EPSG Dataset :: v12.003

Azimuthal Equidistant

Coordinate Operation Method Details [VALID]

Name:

Azimuthal Equidistant

Code:

1125

Operation is Reversible:

Yes

Formula:

The Equi-7 projection developed at the Vienna University of Technology (TU Wien) for use with continental-scale satellite imagery georeferencing utilises the azimuthal equidistant projection with rigorous calculations for the direct and inverse geodetic problems [1] as developed by Karney (2013) [2]. The equations have been implemented in C in the Proj library [3]. The projection is neither conformal nor equal area.

For the forward conversion of latitude and longitude to easting and northing:
E = FE + s(12) sin Az(12)
N = FN + s(12) cos Az(12)
where s(12) is the distance along the geodesic from projection origin φo,λo to point φ,λ and Az(12) is its true azimuth, s(12) and Az(12) being computed using Karney's formula for the inverse geodetic problem.

Reverse conversion of easting and northing to latitude and longitude:
Az(12) = atan2(E-FE, N-FN)
s(12) = [(E-FE)^2 + (N-FN)^2]^(1/2)
Then φ,λ are computed from φo,λo, s(12) and Az(12) using Karney's formula for the direct geodetic problem.

Notes:
1. Direct geodetic problem: given coordinates φ1,λ1, geodesic distance s(12) and true azimuth Az(12), find coordinates φ2,λ2. Inverse geodetic problem: given coordinates of two points φ1,λ1, and φ2,λ2, find the geodesic distance s(12) and true azimuth Az(12).
2. Karney, C. F. F. (2013). Algorithms for geodesics. Journal of Geodesy, 87(1):43-55.
3. https://github.com/OSGeo/PROJ/blob/master/src/projections/aeqd.cpp

Example:

For the WGS 84 / Equi7 Europe zone:
Latitude of natural origin (φo) = 53.0°N
Longitude of natural origin (λo) = 24.0°E
False easting = 5,837,287.820 m
False northing = 2,121,415.696 m

Then for point latitude φ = 63.0°N, longitude λ = 44.0°E,
Easting E = 6,840,895.297 m, Northing N = 3,382,726.731 m.

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.

Meta Data

Information Source:

Bauer-Marschallinger, B., Sabel, D., and Wagner, W. (2014). Optimisation of global grids for high-resolution remote sensing data. Computers & Geosciences, 72(0):84-93.

Data Source:

EPSG

Revision Date:

February 24, 2024

Change ID:

[2022.081] [2024.005]

Alias:

Alias	Naming System	Remarks
Azimuthal Equidistant (Karney)	EPSG alias

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.