EPSG:9817

Lambert Conic Near-Conformal

Attributes

Data source: OGP

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

Revision date: 2018-08-29

Remarks: The Lambert Near-Conformal projection is derived from the Lambert Conformal Conic projection by truncating the series expansion of the projection formulae.

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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-9817&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::1999.811&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::2004.610&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::2005.390&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::2008.029&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::2010.024&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: Deir ez Zor / Levant Zone Parameters: Ellipsoid Clarke 1880 (IGN) a = 6378249.2 m 1/f = 293.46602 then b = 6356515.000 n = 0.001706682563 Latitude Natural Origin = 34°39&#39;00&quot;N = 0.604756586 rad Longitude Natural Origin = 37°21&#39;00&quot;E= 0.651880476 rad Scale factor at origin ko = 0.99962560 False Eastings FE = 300000.00 m False Northings FN = 300000.00 m Forward calculation for: Latitude of 37°31&#39;17.625&quot;N = 0.654874806 rad Longitude of 34°08&#39;11.291&quot;E = 0.595793792 rad first gives A = 4.1067494 * 10e-15 A’=111131.8633 B’= 16300.64407 C’= 17.38751 D’= 0.02308 E’= 0.000033 so = 3835482.233 s = 4154101.458 m = 318619.225 M = 318632.72 Ms = 30.82262319 q = -0.03188875 ro = 9235264.405 r = 8916631.685 Then Easting E = 15707.96 m (c.f. E = 15708.00 using full formulae) Northing N = 623165.96 m (c.f. N = 623167.20 using full formulae) Reverse calculation for the same easting and northing first gives q&#39; = -0.03188875 r’ = 8916631.685 M’= 318632.72 Latitude = 0.654874806 rad = 37°31&#39;17.625&quot;N Longitude = 0.595793792 rad = 34°08&#39;11.291&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;IOGP&quot;</span><span class="nt">&gt;</span>urn:ogc:def:method:EPSG::9817<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Lambert Conic Near-Conformal<span class="nt">&lt;/gml:name&gt;</span> <span class="nt">&lt;gml:remarks&gt;</span>The Lambert Near-Conformal projection is derived from the Lambert Conformal Conic projection by truncating the series expansion of the projection formulae.<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. To compute the Lambert Conic Near-Conformal the following formulae are used. First compute constants for the projection: n = f / (2-f) A = 1 / (6 rhoO nuO) A’ = a [ 1- n + 5 (n^2 - n^3 ) / 4 + 81 ( n^4 - n^5 ) / 64]*pi /180 B’ = 3 a [ n - n^2 + 7 ( n^3 - n^4 ) / 8 + 55 n^5 / 64] / 2 C’ = 15 a [ n^2 -n^3 + 3 ( n^4 - n^5 ) / 4 ] / 16 D’ = 35 a [ n^3 - n^4 + 11 n^5 / 16 ] / 48 E’ = 315 a [ n^4 - n^5 ] / 512 r0 = ko nu0 / tan(lat0) s0 = A’ latO - B’ sin(2 latO) + C’ sin(4 latO) - D’ sin(6 latO) + E’ sin(8 latO) where in the first term latO is in degrees, in the other terms latO is in radians. Then for the computation of easting and northing from latitude and longitude: s = A’ lat - B’ sin(2 lat) + C’ sin(4 lat) - D’ sin(6 lat) + E’ sin(8 lat) where in the first term latO is in degrees, in the other terms latO is in radians. M = s - sO M = ko ( m + A m^3) r = rO - M theta = (lon - lonO) sin(latO) and E = FE + r sin(theta) N = FN + M + r sin(theta) tan(theta/2) The reverse formulas for latitude and longitude from Easting and Northing are: theta&#39; = atan2 {(E – FE) , [rO – (N – FN)]} (see GN7-2 implementation notes in preface for atan2 convention) r&#39; = +/- {(E – FE)^2 + [rO – (N – FN)]}^2}^0.5, taking the sign of latO M&#39; = rO – r&#39; If an exact solution is required, it is necessary to solve for m and lat using iteration of the two equations: m&#39;= m&#39; – [M&#39; – ko m&#39; – ko A (m&#39;)^3] / [– ko – 3 ko A (m&#39;)^2] using M&#39; for m&#39; in the first iteration. This will usually converge (to within 1mm) in a single iteration. Then lat&#39; = lat&#39; +{m&#39; + sO – [A&#39; lat&#39; (180/pi) – B&#39; sin(2 lat&#39;) + C&#39; sin(4 lat&#39;) – D&#39; sin(6lat&#39;) + E&#39; sin(8 lat&#39;)]}/A&#39; (pi/180) first using lat&#39; = latO + m&#39;/A&#39; (pi/180). However the following non-iterative solution is accurate to better than 0.001&quot; (3mm) within 5 degrees latitude of the projection origin and should suffice for most purposes: m&#39; = M&#39; – [M&#39; ko M&#39; – ko A (M&#39;)^3] / [– ko – 3 ko A (M&#39;)^2] lat&#39; = latO + m&#39;/A&#39; (pi/180) s&#39; = A &#39; lat&#39; – B&#39; sin(2 lat&#39;) + C&#39; sin(4 lat&#39;) – D&#39; sin(6 lat&#39;) + E&#39; sin(8 lat&#39;) where in the first term lat&#39; is in degrees, in the other terms lat&#39; is in radians. Ds&#39; = A&#39;(180 / pi) – 2B&#39; cos(2 lat&#39;) + 4C&#39; cos(4 lat&#39;) – 6D&#39; cos(6 lat&#39;) + 8E&#39; cos(8 lat&#39;) lat = lat&#39; – [(m&#39; + sO – s&#39;) / (–ds&#39;)] radians Then after solution of lat using either method above lon = lonO + theta&#39; / sin(latO) where lonO and lon are in radians.<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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 <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="iogp-method-9817">
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      <epsg:example>For Projected Coordinate System: Deir ez Zor / Levant Zone

