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