## 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)].

          -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 -Oox/oy -Ppx/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, project, sample1d