EPSG Dataset :: v12.003

Polar Stereographic (variant B)

Coordinate Operation Method Details [VALID]

Name:

Polar Stereographic (variant B)

Code:

9829

Operation is Reversible:

Yes

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.

First calculate the scale factor at natural origin:
for the south pole case
tF = tan (pi/4 + latF/2) / {[(1 + e sin(latF)) / (1 – e sin(latF))]^(e/2)}

but for the north pole case
tF = tan (pi/4 - latF/2) * {[(1 + e sin(latF)) / (1 – e sin(latF))]^(e/2)}

then for both cases
mF = cos(latF) / (1 – e^2 sin^2(latF))^0.5
ko = mF {[(1+e)^(1+e) (1–e)^(1–e)]0.5} / (2 tF)

The forward and reverse conversions then follow the formulae for the
Polar Stereographic (variant A) method:

For the forward conversion from latitude and longitude, for the south pole case

E = FE + rho * sin(lon – lonO)
N = FN + rho * cos(lon – lonO)
where
t = tan(pi/4 + lat/2) / {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)}
rho = 2*a*ko*t / {[(1+e)^(1+e) (1–e)^(1–e)]^0.5}

For the north pole case,
rho and E are found as for the south pole case but
t = tan(pi/4 – lat/2) * {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)}
N = FN – rho * cos(lon – lonO)

For the reverse conversion from easting and northing to latitude and longitude,
lat = chi + (e^2/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2 chi)
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4 chi)
+ (7e^6/120 + 81e^8/1120) sin(6 chi) + (4279e^8/161280) sin(8 chi)

where rho' = [(E-FE)^2 + (N – FN)^2]^0.5
t' =rho' {[(1+e)^(1+e) * (1– e)^(1-e)]^0.5} / (2 a ko)
and for the south pole case
chi = 2 atan(t' ) – pi/2
but for the north pole case
chi = pi/2 - 2 atan t'

Then for for both north and south cases if E = FE, lon = lonO
else for the south pole case
lon = lonO + atan2[(E – FE),(N – FN)]
and for the north pole case
lon = lonO + atan2[(E – FE),(FN – N)]
(see implementation notes in preface for atan2 convention)

Example:

For Projected Coordinate Reference System: WGS 84 / Australian Antarctic Polar Stereographic

Parameters:
Ellipsoid: WGS 84
a = 6378137.0 metres 1/f = 298.2572236
then e = 0.081819191

Latitude of standard parallel (latF): 71°00'00.000"S = -1.239183769 rad
Longitude of origin (lonO): 70°00'00.000"E = 1.221730476 rad
False easting (FE): 6000000.00 metres
False northing (FN): 6000000.00 metres

Forward calculation for:
Latitude (lat) = 75°00'00.000"S = -1.308996939 rad
Longitude(lon) = 120°00'00.000"E = 2.094395102 rad

tF = 0.168407325
mF = 0.326546781
ko = 0.97276901
t = 0.132508348
pho = 1638783.238
whence
E = 7255380.79 m
N = 7053389.56 m

Reverse calculation for the same Easting and Northing (7255380.79 E, 7053389.56 N) first gives:
tF = 0.168407325 mF = 0.326546781 and ko = 0.97276901
then rho' = 1638783.236 t' = 0.132508347 chi = -1.3073146

Then Latitude (lat) = 75°00'00.000"S
Longitude (lon) = 120°00'00.000"E

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of standard parallel	8832	No	For polar aspect azimuthal projections, the parallel on which the scale factor is defined to be unity.
Longitude of origin	8833	No	For polar aspect azimuthal projections, the meridian along which the northing axis increments and also across which parallels of latitude increment towards the north pole.
False easting	8806	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
False northing	8807	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.

Meta Data

Information Source:

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

Data Source:

EPSG

Revision Date:

August 29, 2018

Change ID:

[2004.43] [2010.054] [2017.024]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.