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+ +
+

geod

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+

Synopsis

+
+

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

+

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

+
+
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+

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.

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+ +
+
+-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 Cartographic projection for 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=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.

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+
+

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.

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Further reading

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  1. GeographicLib.

    2. +

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

    3. +

  3. A geodesic bibliography.

    4. +
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