1FITCIRCLE(1) Generic Mapping Tools FITCIRCLE(1)
2
6 fitcircle - find mean position and pole of best-fit great [or small]
7 circle to points on a sphere.
8
10 fitcircle [ xyfile ] -Lnorm [ -H[i][nrec] ] [ -S[lat] ] [ -V ] [
11 -:[i|o] ] [ -bi[s|S|d|D[ncol]|c[var1/...]] ] [ -f[i|o]colinfo ]
12
14 fitcircle reads lon,lat [or lat,lon] values from the first two columns
15 on standard input [or xyfile]. These are converted to Cartesian three-
16 vectors on the unit sphere. Then two locations are found: the mean of
17 the input positions, and the pole to the great circle which best fits
18 the input positions. The user may choose one or both of two possible
19 solutions to this problem. The first is called -L1 and the second is
20 called -L2. When the data are closely grouped along a great circle
21 both solutions are similar. If the data have large dispersion, the
22 pole to the great circle will be less well determined than the mean.
23 Compare both solutions as a qualitative check.
24 The -L1 solution is so called because it approximates the minimization
26 of the sum of absolute values of cosines of angular distances. This
27 solution finds the mean position as the Fisher average of the data, and
28 the pole position as the Fisher average of the cross-products between
29 the mean and the data. Averaging cross-products gives weight to points
30 in proportion to their distance from the mean, analogous to the "lever‐
31 age" of distant points in linear regression in the plane.
32 The -L2 solution is so called because it approximates the minimization
34 of the sum of squares of cosines of angular distances. It creates a 3
35 by 3 matrix of sums of squares of components of the data vectors. The
36 eigenvectors of this matrix give the mean and pole locations. This
37 method may be more subject to roundoff errors when there are thousands
38 of data. The pole is given by the eigenvector corresponding to the
39 smallest eigenvalue; it is the least-well represented factor in the
40 data and is not easily estimated by either method.
41 -L Specify the desired norm as 1 or 2, or use -L or -L3 to see
43 both solutions.
44
46 xyfile ASCII [or binary, see -b] file containing lon,lat [lat,lon] val‐
47 ues in the first 2 columns. If no file is specified, fitcircle
48 will read from standard input.
49 -H Input file(s) has header record(s). If used, the default number
51 of header records is N_HEADER_RECS. Use -Hi if only input data
52 should have header records [Default will write out header
53 records if the input data have them]. Blank lines and lines
54 starting with # are always skipped.
55 -S Attempt to fit a small circle instead of a great circle. The
57 pole will be constrained to lie on the great circle connecting
58 the pole of the best-fit great circle and the mean location of
59 the data. Optionally append the desired fixed latitude of the
60 small circle [Default will determine the latitude].
61 -V Selects verbose mode, which will send progress reports to stderr
63 [Default runs "silently"].
64 -: Toggles between (longitude,latitude) and (latitude,longitude)
66 input and/or output. [Default is (longitude,latitude)]. Append
67 i to select input only or o to select output only. [Default
68 affects both].
69 -bi Selects binary input. Append s for single precision [Default is
71 d (double)]. Uppercase S or D will force byte-swapping.
72 Optionally, append ncol, the number of columns in your binary
73 input file if it exceeds the columns needed by the program. Or
74 append c if the input file is netCDF. Optionally, append
75 var1/var2/... to specify the variables to be read. [Default is
76 2 input columns].
77 -f Special formatting of input and/or output columns (time or geo‐
79 graphical data). Specify i or o to make this apply only to
80 input or output [Default applies to both]. Give one or more
81 columns (or column ranges) separated by commas. Append T (abso‐
82 lute calendar time), t (relative time in chosen TIME_UNIT since
83 TIME_EPOCH), x (longitude), y (latitude), or f (floating point)
84 to each column or column range item. Shorthand -f[i|o]g means
85 -f[i|o]0x,1y (geographic coordinates).
86
88 The ASCII output formats of numerical data are controlled by parameters
89 in your .gmtdefaults4 file. Longitude and latitude are formatted
90 according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted
91 according to D_FORMAT. Be aware that the format in effect can lead to
92 loss of precision in the output, which can lead to various problems
93 downstream. If you find the output is not written with enough preci‐
94 sion, consider switching to binary output (-bo if available) or specify
95 more decimals using the D_FORMAT setting.
96
98 Suppose you have lon,lat,grav data along a twisty ship track in the
99 file ship.xyg. You want to project this data onto a great circle and
100 resample it in distance, in order to filter it or check its spectrum.
101 Do the following:
102 fitcircle ship.xyg -L2
104 project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > out‐
106 put.pg
107 Here, ox/oy is the lon/lat of the mean from fitcircle, and px/py is the
109 lon/lat of the pole. The file output.pg has distance, gravity data
110 sampled every 1 km along the great circle which best fits ship.xyg
111
113 GMT(1), project(1), sample1d(1)
114GMT 4.5.6 10 Mar 2011 FITCIRCLE(1)