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geod - direct geodesic computations
invgeod - inverse geodesic computations
geod +ellps=<ellipse> [ -afFIlptwW [ args ] ] [ +args ] file[s]
invgeod +ellps=<ellipse> [ -afFIlptwW [ args ] ] [ +args ]
geod (direct) and invgeod (inverse) perform geodesic ("Great
Circle") computations for determining 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 longitudes (inverse). The results
are accurate to round off for |f| < 1/50, where f is
flattening. invgeod may not be available on all platforms; in
this case call geod with the -I option.
The following command-line options can appear in any order:
-I Specifies that the inverse geodesic computation is to be
performed. May be used with execution of geod as an
alternative to invgeod execution.
-a Latitude and longitudes of the initial and terminal
points, forward and back azimuths and distance are
-ta A specifies a character employed as the first character
to denote a control line to be passed through without
-le Gives a listing of all the ellipsoids that may be
selected with the +ellps= option.
-lu Gives a listing of all the units that may be selected
with the +units= option.
Format is a printf format string to control the output
form of the geographic coordinate values (f) or distance
value (F). The default mode is DMS for geographic
coordinates and "%.3f" for distance.
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 zeroes.
-p This option causes the azimuthal values to be output as
unsigned DMS numbers between 0 and 360 degrees. Also
The +args command-line options are associated with geodetic
parameters for specifying the ellipsoidal or sphere to use.
See proj documentation for full list of these parameters and
controls. The options are processed in left to right order
from the command line. Reentry of an option is ignored with
the first occurrence assumed to be the desired value.
One or more files (processed in left to right order) specify
the source of data to be transformed. A - will specify the
location of processing standard input. If no files are
specified, 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, longitude 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 longitude) and
azimuthal data must be in decimal degrees or DMS format and
input distance data must be in units consistent with the
ellipsoid major axis or sphere radius units. The latitude must
lie in the range [-90d,90d]. 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
initial 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=distance 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. statute miles from Boston, MA, to Portland,
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 Portland to Boston followed by
An example of forward geodesic use is to use the Boston
location and determine Portland's location by azimuth and
geod +ellps=clrk66 <<EOF +units=us-mi
42d15'N 71d07'W -66d31'50.141" 2587.504
45d31'0.003"N 123d40'59.985"W 75d39'13.094"
Note: lack of precision in the distance value compromises the
precision of the Portland location.
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