# fitcircle

fitcircle(cmd0::String="", arg1=nothing, kwargs...)

keywords: GMT, Julia, fit circles

Find mean position and great [or small] circle fit to points on sphere

## Description

Reads lon,lat [or lat,lon] values from the first two columns. 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 (i.e. norm=1) and the second is called L2 (i.e. norm=2). 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.

## Required Arguments

• table
One or more data tables holding a number of data columns.

• L or norm : – norm=1 | norm=2 | norm=3
Specify the desired norm as 1 or 2, or use or norm=3 to see both solutions.

## Optional Arguments

• F or coord or coordinates : – coord=flags
Traditionally, fitcircle will write its results in the form of a text report, with the values intermingled with report sentences. Use coord to only return data coordinates, and append flags to specify which coordinates you would like. You can choose one or more items from flat Earth mean location, mean location, north pole of great circle, south pole of great circle, and circle (pole of small circle and its colatitude, which requires small_circle).

• S or small_circle : – small_circle=true | small_circle=lat
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. Optionally append the desired fixed latitude of the small circle [Default will determine the optimal latitude].

• V or verbose : – verbose=true | verbose=level
Select verbosity level. More at verbose

• a or aspatial : – aspatial=??
Control how aspatial data are handled in GMT during input and output. More at

• bi or binary_in : – binary_in=??
Select native binary format for primary table input. More at

• di or nodata_in : – nodata_in=??
Substitute specific values with NaN. More at

• e or pattern : – pattern=??
Only accept ASCII data records that contain the specified pattern. More at

• f or colinfo : – colinfo=??
Specify the data types of input and/or output columns (time or geographical data). More at

• g or gap : – gap=??
Examine the spacing between consecutive data points in order to impose breaks in the line. More at

Specify that input and/or output file(s) have n header records. More at

• i or incol or incols : – incol=col_num | incol="opts"
Select input columns and transformations (0 is first column, t is trailing text, append word to read one word only). More at incol

• o or outcol : – outcol=??
Select specific data columns for primary output, in arbitrary order. More at

• q or inrows : – inrows=??
Select specific data rows to be read and/or written. More at

• yx : – yx=true
Swap 1st and 2nd column on input and/or output. More at

## Examples

To find the parameters of a great circle that most closely fits the (lon,lat) points in the remote file @sat_03.txt (hosted in a GMT server) in a least-squares sense, try

fitcircle("@sat_03.txt", norm=2, coord=:mean)

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:

Df = fitcircle("ship.xyg", norm=2)
D1 = project("ship.xyg", origin=(ox,oy), pole=(px,py), sort=true, outvars=:pz);
D2 = sample1d(D1, S=-100, I=1);

Here, ox,oy is the lon/lat of the mean from fitcircle, and px,py is the lon/lat of the pole. The output has distance, gravity data sampled every 1 km along the great circle which best fits ship.xyg

If you have lon, lat points in the file data.txt and wish to return the northern hemisphere great circle pole location using the L2 norm, try

D = fitcircle("data.txt", norm=2, coordinates=:north)