FITCIRCLE(1) Generic Mapping Tools FITCIRCLE(1)NAMEfitcircle - find mean position and pole of best-fit great [or small]
circle to points on a sphere.
SYNOPSISfitcircle [ xyfile ] -Lnorm [ -H[i][nrec] ] [ -S[lat] ] [ -V ] [
-:[i|o] ] [ -bi[s|S|d|D[ncol]|c[var1/...]] ] [ -f[i|o]colinfo ]
DESCRIPTIONfitcircle reads lon,lat [or lat,lon] values from the first two columns
on standard input [or xyfile]. 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 "lever‐
age" 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 method.
-L Specify the desired norm as 1 or 2, or use -L or -L3 to see
both solutions.
OPTIONS
xyfile ASCII [or binary, see -b] file containing lon,lat [lat,lon] val‐
ues in the first 2 columns. If no file is specified, fitcircle
will read from standard input.
-H Input file(s) has header record(s). If used, the default number
of header records is N_HEADER_RECS. Use -Hi if only input data
should have header records [Default will write out header
records if the input data have them]. Blank lines and lines
starting with # are always skipped.
-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 Selects verbose mode, which will send progress reports to stderr
[Default runs "silently"].
-: Toggles between (longitude,latitude) and (latitude,longitude)
input and/or output. [Default is (longitude,latitude)]. Append
i to select input only or o to select output only. [Default
affects both].
-bi Selects binary input. Append s for single precision [Default is
d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of columns in your binary
input file if it exceeds the columns needed by the program. Or
append c if the input file is netCDF. Optionally, append
var1/var2/... to specify the variables to be read. [Default is
2 input columns].
-f Special formatting of input and/or output columns (time or geo‐
graphical data). Specify i or o to make this apply only to
input or output [Default applies to both]. Give one or more
columns (or column ranges) separated by commas. Append T (abso‐
lute calendar time), t (relative time in chosen TIME_UNIT since
TIME_EPOCH), x (longitude), y (latitude), or f (floating point)
to each column or column range item. Shorthand -f[i|o]g means
-f[i|o]0x,1y (geographic coordinates).
ASCII FORMAT PRECISION
The ASCII output formats of numerical data are controlled by parameters
in your .gmtdefaults4 file. Longitude and latitude are formatted
according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted
according to D_FORMAT. 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 preci‐
sion, consider switching to binary output (-bo if available) or specify
more decimals using the D_FORMAT setting.
EXAMPLES
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:
fitcircle ship.xyg -L 2
project ship.xyg -Cox/oy -Tpx/py -S -F pz | sample1d -S-100 -I 1 > out‐
put.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
SEE ALSOGMT(1), project(1), sample1d(1)GMT 4.5.14 1 Nov 2015 FITCIRCLE(1)
