fitcircle

       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  con­
       verted 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 .gmt­
              defaults  file.  If  used,  GMT default is 1 header
              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  (lati­
              tude,longitude)  input/output.  [Default is (longi­
              tude,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 -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(l), project(l), sample1d(l)