GEOD(1)                                                                GEOD(1)

       geod - direct geodesic computations
       invgeod - inverse geodesic computations

       geod  +ellps=<ellipse> [ -afFIlptwW [ args ] ] [
       +args ] file[s]
       invgeod +ellps=<ellipse> [ -afFIlptwW [ args ] ]
       [ +args ] file[s]

       Geod  (direct)  and  invgeod  (inverse)  perform
       geodesic (Great Circle) computations for  deter‐
       mining latitude, longitude and back azimuth of a
       terminus point given a initial  point  latitude,
       longitude,  azimuth and distance (direct) or the
       forward and back azimuths and  distance  between
       an initial and terminus point latitudes and lon‐
       gitudes (inverse).

       The following  runline  control  parameters  can
       appear in any order:

       -I     Specifies  that the inverse geodesic com‐
              putation is to be performed.  May be used
              with  execution of goed as an alternative
              to invgeod execution.

       -a     Latitude and longitudes  of  the  initial
              and  terminal  points,  forward  and back
              azimuths and distance are output.

       -ta    A specifies a character employed  as  the
              first  character to denote a control line
              to be passed through without  processing.

       -le    Gives  a  listing  of  all the ellipsoids
              that may be  selected  with  the  +ellps=

       -lu    Gives a listing of all the units that may
              be selected with the +units= option.

       -[f|F] format
              Format is a printf format string to  con‐
              trol  the  output  form of the geographic
              coordinate values (f) or  distance  value
              (F).   The  default  mode is DMS for geo‐
              graphic coordinates and "%.3f"  for  dis‐

              N is the number of significant fractional
              digits to employ for seconds output (when
              the  option  is  not  specified,  -w3  is
              assumed).  When -W is employed the fields
              will   be  constant  width  with  leading

       -p     This option causes the  azimuthal  values
              to  be  output  as  unsigned  DMS numbers
              between 0 and 360 degrees.  Also note -f.

       The +args run-line arguments are associated with
       geodetic parameters for  specifying  the  ellip‐
       soidal or sphere to use.  See proj documentation
       for full list of these  parameters  and  contrl.
       The options are processed in left to right order
       from the run line.   Reentry  of  an  option  is
       ignored  with  the first occurance assumed to be
       the desired value.

       One or more files (processed in  left  to  right
       order)  specify  the source of data to be trans‐
       formed.  A - will specify the location  of  pro‐
       cessing  standard input.  If no files are speci‐
       fied, the input is assumed to be from stdin.

       For direct determinations input data must be  in
       latitude,  longitude, azimuth and distance order
       and output will be latitude, longitude and  back
       azimuth of the terminus point.  Latitude, longi‐
       tude of the initial and terminus point are input
       for  the inverse mode and respective forward and
       back  azimuth  from  the  initial  and  terminus
       points   are  output  along  with  the  distance
       between the points.

       Input geographic coordinates (latitude and  lon‐
       gitude) and azimuthal data must be in DMS format
       and input distance data must be in units consis‐
       tent  with  the  ellipsoid  major axis or sphere
       radius  units.   Output  geographic  coordinates
       will  be  in  DMS  (if  the  -f  switch  is  not
       employed) to 0.001" with  trailing,  zero-valued
       minute-second  fields  deleted.  Output distance
       data will be in the same units as the  ellipsoid
       or sphere radius.

       The  Earth’s  ellipsoidal figure may be selected
       in the same manner  as  program  proj  by  using
       +ellps=, +a=, +es=, etc.

       Geod  may also be used to determine intermediate
       points along either a geodesic line between  two
       points  or  along  an  arc of specified distance
       from a geographic point.  In both cases an  ini‐
       tial point must be specified with +lat_1=lat and
       +lon_1=lon  parameters  and  either  a  terminus
       point  +lat_2=lat  and  +lon_2=lon or a distance
       and azimuth from the initial point with  +S=dis‐
       tance and +A=azimuth must be specified.

       If  points along a geodesic are to be determined
       then either +n_S=integer specifying  the  number
       of  intermediate  points  and/or +del_S=distance
       specifying  the  incremental  distance   between
       points must be specified.

       To  determine  points  along  an arc equidistant
       from the initial  point  both  +del_A=angle  and
       +n_A=integer  must  be specified which determine
       the respective angular increments and number  of
       points to be determined.

       The  following  script  determines  the geodesic
       azimuths and distance in U.S. stature miles from
       Boston, MA, to Portland, OR:
             geod +ellps=clrk66 <<EOF -I +units=us-mi
             42d15’N 71d07’W 45d31’N 123d41’W
       which gives the results:
             -66d31’50.141"   75d39’13.083"   2587.504
       where  the first two values are the azimuth from
       Boston to Portland, the back azimuth from  Port‐
       land to Boston followed by the distance.

       An example of forward geodesic use is to use the
       Boston location and determine  Portland’s  loca‐
       tion by azimuth and distance:
             geod +ellps=clrk66 <<EOF +units=us-mi
             42d15’N 71d07’W -66d31’50.141" 2587.504
       which gives:
             45d31’0.003"N              123d40’59.985"W
       Note: lack of precision in  the  distance  value
       compromises  the precision of the Portland loca‐

       Thomas, P.D., 1970, Spheroidal Geodesics, Refer‐
       ence   Systems  &  Local  Geometry:  U.S.  Naval
       Oceanographic  Office, S-138.


                              2000/03/21 Rel. 4.4                      GEOD(1)