Provided by: gmt_4.5.11-1build1_amd64

**NAME**

fitcircle - find mean position and pole of best-fit great [or small] circle to points on a sphere.

**SYNOPSIS**

fitcircle[xyfile]-Lnorm[-H[i][nrec] ] [-S[lat] ] [-V] [-:[i|o] ] [-bi[s|S|d|D[ncol]|c[var1/...]] ] [-f[i|o]colinfo]

**DESCRIPTION**

fitcirclereads lon,lat [or lat,lon] values from the first two columns on standard input [orxyfile]. 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-L1and 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-L1solution 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-L2solution 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.-LSpecify the desirednormas 1 or 2, or use-Lor-L3to see both solutions.

**OPTIONS**

xyfileASCII [or binary, see-b] file containing lon,lat [lat,lon] values in the first 2 columns. If no file is specified,fitcirclewill read from standard input.-HInput file(s) has header record(s). If used, the default number of header records isN_HEADER_RECS. Use-Hiif only input data should have header records [Default will write out header records if the input data have them]. Blank lines and lines starting with # are always skipped.-SAttempt 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. Optionally append the desired fixed latitude of the small circle [Default will determine the latitude].-VSelects verbose mode, which will send progress reports to stderr [Default runs "silently"].-:Toggles between (longitude,latitude) and (latitude,longitude) input and/or output. [Default is (longitude,latitude)]. Appendito select input only oroto select output only. [Default affects both].-biSelects binary input. Appendsfor single precision [Default isd(double)]. UppercaseSorDwill force byte-swapping. Optionally, appendncol, the number of columns in your binary input file if it exceeds the columns needed by the program. Or appendcif the input file is netCDF. Optionally, appendvar1/var2/...to specify the variables to be read. [Default is 2 input columns].-fSpecial formatting of input and/or output columns (time or geographical data). Specifyioroto make this apply only to input or output [Default applies to both]. Give one or more columns (or column ranges) separated by commas. AppendT(absolute calendar time),t(relative time in chosenTIME_UNITsinceTIME_EPOCH),x(longitude),y(latitude), orf(floating point) to each column or column range item. Shorthand-f[i|o]gmeans-f[i|o]0x,1y(geographic coordinates).

**ASCII** **FORMAT** **PRECISION**

The ASCII output formats of numerical data are controlled by parameters in your .gmtdefaults4 file. Longitude and latitude are formatted according toOUTPUT_DEGREE_FORMAT, whereas other values are formatted according toD_FORMAT. Be aware that the format in effect can lead to loss of precision in the output, which can lead to various problems downstream. If you find the output is not written with enough precision, consider switching to binary output (-boif available) or specify more decimals using theD_FORMATsetting.

**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. Do the following:fitcircleship.xyg-L2projectship.xyg-Cox/oy-Tpx/py-S-Fpz |sample1d-S-100-I1 > output.pg Here,ox/oyis the lon/lat of the mean fromfitcircle, andpx/pyis 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(1),project(1),sample1d(1)