EPSG:1052

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.

The forward conversion from latitude and longitude to easting and northing is:

E = FE + A * nu * cos(lat) * (lon – lonO)
N = FN + G * rhoO * [(lat – latO) + {B *(lon – lonO)^2 * nu^2 * cos^2(lat)}] 

where
latO, lonO and hO are the latitude, longitude and height of the projection origin,

rho is the radius of curvature of the ellipsoid in the plane of the meridian at latitude lat, rhoO at latitude latO, and rhoM at mid-latitude (latO + lat)/2; rho = a(1 – e^2)/(1 – e^2 * sin^2(lat))^1.5 for  lat, latO and latM

nu is the radius of curvature of the ellipsoid perpendicular to the meridian at latitude lat with nuO at latitude latO; nu = a /(1 – e^2 * sin^2(lat))^0.5 for lat and latO

e is the eccentricity of the ellipsoid and e^2 = (a^2 – b^2)/a^2 = 2f – f^2
a is the ellipsoidal semi-major and 1/f is the inverse flattening

A = 1 + hO/nuO
B = tan(latO) / 2 * rhoO * nuO
G = 1 + hO/latM

The reverse conversion from easting and northing to latitude and longitude is: 

lat = latO + [(N – FN) / D]  – B [(E–FE) / C]^2
lon = lonO + (E – FE) / C *nu * cos(lat)

where
B is as in the forward conversion,
C = 1 + hO/a
D = rhoO * (1 + hO/a(1-e^2))