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 "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  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 > 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(1gmt), project(1gmt), sample1d(1gmt)

                                            1 Jan 2004                               FITCIRCLE(l)