Polar Stereographic (variant C)
| Coordinate Operation Method Details [VALID] | |||||||||||||||||||||
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| Name: | Polar Stereographic (variant C) | ||||||||||||||||||||
| Code: | 9830 | ||||||||||||||||||||
| 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. For the forward conversion from latitude and longitude, for the south pole case E = EF + rho * sin (lon – lonO) N = NF – rhoF + rho * cos (lon – lonO) where mF = cos latF / (1 – e^2 sin^2(latF))^0.5 tF = tan (p/4 + latF/2) / {[(1 + e sin(latF)) / (1 – e sin(latF))]^(e/2)} t = tan (p/4 + lat/2) / {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)} rhoF = a mF rho = rhoF * t / tF For the north pole case, mF, *F, * and E are found as for the south pole case but tF = tan (p/4 – latF/2) * {[(1 + e sin(latF)) / (1 – e sin(latF))]^(e/2)} t = tan (p/4 – lat/2) * {[(1 + e sin(lat)) / (1 – e sin(lat))]^(e/2)} N = NF + rhoF – [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 for the south pole case rho' = [(E-EF)^2 + (N – NF + rhoF)^2] ^0.5 t' = rho' * tF / rhoF chi = 2 atan(t') – pi/2 and where mF and tF are as for the forward conversion For reverse conversion north pole case, mF, tF and rhoF are found as for the north pole case of the forward conversion, and rho' = [(E-EF)^2 + (N – NF – rhoF)^2]^0.5 t' is found as for the south pole case of the reverse conversion = rho' * tF / rhoF chi = pi/2 - 2 atan(t') Then for for both north and south pole cases if E = EF, lon = lonO else for the south pole case lon = lonO + atan2[(E – EF),(N – NF + rhoF)] and for the north pole case lon = lonO + atan2[(E – EF),(NF + rhoF – N)] (see implementation notes in GN7-2 preface for atan2 convention) |
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| Example: | For Projected Coordinate Reference System: Petrels 1972 / Terre Adelie Polar Stereographic Parameters: Ellipsoid:International 1924 a = 6378388.0 metres 1/f = 297.0 then e = 0.081991890 Latitude of false origin (latF): 67°00'00.000"S = -1.169370599 rad Longitude of origin (lonO): 140°00'00.000"E = 2.443460953 rad Easting at false origin (EF): 300000.00 metres Northing at false origin (NF): 200000.00 metres Forward calculation for: Latitude (lat) = 66°36'18.820"S = -1.162480524 rad Longitude (lon) = 140°04'17.040"E = 2.444707118 rad mF = 0.391848769 rhoF = 2499363.488 tF = 0.204717630 t = 0.208326304 rho = 2543421.183 whence E = 303169.52 m N = 244055.72 m Reverse calculation for the same Easting and Northing (303169.522 E, 244055.721 N) first gives: mF = 0.391848769 rhoF = 2499363.488 tF = 0.204717630 then rho' = 2543421.183 t' = 0.208326304 chi = -1.1600190 Then Latitude (lat) = 66°36'18.820"S Longitude (lon) =140°04'17.040"E |
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| Method Parameters: |
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| Information Source: | EPSG guidance note #7-2, http://www.epsg.org | ||||||||||||||||||||
| Data Source: | EPSG | ||||||||||||||||||||
| Revision Date: | August 29, 2018 | ||||||||||||||||||||
| Change ID: | [2010.054] [2017.024] | ||||||||||||||||||||