Parameters:
Ellipsoid  Clarke 1880 (IGN)  a = 6378249.2 m  1/f = 293.46602
then b = 6356515.000    n = 0.001706682563

Latitude Natural Origin  = 34°39'00"N = 0.604756586 rad
Longitude Natural Origin = 37°21'00"E=  0.651880476 rad
Scale factor at origin ko = 0.99962560
False Eastings FE  = 300000.00 m
False Northings FN  = 300000.00 m

Forward calculation for: 
Latitude of 37°31'17.625"N = 0.654874806 rad
Longitude of 34°08'11.291"E = 0.595793792 rad
first gives
A = 4.1067494 * 10e-15      A’=111131.8633
B’= 16300.64407     C’= 17.38751     D’= 0.02308      E’= 0.000033
so = 3835482.233    s  = 4154101.458     m = 318619.225
M = 318632.72         Ms = 30.82262319
q = -0.03188875       ro = 9235264.405     r = 8916631.685

Then Easting E =   15707.96 m (c.f. E =   15708.00 using full formulae)
         Northing N =      623165.96 m (c.f. N = 623167.20 using full formulae)

Reverse calculation for the same easting and northing first gives

q' = -0.03188875
r’  =  8916631.685
M’= 318632.72 

Latitude =      0.654874806 rad = 37°31'17.625"N
Longitude = 0.595793792 rad =  34°08'11.291"E</epsg:example>
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  <gml:identifier codeSpace="IOGP">urn:ogc:def:method:EPSG::9817</gml:identifier>
  <gml:name>Lambert Conic Near-Conformal</gml:name>
  <gml:remarks>The Lambert Near-Conformal projection is derived from the Lambert Conformal Conic projection by truncating the series expansion of the projection formulae.</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.

To compute the Lambert Conic Near-Conformal the following formulae are used. First compute constants for the projection:

n = f / (2-f)
A = 1 / (6 rhoO nuO) 
A’ = a [ 1- n + 5 (n^2 - n^3 ) / 4 + 81 ( n^4 - n^5 ) / 64]*pi /180 
B’ = 3 a [ n - n^2 + 7 ( n^3 - n^4 ) / 8 + 55 n^5 / 64] / 2
C’ = 15 a [ n^2 -n^3 + 3 ( n^4 - n^5 ) / 4 ] / 16
D’ = 35 a [ n^3 - n^4 + 11 n^5 / 16 ] / 48
E’ = 315 a [ n^4 - n^5 ] / 512
r0 = ko nu0 / tan(lat0)
s0 = A’ latO - B’ sin(2 latO) + C’ sin(4 latO) - D’ sin(6 latO) + E’ sin(8 latO) where in the first term latO is in degrees, in the other terms latO is in radians.

Then for the computation of easting and northing from latitude and longitude:

s = A’ lat - B’ sin(2 lat) + C’ sin(4 lat) - D’ sin(6 lat) + E’ sin(8 lat) where in the first term latO is in degrees, in the other terms latO is in radians.
M = s - sO
M = ko ( m + A m^3)
r = rO - M
theta = (lon - lonO) sin(latO)

and
E = FE + r sin(theta)
N = FN + M + r sin(theta) tan(theta/2)

The reverse formulas for latitude and longitude from Easting and Northing are:

theta' = atan2 {(E –  FE) , [rO –  (N –  FN)]} (see GN7-2 implementation notes in preface for atan2 convention)
r' = +/- {(E –  FE)^2 + [rO –  (N –  FN)]}^2}^0.5, taking the sign of latO 
M' = rO – r'

If an exact solution is required, it is necessary to solve for m and lat using iteration of the two equations:
m'= 	m' – [M' – ko m' – ko A (m')^3] / [– ko – 3 ko A (m')^2]
using M' for m' in the first iteration. This will usually converge (to within 1mm) in a single iteration. Then
lat' = lat' +{m' + sO – [A' lat' (180/pi) – B' sin(2 lat')  + C' sin(4 lat')  –  D' sin(6lat') + E' sin(8 lat')]}/A' (pi/180)
first using lat' = latO + m'/A' (pi/180).

However the following non-iterative solution is accurate to better than 0.001" (3mm) within 5 degrees latitude of the projection origin and should suffice for most purposes:
m' = 	M' – [M' ko M' – ko A (M')^3] / [– ko – 3 ko A (M')^2]
lat' = latO + m'/A' (pi/180)
s' = A	' lat' –  B' sin(2 lat')  + C' sin(4 lat')  –  D' sin(6 lat') + E' sin(8 lat')
		where in the first term lat' is in degrees, in the other terms lat' is in radians.
Ds' = 	A'(180 / pi) – 2B' cos(2 lat')  + 4C' cos(4 lat')  –  6D' cos(6 lat') + 8E' cos(8 lat')
lat = lat' – [(m' + sO – s') / (–ds')] radians

Then after solution of lat using either method above
lon = lonO + theta' / sin(latO) where lonO and lon are in radians.</gml:formula>
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