# Azimuthal Equidistant - 40,000 Km range

I've been looking at making an azimuthal equidistant map. There are several web sites that offer to make one, based on my location, but they all have the same problem. They assume my antenna rotates 360 degrees - so they map the entire world, staarting from my location, and finishing at 20,000km (1/2 earth circumference).

However, my antenna setup only covers 180 degrees. As such, I'm looking for a "half circle" shaped map, that ranges to 40,000 km.

Does such a map exist? Is "azimuthal equidistant" simply the wrong search term, leading me astray?

• "Azimuthal Equidistant" is a good term. Another name for this projection is the "exponential map" of differential geometry. I doubt you will find GIS software to compute this projection for distances beyond 20,000 Km because at 20,000 Km the map becomes singular and beyond it reverses orientation. Apr 7, 2014 at 15:35

I discribed a workflow to get aeqd maps using a sphere instead of an ellipsoid here: Manipulating Azimuthal Equidistant Projections in QGIS

If you only want to have 180°, I suggest clipping the resulting picture with a polygon in aeqd projection would be the solution.

For a bearing from -45° to 135° from the center of projection at 7E 51N, the clipping polygon can be created by using this text file:

``````Nr;WKT
1;POLYGON ((-22000000 22000000, 22000000 22000000, 22000000 -22000000, -22000000 22000000))
``````

and the result is:

From your question, I gather you want to extent behind your antipodal point. I don't know any projection code that does that. The formulas for azimuthal projections should be the right ones, but the map gets very distorted.

The coordinates should be something like

`````` rho =  2 * pi * R - rho(aeqd)
theta = theta(aeqd) - 180°
``````

John P. Snyder, "Map Projections - A Working Manual" http://pubs.er.usgs.gov/publication/pp1395

has the formulas for the standard aeqd projection on page 195.