1FITCIRCLE(1) GMT 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 [ table ] -Lnorm [ -Fflags ] [ -S[lat] ] [ -V[level] ] [
11 -bibinary ] [ -dinodata ] [ -eregexp ] [ -fflags ] [ -ggaps ] [ -hhead‐
12 ers ] [ -iflags ] [ -oflags ] [ -:[i|o] ]
13 Note: No space is allowed between the option flag and the associated
15 arguments.
16
18 fitcircle reads lon,lat [or lat,lon] values from the first two columns
19 on standard input [or table]. These are converted to Cartesian
20 three-vectors on the unit sphere. Then two locations are found: the
21 mean of the input positions, and the pole to the great circle which
22 best fits the input positions. The user may choose one or both of two
23 possible solutions to this problem. The first is called -L1 and the
24 second is called -L2. When the data are closely grouped along a great
25 circle both solutions are similar. If the data have large dispersion,
26 the pole to the great circle will be less well determined than the
27 mean. Compare both solutions as a qualitative check.
28 The -L1 solution is so called because it approximates the minimization
30 of the sum of absolute values of cosines of angular distances. This
31 solution finds the mean position as the Fisher average of the data, and
32 the pole position as the Fisher average of the cross-products between
33 the mean and the data. Averaging cross-products gives weight to points
34 in proportion to their distance from the mean, analogous to the "lever‐
35 age" of distant points in linear regression in the plane.
36 The -L2 solution is so called because it approximates the minimization
38 of the sum of squares of cosines of angular distances. It creates a 3
39 by 3 matrix of sums of squares of components of the data vectors. The
40 eigenvectors of this matrix give the mean and pole locations. This
41 method may be more subject to roundoff errors when there are thousands
42 of data. The pole is given by the eigenvector corresponding to the
43 smallest eigenvalue; it is the least-well represented factor in the
44 data and is not easily estimated by either method.
45
47 -Lnorm Specify the desired norm as 1 or 2, or use -L or -L3 to see both
48 solutions.
49
51 table One or more ASCII [or binary, see -bi] files containing lon,lat
52 [or lat,lon; see -:[i|o]] values in the first 2 columns. If no
53 file is specified, fitcircle will read from standard input.
54 -Ff|m|n|s|c
56 Normally, fitcircle will write its results in the form of a text
57 report, with the values intermingled with report sentences. Use
58 -F to only return data coordinates, and append flags to specify
59 which coordinates you would like. You can choose from f (Flat
60 Earth mean location), m (mean location), n (north pole of great
61 circle), s (south pole of great circle), and c (pole of small
62 circle and its colatitude, which requires -S).
63 -S[lat]
65 Attempt to fit a small circle instead of a great circle. The
66 pole will be constrained to lie on the great circle connecting
67 the pole of the best-fit great circle and the mean location of
68 the data. Optionally append the desired fixed latitude of the
69 small circle [Default will determine the latitude].
70 -V[level] (more ...)
72 Select verbosity level [c].
73 -bi[ncols][t] (more ...)
75 Select native binary input. [Default is 2 input columns].
76 -dinodata (more ...)
78 Replace input columns that equal nodata with NaN.
79 -e[~]"pattern" | -e[~]/regexp/[i] (more ...)
81 Only accept data records that match the given pattern.
82 -f[i|o]colinfo (more ...)
84 Specify data types of input and/or output columns.
85 -g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more ...)
87 Determine data gaps and line breaks.
88 -h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
90 Skip or produce header record(s).
91 -icols[+l][+sscale][+ooffset][,...] (more ...)
93 Select input columns and transformations (0 is first column).
94 -ocols[,...] (more ...)
96 Select output columns (0 is first column).
97 -:[i|o] (more ...)
99 Swap 1st and 2nd column on input and/or output.
100 -^ or just -
102 Print a short message about the syntax of the command, then
103 exits (NOTE: on Windows just use -).
104 -+ or just +
106 Print an extensive usage (help) message, including the explana‐
107 tion of any module-specific option (but not the GMT common
108 options), then exits.
109 -? or no arguments
111 Print a complete usage (help) message, including the explanation
112 of all options, then exits.
113
115 The ASCII output formats of numerical data are controlled by parameters
116 in your gmt.conf file. Longitude and latitude are formatted according
117 to FORMAT_GEO_OUT, absolute time is under the control of FOR‐
118 MAT_DATE_OUT and FORMAT_CLOCK_OUT, whereas general floating point val‐
119 ues are formatted according to FORMAT_FLOAT_OUT. Be aware that the for‐
120 mat in effect can lead to loss of precision in ASCII output, which can
121 lead to various problems downstream. If you find the output is not
122 written with enough precision, consider switching to binary output (-bo
123 if available) or specify more decimals using the FORMAT_FLOAT_OUT set‐
124 ting.
125
127 Suppose you have lon,lat,grav data along a twisty ship track in the
128 file ship.xyg. You want to project this data onto a great circle and
129 resample it in distance, in order to filter it or check its spectrum.
130 Do the following:
131 gmt fitcircle ship.xyg -L2
133 gmt project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > output.pg
134 Here, ox/oy is the lon/lat of the mean from fitcircle, and px/py is the
136 lon/lat of the pole. The file output.pg has distance, gravity data sam‐
137 pled every 1 km along the great circle which best fits ship.xyg
138 If you have lon, lat points in the file data.txt and wish to return the
140 northern hemisphere great circle pole location using the L2 norm, try
141 gmt fitcircle data.txt -L2 -Fn > pole.txt
143
145 gmt, gmtvector, project, mapproject, sample1d
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148 2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
1495.4.5 Feb 24, 2019 FITCIRCLE(1)