[Proj] Program Geod

[Gerald I. Evenden]

I noticed a factor with Karney's geodesic program Geod where the azimuth of 
the geodesic at point 2, usually referred to as the "back azimuth", pointed 
away from the first point.  That is, it is off by Pi.

To demonstrate what I believe to be the normal way that the back azimuth is 
presented I have attached example runs from NGS and my routine geodesic.
I appologize for claiming to be a "source".
-------------------------------------------------------------------------------------------------------
Inverse from   
http://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse2.prl
(NGS' Vincente procedure)

Ellipsoid : GRS80 / WGS84  (NAD83)        
  Equatorial axis,    a   =    6378137.0000
  Polar axis,         b   =    6356752.3141
  Inverse flattening, 1/f =  298.25722210088
   
  First  Station : p1                            
   ---------------- 
    LAT =  10  0  0.00000 North 
    LON =   5  0  0.00000 East  
   
  Second Station : p2                            
   ---------------- 
    LAT =  60  0  0.00000 North 
    LON = 140  0  0.00000 East  
   
  Forward azimuth        FAZ =  21  9 40.4155 From North
  Back azimuth           BAZ = 314 49 18.3799 From North
  Ellipsoidal distance     S =  11287082.3529 m
----------------------------------------------------------------------------------------------------
From geodesic on charon:

$ geodesic -- "earth ellps=wgs84" "display prec=4"
Geodesic Computer v. 2.0
Free software under X11 license
geod: p1 5 10
geod: p2 140 60
   Point 1
      Lon:    5d00'00.000000"E
      Lat:   10d00'00.000000"N
      Hgt:   0.000000
   Point 2
      Lon:  140d00'00.000000"E
      Lat:   60d00'00.000000"N
      Hgt:   0.000000
   Azimuth p1->p2: 21d9'40.4154961"
   Distance: 11287082.3529
   Azimuth p2->p1: 314d49'18.3799053"
------------------------------------------------------------------------------------------------
From Karney's program Geod

$ ./Geod -i -d -p 4
10 5 60 140
021d09'40.41550" 134d49'18.37991" 11287082.3529

   ^forward azi          ^"back" azi - pi        ^dist

---------------------------------
C makes prettier output  ;-)
-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist