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 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 solutions.


OPTIONS

       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 .gmtdefaults file.  If used, GMT
              default is 1 header record.

       -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/output.   [Default  is  (longitude,latitude)].  Applies to
              geographic coordinates only.

       -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  -Cox/oy  -Tpx/py -S -pz | sample1d -S-100 -I1 > out-
       put.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)



VERSION                              DATE                         FITCIRCLE(l)

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