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<title>SPHTRIANGULATE</title>
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<h1 align="center">SPHTRIANGULATE</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="#GRID VALUES PRECISION">GRID VALUES PRECISION</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<a href="#REFERENCES">REFERENCES</a><br>
<hr>
<h2>NAME
<a name="NAME"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">sphtriangulate
− Perform optimal Delaunay triangulation or Voronoi
construction of spherical data</p>
<h2>SYNOPSIS
<a name="SYNOPSIS"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><b>sphtriangulate</b>
<i>infiles</i> [ <b>−A</b> ] [ <b>−C</b> ] [
<b>−D</b> ] [ <b>−H</b>[<b>i</b>][<i>nrec</i>] ]
[ <b>−L</b><i>unit</i> ] [ <b>−N</b><i>nfile</i>
] [ <b>−Qd</b>|<b>v</b> ] [ <b>−T</b> ] [
<b>−V</b> ] [ <b>−:</b>[<b>i</b>|<b>o</b>] ] [
<b>−b</b>[<b>i</b>|<b>o</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>−m</b>[<b>i</b>|<b>o</b>][<i>flag</i>] ]</p>
<h2>DESCRIPTION
<a name="DESCRIPTION"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><b>sphtriangulate</b>
reads one or more ASCII [or binary] files (or standard
input) containing lon, lat and performs a spherical Delaunay
triangulation, i.e., it find how the points should be
connected to give the most equilateral triangulation
possible on the sphere. Optionally, you may choose
<b>−Qv</b> which will do further processing to obtain
the Voronoi polygons. Normally, either set of polygons will
be written as fillable multi-segment output; use
<b>−T</b> to write unique arcs instead. As an option,
compute the area of each triangle or polygon. The algorithm
used is STRIPACK. <i><br>
infiles</i></p>
<p style="margin-left:22%;">Data files with the point
coordinates in ASCII (or binary; see <b>−b</b>). If no
files are given the standard input is read.</p>
<h2>OPTIONS
<a name="OPTIONS"></a>
</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="4%">
<p style="margin-top: 1em"><b>−A</b></p></td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em">Compute the area of the
spherical triangles (<b>−Qd</b>) or polygons
(<b>−Qv</b>) and write the areas (in chosen units; see
<b>−L</b>) in the multisegment output headers [no
areas calculated].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−C</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>For large data set you can save some memory (at the
expense of more processing) by only storing one form of
location coordinates (geographic or Cartesian 3-D vectors)
at any given time, translating from one form to the other
when necessary [Default keeps both arrays in memory].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−D</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Used with <b>−m</b> to skip the last (repeated)
input vertex at the end of a closed segment if it equals the
first point in the segment. Requires <b>−m</b>
[Default uses all points].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−H</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−L</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Specify the unit used for distance and area
calculations. Choose among <b>e</b> (m), <b>k</b> (km),
<b>m</b> (mile), <b>n</b> (nautical mile), or <b>d</b>
(spherical degree). A spherical approximation is used unless
<b><A HREF="gmtdefaults.html#ELLIPSOID">ELLIPSOID</A></b> is set to an actual ellipsoid. When degree
is selected the areas are given in steradians.</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−N</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Write the information pertaining to each polygon (for
Delaunay: the three node number and the triangle area; for
Voronoi the unique node lon, lat and polygon area) to a
separate file [Default puts this information in the segment
headers of the output file]. Required if binary output is
needed.</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−Q</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Select between BD(d)elaunay or BD(v)oronoi mode
[Delaunay].</p> </td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−T</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Write the unique arcs of the construction [Default
writes fillable triangles or polygons]. When used with
<b>−A</b> we store arc length in the segment header in
chosen unit (see <b>−L</b>).</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−V</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Selects verbose mode, which will send progress reports
to stderr [Default runs "silently"].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−:</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−bi</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>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>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−bo</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Selects binary output. 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 desired columns in your binary
output file. [Default is same as input].</p></td></tr>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p><b>−m</b></p></td>
<td width="7%"></td>
<td width="78%">
<p>Multiple segment file(s). Segments are separated by a
special record. For ASCII files the first character must be
<i>flag</i> [Default is ’>’]. For binary
files all fields must be NaN and <b>−b</b> must set
the number of output columns explicitly. By default the
<b>−m</b> setting applies to both input and output.
Use <b>−mi</b> and <b>−mo</b> to give separate
settings to input and output.</p></td></tr>
</table>
<h2>ASCII FORMAT PRECISION
<a name="ASCII FORMAT PRECISION"></a>
</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>
<h2>GRID VALUES PRECISION
<a name="GRID VALUES PRECISION"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">Regardless of
the precision of the input data, GMT programs that create
grid files will internally hold the grids in 4-byte floating
point arrays. This is done to conserve memory and
furthermore most if not all real data can be stored using
4-byte floating point values. Data with higher precision
(i.e., double precision values) will lose that precision
once GMT operates on the grid or writes out new grids. To
limit loss of precision when processing data you should
always consider normalizing the data prior to
processing.</p>
<h2>EXAMPLES
<a name="EXAMPLES"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">To triangulate
the points in the file testdata.txt, and make a Voronoi
diagram via <b><A HREF="psxy.html">psxy</A></b>, use</p>
<p style="margin-left:11%; margin-top: 1em"><b>sphtriangulate</b>
testdata.txt <b>−Qv</b> | psxy <b>−Rg
−JG</b>30/30/6i <b>−M −L −P
−W</b>1p <b>−B</b>0g30 | gv −</p>
<p style="margin-left:11%; margin-top: 1em">To compute the
optimal Delaunay triangulation network based on the multiple
segment file globalnodes.d and save the area of each
triangle in the header record, try</p>
<p style="margin-left:11%; margin-top: 1em"><b>sphtriangulate</b>
globalnodes.d <b>−M −Qd −A</b> >
global_tri.d</p>
<h2>SEE ALSO
<a name="SEE ALSO"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="triangulate.html">triangulate</A></i>(1) <i><A HREF="sphinterpolate.html">sphinterpolate</A></i>(1)
<i><A HREF="sphdistance.html">sphdistance</A></i>(1)</p>
<h2>REFERENCES
<a name="REFERENCES"></a>
</h2>
<p style="margin-left:11%; margin-top: 1em">Renka, R, J.,
1997, Algorithm 772: STRIPACK: Delaunay Triangulation and
Voronoi Diagram on the Surface of a Sphere, <i>AMC Trans.
Math. Software, 23</i> (3), 416−434.</p>
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