EPSG:1125

Azimuthal Equidistant

Attributes

Data source: EPSG

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.

Revision date: 2024-02-24

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.
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