# Polar Stereographic

Name | Polar Stereographic
EPSG Code | 9810
GeoTIFF Code | CT_PolarStereographic (15)
OGC WKT Name | Polar_Stereographic
Supported By | EPSG, GeoTIFF, PROJ.4, OGC WKT

### Projection Parameters

Name | EPSG # | GeoTIFF ID | OGC WKT | Units | Notes
--- | --- | --- | --- | --- | ---
Latitude of natural origin | 1 | NatOriginLat | latitude_of_origin | Angular |
Longitude of natural origin | 2 | StraightVertPoleLong | central_meridian | Angular |
Scale factor at natural origin | 5 | ScaleAtNatOrigin | scale_factor | Unitless | Not in original GeoTIFF ... I added for similarity with EPSG. Defaults to 1.0.
False Easting | 6 | FalseEasting | false_easting | Linear |
False Northing | 7 | FalseNorthing | false_northing | Linear |

### Notes

There are substantial questions about Stereographic projections in Random Issues.

### Examples

Latitude of natural origin: 71N
Longitude of natural origin: 96W
Scale factor at natural origin: 1.0

Projected X | Projected Y | Longitude | Latitude
--- | --- | --- | ---
-2529570 | -5341800 | 121d20'22.38"W | 39d6'4.508"N

### PROJ.4 Organization

North Pole (NatOriginLat > 0):

      +proj=stere +lat_ts=Latitude at natural origin
                  +lat_0=90
                  +lon_0=Longitude at natural origin
    	      +k_0=Scale factor at natural origin (normally 1.0)
                  +x_0=False Easting
                  +y_0=False Northing

South Pole (NatOriginLat < 0):

      +proj=stere +lat_ts=Latitude at natural origin
                  +lat_0=-90
                  +lon_0=Longitude at natural origin
    	      +k_0=Scale factor at natural origin (normally 1.0)
                  +x_0=False Easting
                  +y_0=False Northing

### EPSG Notes

For the forward transformation from latitude and longitude:

    E = FE + rho sin(lon - lon0)
    N = FN - rho cos(lon - lon0)
    where
    rho = 2 a ko t /{[((1+e)^(1+e)) ((1-e)^(1-e))]^0.5}
    t = tan (pi/4 - lat/2) / [(1-esin(lat) ) / (1 + e sin(lat))]^(e/2)

For the reverse transformation:

    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)

    lon = lon0+ arctan [(E-FE) / (FN-N)]

    where chi  = pi/2 - 2 arctan t
    t   =  rho [((1+e)^(1+e)) ((1-e)^(1-e))]^0.5} / 2 a ko
    rho = [(E-FE)^2  + (N - FN)^2]^0.5