# EPSG:1052

## Colombia Urban

### Attributes

Data source: EPSG

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

Revision date: 2013-05-20

### 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.

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))```

### Example

```For Projected Coordinate Reference System: MAGNA-SIRGAS / Bogota urban grid
Parameters:
Ellipsoid:	GRS 1980	a = 6378137.0 metres		1/f = 298.2572221
then 	e^2 = 0.006694380

Latitude of natural origin = 4°40'49.75"N = 0.081689893 rad
Longitude of natural origin = 74°08'47.73"W = -1.294102154 rad
False easting = 92334.879 metres
False northing = 109320.965 metres
Height of projection origin = 2550.000	metres

Forward calculation for:
Latitude	= 4°48'00.000"N = 0.083775804 rad
Longitude	= 74°15'00.000"W = -1.295906970 rad

First calculate constants for the projection:

rho_O = 6335862.944
nu_O = 6378279.154
A = 1.000399794
B = 1.012970E-15
C = 1.000399803
D = 6338413.114

Then
nu = 6378286.489
G = 1.000402470
and then
E =  80859.033m
N = 122543.174m

Reverse calculation for the same Easting and Northing (80859.033E, 122543.174N) first gives:

Latitude	= 4°48'00.000"N
then nu =	6378286.489
and Longitude = 74°15'00.000"W```