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<HTML>
<HEAD>
<TITLE>fitcircle</TITLE>
</HEAD>
<BODY>
<H1>fitcircle</H1>
<HR>
<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
fitcircle - find mean position and pole of best-fit great
[or small] circle to points on a sphere.
</PRE>
<H2>SYNOPSIS</H2><PRE>
<B>fitcircle</B> [ <I>xyfile</I> ] <B>-L</B><I>norm</I> [ <B>-H</B>[<I>nrec</I>] ] [ <B>-S</B> ] [ <B>-V</B> ] [
<B>-:</B> ] [ <B>-bi</B>[<B>s</B>][<I>n</I>] ]
</PRE>
<H2>DESCRIPTION</H2><PRE>
<B>fitcircle</B> reads lon,lat [or lat,lon] values from the first
two columns on standard input [or <I>xyfile</I>]. 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 <B>-L1</B> and the
second is called <B>-L2</B>. 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 <B>-L1</B> 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 <B>-L2</B> 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.
<B>-L</B> Specify the desired <I>norm</I> as 1 or 2, or use <B>-L</B> or
<B>-L3</B> to see both solutions.
</PRE>
<H2>OPTIONS</H2><PRE>
<I>xyfile</I> ASCII [or binary, see <B>-b</B>] file containing lon,lat
[lat,lon] values in the first 2 columns. If no file
is specified, <B>fitcircle</B> will read from standard
input.
<B>-H</B> Input file(s) has Header record(s). Number of
header records can be changed by editing your .gmt
defaults file. If used, <B><A HREF="GMT.html">GMT</A></B> 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.
<B>-V</B> Selects verbose mode, which will send progress
reports to stderr [Default runs "silently"].
<B>-:</B> Toggles between (longitude,latitude) and (lati
tude,longitude) input/output. [Default is (longi
tude,latitude)]. Applies to geographic coordinates
only.
<B>-bi</B> Selects binary input. Append <B>s</B> for single precision
[Default is double]. Append <I>n</I> for the number of
columns in the binary file(s). [Default is 2 input
columns].
</PRE>
<H2>EXAMPLES</H2><PRE>
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:
<B>fitcircle</B> ship.xyg <B>-L</B>2
<B><A HREF="project.html">project</A></B> ship.xyg <B>-O</B><I>ox</I>/<I>oy</I> <B>-P</B><I>px</I>/<I>py</I> <B>-S</B> <B>-pz</B> | sample1d <B>-S</B>-100
<B>-I</B>1 > output.pg
Here, <I>ox</I>/<I>oy</I> is the lon/lat of the mean from <B>fitcircle</B>, and
<I>px</I>/<I>py</I> 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
</PRE>
<H2>SEE ALSO</H2><PRE>
<I>gmt</I>(l), <I><A HREF="project.html">project</A></I>(l), <I><A HREF="sample1d.html">sample1d</A></I>(l)
</PRE>
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