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
              the data.

       -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
              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 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)

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