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<html>
<head>
<title>
CVT_MOD - Centroidal Voronoi Tessellation on Logical Torus
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_MOD <br> Centroidal Voronoi Tessellation on Logical Torus
</h1>
<hr>
<p>
<b>CVT_MOD</b>
is a FORTRAN90 library which
creates Centroidal Voronoi Tessellation (CVT) datasets in which the
geometry is a logical torus.
</p>
<p>
A 2D unit logical torus is the unit square, but with "wraparound".
This is the connectivity frequently seen in video games, in which
a spaceship flies off the top of the screen and immediately reappears
at the bottom of the screen. In the general M-dimensional case,
the extreme minimum and maximum values of each coordinate are
identified, and modular arithmetic may be used to determine
distances.
</p>
<p>
For details on the underlying CVT calculation, refer to
<b>CVT_DATASET</b>. This program is a modification of that one, in
which distances are computed using modular arithmetic. For the
current code, the region is a unit hypercube, although there's
no real difficulty in allowing the widths in each dimension to
vary.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/cvt_dataset/cvt_dataset.html">
CVT_DATASET</a>,
a FORTRAN90 program which
defines and computes a CVT.
</p>
<p>
<a href = "../../data/table/table.html">
TABLE</a> ,
a file format which
is used for the output of <b>CVT_MOD</b>.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
John Burkardt, Max Gunzburger, Janet Peterson and Rebecca Brannon,<br>
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,<br>
Sandia National Laboratories Technical Report SAND2002-0099,<br>
February 2002.
</li>
<li>
Qiang Du, Vance Faber, and Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Lili Ju, Qiang Du, and Max Gunzburger,<br>
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,<br>
Parallel Computing,<br>
Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cvt_mod.f90">cvt_mod.f90</a>, the source code.
</li>
<li>
<a href = "cvt_mod.sh">cvt_mod.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cvt_mod_prb.f90">cvt_mod_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "cvt_mod_prb.sh">cvt_mod_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "cvt_mod_prb_output.txt">cvt_mod_prb_output.txt</a>,
the output from a run of the sample program.
</li>
<li>
<a href = "cvt_mod_02_00400.txt">cvt_mod_02_00400.txt</a>,
a set of 400 CVT (mod 1) points on a 1.0 x 2.0 domain.
</li>
<li>
<a href = "cvt_mod_02_00400.png">cvt_mod_02_00400.png</a>,
a PNG image of the set.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>CVT_ITERATION_MOD</b> takes one step of the CVT iteration.
</li>
<li>
<b>CVT_MOD_WRITE</b> writes a CVT MOD dataset to a file.
</li>
<li>
<b>DATA_READ</b> reads generator coordinate data from a file.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>FIND_CLOSEST_MOD</b> finds the Voronoi cell generator closest to a point X.
</li>
<li>
<b>GET_SEED</b> returns a seed for the random number generator.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_TO_HALTON_VECTOR</b> computes an element of a vector Halton sequence.
</li>
<li>
<b>PARAM_PRINT</b> prints the program parameters.
</li>
<li>
<b>PRIME</b> returns any of the first PRIME_MAX prime numbers.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>REGION_SAMPLER_MOD</b> returns a sample point in the physical region.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_CAP</b> replaces any lowercase letters by uppercase ones in a string.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TEST_REGION</b> determines if a point is within the physical region.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>TUPLE_NEXT_FAST</b> computes the next element of a tuple space, "fast".
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 12 November 2006.
</i>
<!-- John Burkardt -->
</body>
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</html>