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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>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">sphtriangulate
− Perform optimal Delaunay triangulation or Voronoi
construction of spherical data</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</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>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</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>
<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="4%">
<p style="margin-top: 1em" valign="top"><b>−A</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−C</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−D</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−H</b></p> </td>
<td width="7%"></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="4%">
<p style="margin-top: 1em" valign="top"><b>−L</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−Q</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Select between
BD(d)elaunay or BD(v)oronoi mode [Delaunay].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−T</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="7%"></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="4%">
<p style="margin-top: 1em" valign="top"><b>−:</b></p> </td>
<td width="7%"></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="4%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="7%"></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="4%">
<p style="margin-top: 1em" valign="top"><b>−bo</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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 valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−m</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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>
</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="GRID VALUES PRECISION"></a>
<h2>GRID VALUES PRECISION</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>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</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>
<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="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>
<a name="REFERENCES"></a>
<h2>REFERENCES</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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