# 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.

#### Export

Definition: OGP XML

```<?xml version="1.0" encoding="UTF-8"?>
<epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
<epsg:revisionDate>2018-08-29</epsg:revisionDate>
<epsg:changes>
</epsg:changes>
<epsg:show>true</epsg:show>
<epsg:isDeprecated>false</epsg:isDeprecated>
<epsg:isOperationReversible>true</epsg:isOperationReversible>
<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>
<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>