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fitcircle - find mean position and pole of best-fit great [or small] circle to points on a


fitcircle [ table ] norm [ flags ] [ [lat] ] [ [level] ] [ -bi<binary> ] [ -di<nodata> ] [
-f<flags> ] [ -g<gaps> ] [ -h<headers> ] [ -i<flags> ] [ -o<flags> ] [ -:[i|o] ]

Note: No space is allowed between the option flag and the associated arguments.


fitcircle reads lon,lat [or lat,lon] values from the first two columns on standard input
[or table]. These are converted to Cartesian three-vectors on the unit sphere. Then two
locations are found: the mean of the input positions, and the pole to the great circle
which best fits the input positions. The user may choose one or both of two possible
solutions to this problem. The first is called -L1 and the second is called -L2. When the
data are closely grouped along a great circle both solutions are similar. If the data have
large dispersion, the pole to the great circle will be less well determined than the mean.
Compare both solutions as a qualitative check.

The -L1 solution is so called because it approximates the minimization of the sum of
absolute values of cosines of angular distances. This solution finds the mean position as
the Fisher average of the data, and the pole position as the Fisher average of the
cross-products between the mean and the data. Averaging cross-products gives weight to
points in proportion to their distance from the mean, analogous to the "leverage" of
distant points in linear regression in the plane.

The -L2 solution is so called because it approximates the minimization of the sum of
squares of cosines of angular distances. It creates a 3 by 3 matrix of sums of squares of
components of the data vectors. The eigenvectors of this matrix give the mean and pole
locations. This method may be more subject to roundoff errors when there are thousands of
data. The pole is given by the eigenvector corresponding to the smallest eigenvalue; it is
the least-well represented factor in the data and is not easily estimated by either


-Lnorm Specify the desired norm as 1 or 2, or use -L or -L3 to see both solutions.


table One or more ASCII [or binary, see -bi] files containing lon,lat [or lat,lon; see
-:[i|o]] values in the first 2 columns. If no file is specified, fitcircle will
read from standard input.

Normally, fitcircle will write its results in the form of a text report, with the
values intermingled with report sentences. Use -F to only return data coordinates,
and append flags to specify which coordinates you would like. You can choose from f
(Flat Earth mean location), m (mean location), n (north pole of great circle), s
(south pole of great circle), and c ** (pole of small circle and its colatitude,
which requires **-S).

Attempt to fit a small circle instead of a great circle. The pole will be
constrained to lie on the great circle connecting the pole of the best-fit great
circle and the mean location of the data. Optionally append the desired fixed
latitude of the small circle [Default will determine the latitude].

-V[level] (more ...)
Select verbosity level [c].

-bi[ncols][t] (more ...)
Select native binary input. [Default is 2 input columns].

-dinodata (more ...)
Replace input columns that equal nodata with NaN.

-f[i|o]colinfo (more ...)
Specify data types of input and/or output columns.

-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more ...)
Determine data gaps and line breaks.

-h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
Skip or produce header record(s).

-icols[l][sscale][ooffset][,...] (more ...)
Select input columns (0 is first column).

-ocols[,...] (more ...)
Select output columns (0 is first column).

-:[i|o] (more ...)
Swap 1st and 2nd column on input and/or output.

-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows
use just -).

-+ or just +
Print an extensive usage (help) message, including the explanation of any
module-specific option (but not the GMT common options), then exits.

-? or no arguments
Print a complete usage (help) message, including the explanation of options, then

Print GMT version and exit.

Print full path to GMT share directory and exit.


The ASCII output formats of numerical data are controlled by parameters in your gmt.conf
file. Longitude and latitude are formatted according to FORMAT_GEO_OUT, whereas other
values are formatted according to FORMAT_FLOAT_OUT. Be aware that the format in effect can
lead to loss of precision in the output, which can lead to various problems downstream. If
you find the output is not written with enough precision, consider switching to binary
output (-bo if available) or specify more decimals using the FORMAT_FLOAT_OUT setting.


Suppose you have lon,lat,grav data along a twisty ship track in the file ship.xyg. You
want to project this data onto a great circle and resample it in distance, in order to
filter it or check its spectrum. Do the following:

gmt fitcircle ship.xyg -L2
gmt project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > output.pg

Here, ox/oy is the lon/lat of the mean from fitcircle, and px/py is the lon/lat of the
pole. The file output.pg has distance, gravity data sampled every 1 km along the great
circle which best fits ship.xyg

If you have lon, lat points in the file data.txt and wish to return the northern
hemisphere great circle pole location using the L2 norm, try

gmt fitcircle data.txt -L2 -Fn > pole.txt

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