GEOD(1) PROJ GEOD(1)

NAME

geod - Geodesic computations

SYNOPSIS

geod +ellps=<ellipse> [-afFIlptwW [args]] [+opt[=arg] ...] file
...

invgeod +ellps=<ellipse> [-afFIlptwW [args]] [+opt[=arg] ...] file
...

DESCRIPTION

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 use geod
-I instead.

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 output.

-t<a> Where 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= option.

-lu Gives a listing of all the units that may be selected with the
+units= option. (Default units are meters.)

-f <format>
Where format is a printf format string to control the output
form of the geographic coordinate values. The default mode is
DMS.

-F <format>
Where format is a printf format string to control the output
form of the distance value. The default mode is "%.3f".

-w<n> Where n is the number of significant fractional digits to
employ for seconds output (when the option is not specified,
-w3 is assumed).

-W<n> Where n is the number of significant fractional digits to
employ for seconds output. 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 note -f.

The +opt command-line options are associated with geodetic parameters
for specifying the ellipsoidal or sphere to use. 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.

See the PROJ documentation for a full list of these parameters and
controls.

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=long parameters and either a
terminus point +lat_2=lat and +lon_2=long 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.

EXAMPLES

The following script determines the geodesic azimuths and distance in
U.S. statute miles from Boston, MA, to Portland, OR:

geod +ellps=clrk66 -I +units=us-mi <<EOF
42d15'N 71d07'W 45d31'N 123d41'W
EOF

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 the distance.

An example of forward geodesic use is to use the Boston location and
determine Portland's location by azimuth and distance:

geod +ellps=clrk66 +units=us-mi <<EOF
42d15'N 71d07'W -66d31'50.141" 2587.504
EOF

which gives:

45d31'0.003"N 123d40'59.985"W 75d39'13.094"

i.e., the latitude and longitude of Portland, and the back azimuth
from Portland to Boston.

NOTE:
Lack of precision in the distance value compromises the precision
of the Portland location.

FURTHER READING

1. GeographicLib.

2. C. F. F. Karney, Algorithms for Geodesics, J. Geodesy 87(1), 43-55
(2013); addenda.

3. A geodesic bibliography.

SEE ALSO

proj(1), cs2cs(1), cct(1), gie(1), projinfo(1), projsync(1)

BUGS

A list of known bugs can be found at
https://github.com/OSGeo/PROJ/issues where new bug reports can be
submitted to.

HOME PAGE

https://proj.org/

AUTHOR

Charles Karney

COPYRIGHT

1983-2024, PROJ contributors

9.5 01 Dec 2024 GEOD(1)