fitcircle - find mean position and pole of best-fit great [or small]
circle to points on a sphere.
fitcircle [ xyfile ] -Lnorm [ -H[nrec] ] [ -S ] [ -V ] [ -: ] [
-bi[s][n] ] [ -f[i|o]colinfo ]
fitcircle 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
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). Number of header records can
be changed by editing your .gmtdefaults4 file. If used, GMT
default is 1 header record. Use -Hi if only input data should
have header records [Default will write out header records if
the input data have them].
-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
-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
-bi Selects binary input. Append s for single precision [Default is
double]. Append n for the number of columns in the binary
[Default is 2 input columns].
-f Special formatting of input and output columns (time or geo-
graphical data) Specify i(nput) or o(utput) [Default is both
input and output]. Give one or more columns (or column ranges)
separated by commas. Append T (Absolute calendar time), t (time
relative to chosen TIME_EPOCH), x (longitude), y (latitude), g
(geographic coordinate), or f (floating point) to each column or
column range item.
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 -L2
project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > out-
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 sam-
pled every 1 km along the great circle which best fits ship.xyg
gmt(l), project(l), sample1d(l)
GMT4.0 1 Oct 2004 FITCIRCLE(l)
Man(1) output converted with