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<title>FITCIRCLE</title>
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<h1 align=center>FITCIRCLE</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#ASCII FORMAT PRECISION">ASCII FORMAT PRECISION</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<hr>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">fitcircle
− find mean position and pole of best-fit great [or
small] circle to points on a sphere.</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</h2>
<p style="margin-left:11%; margin-top: 1em"><b>fitcircle</b>
[ <i>xyfile</i> ] <b>−L</b><i>norm</i> [
<b>−H</b>[<b>i</b>][<i>nrec</i>] ] [
<b>−S</b>[<i>lat</i>] ] [ <b>−V</b> ] [
<b>−:</b>[<b>i</b>|<b>o</b>] ] [
<b>−bi</b>[<b>s</b>|<b>S</b>|<b>d</b>|<b>D</b>[<i>ncol</i>]|<b>c</b>[<i>var1</i><b>/</b><i>...</i>]]
] [ <b>−f</b>[<b>i</b>|<b>o</b>]<i>colinfo</i> ]</p>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</h2>
<p style="margin-left:11%; margin-top: 1em"><b>fitcircle</b>
reads lon,lat [or lat,lon] values from the first two columns
on standard input [or <i>xyfile</i>]. 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
<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.</p>
<p style="margin-left:11%; margin-top: 1em">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.</p>
<p style="margin-left:11%; margin-top: 1em">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.</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−L</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Specify the desired
<i>norm</i> as 1 or 2, or use <b>−L</b> or
<b>−L3</b> to see both solutions.</p></td>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</h2>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><i>xyfile</i></p></td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−H</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Input file(s) has
header record(s). If used, the default number of header
records is <b><A HREF="gmtdefaults.html#N_HEADER_RECS">N_HEADER_RECS</A></b>. Use <b>−Hi</b> if
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.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−S</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 latitude].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects verbose
mode, which will send progress reports to stderr [Default
runs "silently"].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−:</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Toggles between
(longitude,latitude) and (latitude,longitude) input and/or
output. [Default is (longitude,latitude)]. Append <b>i</b>
to select input only or <b>o</b> to select output only.
[Default affects both].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
input. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of columns in your binary input file if it exceeds
the columns needed by the program. Or append <b>c</b> if the
input file is netCDF. Optionally, append
<i>var1</i><b>/</b><i>var2</i><b>/</b><i>...</i> to specify
the variables to be read. [Default is 2 input columns].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="9%">
<p style="margin-top: 1em" valign="top"><b>−f</b></p> </td>
<td width="2%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Special formatting
of input and/or output columns (time or geographical data).
Specify <b>i</b> or <b>o</b> to make this apply only to
input or output [Default applies to both]. Give one or more
columns (or column ranges) separated by commas. Append
<b>T</b> (absolute calendar time), <b>t</b> (relative time
in chosen <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b> since <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b>),
<b>x</b> (longitude), <b>y</b> (latitude), or <b>f</b>
(floating point) to each column or column range item.
Shorthand <b>−f</b>[<b>i</b>|<b>o</b>]<b>g</b> means
<b>−f</b>[<b>i</b>|<b>o</b>]0<b>x</b>,1<b>y</b>
(geographic coordinates).</p></td>
</table>
<a name="ASCII FORMAT PRECISION"></a>
<h2>ASCII FORMAT PRECISION</h2>
<p style="margin-left:11%; margin-top: 1em">The ASCII
output formats of numerical data are controlled by
parameters in your .gmtdefaults4 file. Longitude and
latitude are formatted according to
<b><A HREF="gmtdefaults.html#OUTPUT_DEGREE_FORMAT">OUTPUT_DEGREE_FORMAT</A></b>, whereas other values are
formatted according to <b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b>. 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 (<b>−bo</b> if
available) or specify more decimals using the
<b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b> setting.</p>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</h2>
<p style="margin-left:11%; margin-top: 1em">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:</p>
<p style="margin-left:11%; margin-top: 1em"><b>fitcircle</b>
ship.xyg <b>−L</b>2</p>
<p style="margin-left:11%; margin-top: 1em"><b><A HREF="project.html">project</A></b>
ship.xyg <b>−C</b><i>ox</i>/<i>oy</i>
<b>−T</b><i>px</i>/<i>py</i> <b>−S
−F</b>pz | <b>sample1d −S</b>−100
<b>−I</b>1 > output.pg</p>
<p style="margin-left:11%; margin-top: 1em">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</p>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="project.html">project</A></i>(1), <i><A HREF="sample1d.html">sample1d</A></i>(1)</p>
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