fitcircle(1) GMT fitcircle(1)
NAME
fitcircle - find mean position and pole of best-fit great [or small]
circle to points on a sphere.
SYNOPSIS
fitcircle [ table ] -Lnorm [ -Fflags ] [ -S[lat] ] [ -V[level] ] [
-bibinary ] [ -dinodata ] [ -eregexp ] [ -fflags ] [ -ggaps ] [ -hhead-
ers ] [ -iflags ] [ -oflags ] [ -:[i|o] ]
Note: No space is allowed between the option flag and the associated
arguments.
DESCRIPTION
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 alever-
agea 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.
REQUIRED ARGUMENTS
-Lnorm Specify the desired norm as 1 or 2, or use -L or -L3 to see both
solutions.
OPTIONAL ARGUMENTS
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.
-Ff|m|n|s|c
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).
-S[lat]
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 a|)
Select verbosity level [c].
-bi[ncols][t] (more a|)
Select native binary input. [Default is 2 input columns].
-dinodata (more a|)
Replace input columns that equal nodata with NaN.
-e[~]^<i>apattern^<i>a | -e[~]/regexp/[i] (more a|)
Only accept data records that match the given pattern.
-f[i|o]colinfo (more a|)
Specify data types of input and/or output columns.
-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more a|)
Determine data gaps and line breaks.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more a|)
Skip or produce header record(s).
-icols[+l][+sscale][+ooffset][,^<i>a|] (more a|)
Select input columns and transformations (0 is first column).
-ocols[,a|] (more a|)
Select output columns (0 is first column).
-:[i|o] (more a|)
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 just use -).
-+ or just +
Print an extensive usage (help) message, including the explana-
tion 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 all options, then exits.
ASCII FORMAT PRECISION
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, absolute time is under the control of FOR-
MAT_DATE_OUT and FORMAT_CLOCK_OUT, whereas general floating point val-
ues are formatted according to FORMAT_FLOAT_OUT. Be aware that the for-
mat in effect can lead to loss of precision in ASCII 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 set-
ting.
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:
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 sam-
pled 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
SEE ALSO
gmt(1), gmtvector(1), project(1), mapproject(1), sample1d(1)
COPYRIGHT
2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.2 Jun 24, 2017 fitcircle(1)
gmt5 5.4.2 - Generated Wed Jun 28 15:20:14 CDT 2017