[Proj] Re: Using Azimuthal Equidistant for Great/Small Circle Generation

[Strebe at aol.com]

This is a perfectly reasonable procedure. A circle centered at the center of 
an azimuthal equidistant is a path whose points are all the same distance from 
that center. That is the definition of small circle. It will also work on the 
ellipsoid, assuming the ellipsoidal form of the azimuthal equidistant is 
properly modelled -- which is not easy. I can't speak for the proj implementation.

There is no need to use the two-hemisphere form. A full-earth azimuthal 
equidistant still has the same properties.

Regards,

daan Strebe
Geocart author
http://www.mapthematics.com


In a message dated 3/8/2006 10:28:14 AM 太平洋標準時, rob.iverson at gmail.com 
writes:

> 
> Sorry for the nearly-off-topic message here!  I don't know where else to 
> turn...
> 
> Is it valid to use the two-hemisphere form of the Azimuthal Equidistant 
> projection to compute great circles and small circles? 
> 
> Here's what I have been doing:  I take a point that is the "center" of the 
> great/small circle, use that as the projection origin for azimuthal 
> equidistant, take the "radius" of the great/small circle (where 90 degrees is a great 
> circle), generate points on a circle centered at the middle of the map, and 
> inverse-project each of those points to get the coordinates on the surface of 
> the earth. 
> 
> This certainly appears to give correct results, but I have no idea if it's 
> valid mathematically.
> 
> If it helps, I am currently using a spherical model of the earth, but I am 
> interested if this technique would work with the ellipsoidal models. 
> 
> Thanks for your help!
> 
> 

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