EPSG Dataset :: v12.003

Colombia Urban

Coordinate Operation Method Details [VALID]

Name:

Colombia Urban

Code:

1052

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.

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

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of natural origin	8801	No	The latitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the latitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0).
Longitude of natural origin	8802	No	The longitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the longitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0). Sometimes known as "central meridian (CM)".
False easting	8806	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
False northing	8807	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.
Projection plane origin height	1039	No	For Colombia urban grids, the height of the projection plane at its origin.

Meta Data

Information Source:

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

Data Source:

EPSG

Revision Date:

May 20, 2013

Change ID:

[2012.044]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.