# EPSG:9829

## Polar Stereographic (variant B)

### Attributes

Data source: EPSG

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

Revision date: 2018-08-29

### 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```