1GEOD(1)                              PROJ                              GEOD(1)
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NAME

6       geod - Geodesic computations
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SYNOPSIS

9          geod +ellps=<ellipse> [-afFIlptwW [args]] [+opt[=arg] ...] file ...
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11          invgeod  +ellps=<ellipse>  [-afFIlptwW [args]] [+opt[=arg] ...] file
12          ...
13

DESCRIPTION

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.
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23       invgeod may not be available on all platforms; in this case use geod -I
24       instead.
25
26       The following command-line options can appear in any order:
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28       -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
32       -a     Latitude and longitudes of the initial and terminal points, for‐
33              ward and back azimuths and distance are output.
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35       -t<a>  Where a specifies a character employed as the first character to
36              denote a control line to be passed through without processing.
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38       -le    Gives  a listing of all the ellipsoids that may be selected with
39              the +ellps= option.
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41       -lu    Gives a listing of all the units that may be selected  with  the
42              +units= option. (Default units are meters.)
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44       -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.
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49       -F <format>
50              Where  format  is  a  printf format string to control the output
51              form of the distance value. The default mode is "%.3f".
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53       -w<n>  Where n is the number of significant fractional digits to employ
54              for seconds output (when the option is not specified, -w3 is as‐
55              sumed).
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57       -W<n>  Where n is the number of significant fractional digits to employ
58              for  seconds output. When -W is employed the fields will be con‐
59              stant width with leading zeroes.
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61       -p     This option causes the azimuthal values to be output as unsigned
62              DMS numbers between 0 and 360 degrees. Also note -f.
63
64       The  +opt  command-line options are associated with geodetic parameters
65       for specifying the ellipsoidal or sphere to use.  controls. The options
66       are  processed in left to right order from the command line. Reentry of
67       an option is ignored with the first occurrence assumed to  be  the  de‐
68       sired value.
69
70       See the PROJ documentation for a full list of these parameters and con‐
71       trols.
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73       One or more files (processed in left to right order) specify the source
74       of  data to be transformed. A - will specify the location of processing
75       standard input. If no files are specified, the input is assumed  to  be
76       from stdin.
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78       For  direct  determinations  input data must be in latitude, longitude,
79       azimuth and distance order and output will be latitude,  longitude  and
80       back  azimuth of the terminus point. Latitude, longitude of the initial
81       and terminus point are input for the inverse mode and  respective  for‐
82       ward  and  back azimuth from the initial and terminus points are output
83       along with the distance between the points.
84
85       Input geographic coordinates (latitude  and  longitude)  and  azimuthal
86       data  must  be in decimal degrees or DMS format and input distance data
87       must be in units consistent with the ellipsoid major axis or sphere ra‐
88       dius  units. The latitude must lie in the range [-90d,90d]. Output geo‐
89       graphic coordinates will be in DMS (if the -f switch is  not  employed)
90       to 0.001" with trailing, zero-valued minute-second fields deleted. Out‐
91       put distance data will be in the same units as the ellipsoid or  sphere
92       radius.
93
94       The  Earth's  ellipsoidal  figure may be selected in the same manner as
95       program proj by using +ellps=, +a=, +es=, etc.
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97       geod may also be used to determine intermediate points along  either  a
98       geodesic  line between two points or along an arc of specified distance
99       from a geographic point. In both cases an initial point must be  speci‐
100       fied  with  +lat_1=lat  and +lon_1=lon parameters and either a terminus
101       point +lat_2=lat and +lon_2=lon or a distance and azimuth from the ini‐
102       tial point with +S=distance and +A=azimuth must be specified.
103
104       If  points along a geodesic are to be determined then either +n_S=inte‐
105       ger specifying the number of intermediate points and/or +del_S=distance
106       specifying the incremental distance between points must be specified.
107
108       To  determine  points  along  an arc equidistant from the initial point
109       both +del_A=angle and +n_A=integer must be  specified  which  determine
110       the  respective  angular  increments  and number of points to be deter‐
111       mined.
112

EXAMPLES

114       The following script determines the geodesic azimuths and  distance  in
115       U.S.  statute miles from Boston, MA, to Portland, OR:
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117          geod +ellps=clrk66 <<EOF -I +units=us-mi
118          42d15'N 71d07'W 45d31'N 123d41'W
119          EOF
120
121       which gives the results:
122
123          -66d31'50.141" 75d39'13.083" 2587.504
124
125       where the first two values are the azimuth from Boston to Portland, the
126       back azimuth from Portland to Boston followed by the distance.
127
128       An example of forward geodesic use is to use the  Boston  location  and
129       determine Portland's location by azimuth and distance:
130
131          geod +ellps=clrk66 <<EOF +units=us-mi
132          42d15'N 71d07'W -66d31'50.141" 2587.504
133          EOF
134
135       which gives:
136
137          45d31'0.003"N 123d40'59.985"W 75d39'13.094"
138
139       NOTE:
140          Lack of precision in the distance value compromises the precision of
141          the Portland location.
142

FURTHER READING

144       1. GeographicLib.
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146       2. C. F. F. Karney, Algorithms for Geodesics, J. Geodesy  87(1),  43–55
147          (2013); addenda.
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149       3. A geodesic bibliography.
150

SEE ALSO

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

155       A      list      of      known     bugs     can     be     found     at
156       https://github.com/OSGeo/PROJ/issues where new bug reports can be  sub‐
157       mitted to.
158

HOME PAGE

160       https://proj.org/
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AUTHOR

163       Charles Karney
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166       1983-2022
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1719.0.1                            Jun 15, 2022                          GEOD(1)
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