1GEOD(1) PROJ GEOD(1)
2
6 geod - Geodesic computations
7
9 geod +ellps=<ellipse> [-afFIlptwW [args]] [+opt[=arg] ...] file ...
10 invgeod +ellps=<ellipse> [-afFIlptwW [args]] [+opt[=arg] ...] file
12 ...
13
15 geod (direct) and invgeod (inverse) perform geodesic (Great Circle)
16 computations for determining latitude, longitude and back azimuth of a
17 terminus point given a initial point latitude, longitude, azimuth and
18 distance (direct) or the forward and back azimuths and distance between
19 an initial and terminus point latitudes and longitudes (inverse). The
20 results are accurate to round off for |f| < 1/50, where f is flatten‐
21 ing.
22 invgeod may not be available on all platforms; in this case use geod -I
24 instead.
25 The following command-line options can appear in any order:
27 -I Specifies that the inverse geodesic computation is to be per‐
29 formed. May be used with execution of geod as an alternative to
30 invgeod execution.
31 -a Latitude and longitudes of the initial and terminal points, for‐
33 ward and back azimuths and distance are output.
34 -t<a> Where a specifies a character employed as the first character to
36 denote a control line to be passed through without processing.
37 -le Gives a listing of all the ellipsoids that may be selected with
39 the +ellps= option.
40 -lu Gives a listing of all the units that may be selected with the
42 +units= option.
43 -f <format>
45 Where format is a printf format string to control the output
46 form of the geographic coordinate values. The default mode is
47 DMS for geographic coordinates and "%.3f" for distance.
48 -F <format>
50 Where format is a printf format string to control the output
51 form of the distance value (-F). The default mode is DMS for ge‐
52 ographic coordinates and "%.3f" for distance.
53 -w<n> Where n is the number of significant fractional digits to employ
55 for seconds output (when the option is not specified, -w3 is as‐
56 sumed).
57 -W<n> Where n is the number of significant fractional digits to employ
59 for seconds output. When -W is employed the fields will be con‐
60 stant width with leading zeroes.
61 -p This option causes the azimuthal values to be output as unsigned
63 DMS numbers between 0 and 360 degrees. Also note -f.
64 The +opt command-line options are associated with geodetic parameters
66 for specifying the ellipsoidal or sphere to use. controls. The options
67 are processed in left to right order from the command line. Reentry of
68 an option is ignored with the first occurrence assumed to be the de‐
69 sired value.
70 See the PROJ documentation for a full list of these parameters and con‐
72 trols.
73 One or more files (processed in left to right order) specify the source
75 of data to be transformed. A - will specify the location of processing
76 standard input. If no files are specified, the input is assumed to be
77 from stdin.
78 For direct determinations input data must be in latitude, longitude,
80 azimuth and distance order and output will be latitude, longitude and
81 back azimuth of the terminus point. Latitude, longitude of the initial
82 and terminus point are input for the inverse mode and respective for‐
83 ward and back azimuth from the initial and terminus points are output
84 along with the distance between the points.
85 Input geographic coordinates (latitude and longitude) and azimuthal
87 data must be in decimal degrees or DMS format and input distance data
88 must be in units consistent with the ellipsoid major axis or sphere ra‐
89 dius units. The latitude must lie in the range [-90d,90d]. Output geo‐
90 graphic coordinates will be in DMS (if the -f switch is not employed)
91 to 0.001" with trailing, zero-valued minute-second fields deleted. Out‐
92 put distance data will be in the same units as the ellipsoid or sphere
93 radius.
94 The Earth's ellipsoidal figure may be selected in the same manner as
96 program proj by using +ellps=, +a=, +es=, etc.
97 geod may also be used to determine intermediate points along either a
99 geodesic line between two points or along an arc of specified distance
100 from a geographic point. In both cases an initial point must be speci‐
101 fied with +lat_1=lat and +lon_1=lon parameters and either a terminus
102 point +lat_2=lat and +lon_2=lon or a distance and azimuth from the ini‐
103 tial point with +S=distance and +A=azimuth must be specified.
104 If points along a geodesic are to be determined then either +n_S=inte‐
106 ger specifying the number of intermediate points and/or +del_S=distance
107 specifying the incremental distance between points must be specified.
108 To determine points along an arc equidistant from the initial point
110 both +del_A=angle and +n_A=integer must be specified which determine
111 the respective angular increments and number of points to be deter‐
112 mined.
113
115 The following script determines the geodesic azimuths and distance in
116 U.S. statute miles from Boston, MA, to Portland, OR:
117 geod +ellps=clrk66 <<EOF -I +units=us-mi
119 42d15'N 71d07'W 45d31'N 123d41'W
120 EOF
121 which gives the results:
123 -66d31'50.141" 75d39'13.083" 2587.504
125 where the first two values are the azimuth from Boston to Portland, the
127 back azimuth from Portland to Boston followed by the distance.
128 An example of forward geodesic use is to use the Boston location and
130 determine Portland's location by azimuth and distance:
131 geod +ellps=clrk66 <<EOF +units=us-mi
133 42d15'N 71d07'W -66d31'50.141" 2587.504
134 EOF
135 which gives:
137 45d31'0.003"N 123d40'59.985"W 75d39'13.094"
139 NOTE:
141 Lack of precision in the distance value compromises the precision of
142 the Portland location.
143
145 1. GeographicLib.
146 2. C. F. F. Karney, Algorithms for Geodesics, J. Geodesy 87(1), 43–55
148 (2013); addenda.
149 3. A geodesic bibliography.
151
153 proj(1), cs2cs(1), cct(1), gie(1), projinfo(1), projsync(1)
154
156 A list of know bugs can be found at
157 https://github.com/OSGeo/PROJ/issues where new bug reports can be sub‐
158 mitted to.
159
161 https://proj.org/
162
164 Charles Karney
165
167 1983-2020
1687.2.1 Dec 25, 2020 GEOD(1)