSpace="OGP">urn:ogc:def:method:EPSG::9839</gml:identifier>
   <gml:name>Vertical Perspective (Orthographic case)</gml:name>
   <gml:remarks>This is a special case of the general Vertical Perspective (method code 9838) in which the viewing point at infinity.</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 orthographic vertical perspective is a special case of the vertical perspective with the viewing point (hv) at infinity. Therefore, all projection "rays" are parallel to one another and all are perpendicular to the tangent plane. Since the rays are parallel, coordinates in the tangent-plane are the same in any other parallel mapping plane, i.e. are consistent for any value of ho, which therefore becomes irrelevant to the forward formulas.

The orthographic vertical perspective forward conversion from 3D geographic coordinates latitude, longitude and ellipsoidal height (lat, lon, h) to Easting (E) and Northing (N) is given by:

E = U = limit (U hv / (hv – W), hv -&gt; infinity)
N = V = limit (V hv / (hv – W), hv -&gt; infinity)

where, as in Sections 2.2.3 and 1.3.17.2:

U = (* + h) cos * sin (* – *O)
V = (* + h) [sin * cos *O – cos * sin *O cos (* – *O)] + e2 (*O sin *O – * sin * ) cos *O 

The reverse calculation from E,N to U,V,W and *,*,h is indeterminate.</gml:formula>
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8834" />
   <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8835" />
</gml:OperationMethod>