# geod¶

`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.

## Synopsis¶

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

## Description¶

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.
-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= option.
-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 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.
-[w|W]n
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
note -f.
```

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.

## Examples¶

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

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

which gives:

```
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.

## Further reading¶

- GeographicLib.
- C. F. F. Karney, Algorithms for Geodesics, J. Geodesy
**87**(1), 43–55 (2013); addenda. - A geodesic bibliography.