FITCIRCLE(l)                                                                                                                          FITCIRCLE(l)

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  geo-
              graphic 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)