DragonFly On-Line Manual Pages

FITCIRCLE(1)                 Generic Mapping Tools                FITCIRCLE(1)

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

SYNOPSIS
       fitcircle [ xyfile ] -Lnorm [ -H[i][nrec] ] [ -S[lat] ] [ -V ] [
       -:[i|o] ] [ -bi[s|S|d|D[ncol]|c[var1/...]] ] [ -f[i|o]colinfo ]

DESCRIPTION
       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
       "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).  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
              geographical 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
              (absolute 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
       precision, 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 >
       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(1), project(1), sample1d(1)

GMT 4.5.14                        1 Nov 2015                      FITCIRCLE(1)