NAME
fitcircle - find mean position and pole of best-fit great
[or small] circle to points on a sphere.
SYNOPSIS
fitcircle [ xyfile ] -Lnorm [ -H[nrec] ] [ -S ] [ -V ] [ -:
] [ -bi[s][n] ]
DESCRIPTION
fitcircle reads lon,lat [or lat,lon] values from the first
two columns on standard input [or xyfile]. These are con-
verted 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
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] values 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 .gmtdefaults
file. If used, GMT default is 1 header record.
-S Attempt to fit a small circle instead of a great cir-
cle. 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.
-V Selects verbose mode, which will send progress reports
to stderr [Default runs "silently"].
-: Toggles between (longitude,latitude) and
(latitude,longitude) input/output. [Default is
(longitude,latitude)].
-bi Selects binary input. Append s for single precision
[Default is double]. Append n for the number of
columns in the binary file(s). [Default is 2 input
columns].
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. Try:
fitcircle ship.xyg -L2
project ship.xyg -Oox/oy -Ppx/py -S -pz | 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
SEE ALSO
gmt(l), project(l), sample1d(l)