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<html>
<head>
<title>
CCVT_BOX - Constrained CVT Calculation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CCVT_BOX <br> Centroidal Voronoi Tessellation <br> Constrained to a Box
</h1>
<hr>
<p>
<b>CCVT_BOX</b>
is a C++ program which
creates a Centroidal Voronoi Tessellation
of points in a 2D box, with points constrained to lie on the boundary
of the region.
</p>
<p>
This is a fairly simple and limited code, and was designed mainly
for testing and experimentation. Current work is investigating
more interesting regions, including holes, and other ways of
"encouraging" some points to move to the boundary and stay there.
</p>
<p>
The original version of <b>CCVT_BOX</b> was written by Lili Ju.
</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">
Languages:
</h3>
<p>
<b>CCVT_BOX</b> is available in
<a href = "../../cpp_src/ccvt_box/ccvt_box.html">a C++ version</a> and
<a href = "../../f_src/ccvt_box/ccvt_box.html">a FORTRAN90 version</a> and
<a href = "../../m_src/ccvt_box/ccvt_box.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cvt/cvt.html">
CVT</a>,
a C++ library which
can compute CVT's.
</p>
<p>
<a href = "../../datasets/cvt/cvt.html">
CVT</a>,
a dataset directory which
contains files describing a number of CVT's.
</p>
<p>
<a href = "../../cpp_src/cvt_dataset/cvt_dataset.html">
CVT_DATASET</a>,
a C++ program which
creates a CVT dataset.
</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, 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, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Qiang Du, Max Gunzburger, Lili Ju,<br>
Meshfree, Probabilistic Determination of Point Sets and Support
Regions for Meshfree Computing,<br>
Computer Methods in Applied Mechanics in Engineering,<br>
Volume 191, 2002, pages 1349-1366;
</li>
<li>
Lili Ju, Qiang Du, Max Gunzburger,<br>
Probabilistic Methods for Centroidal Voronoi Tessellations and
their Parallel Implementations,<br>
Parallel Computing, Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ccvt_box.cpp">ccvt_box.cpp</a>, the source code;
</li>
<li>
<a href = "ccvt_box.sh">ccvt_box.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ccvt_box_input.txt">ccvt_box_input.txt</a>,
input that would normally be entered
interactively by the user.
</li>
<li>
<a href = "ccvt_box_output.txt">ccvt_box_output.txt</a>,
printed output from a run of the program.
</li>
<li>
<a href = "initial.txt">initial.txt</a>,
a TABLE file containing the initial CVT generators.
</li>
<li>
<a href = "initial.png">initial.png</a>,
a PNG image of the initial CVT generators.
</li>
<li>
<a href = "final.txt">final.txt</a>,
a TABLE file containing the final CVT generators.
</li>
<li>
<a href = "final.png">final.png</a>,
a PNG image of the final CVT generators.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for CCVT_BOX.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>CVT_ENERGY</b> computes the CVT energy of a dataset.
</li>
<li>
<b>CVT_SAMPLE</b> returns sample points.
</li>
<li>
<b>CVT_WRITE</b> writes a CVT dataset to a file.
</li>
<li>
<b>DATA_READ</b> reads generator coordinate data from a file.
</li>
<li>
<b>DIGIT_TO_CH</b> returns the base 10 digit character corresponding to a digit.
</li>
<li>
<b>FIND_CLOSEST</b> finds the nearest R point to each S point.
</li>
<li>
<b>GET_SEED</b> returns a random seed for the random number generator.
</li>
<li>
<b>HALHAM_LEAP_CHECK</b> checks LEAP for a Halton or Hammersley sequence.
</li>
<li>
<b>HALHAM_N_CHECK</b> checks N for a Halton or Hammersley sequence.
</li>
<li>
<b>HALHAM_NDIM_CHECK</b> checks NDIM for a Halton or Hammersley sequence.
</li>
<li>
<b>HALHAM_SEED_CHECK</b> checks SEED for a Halton or Hammersley sequence.
</li>
<li>
<b>HALHAM_STEP_CHECK</b> checks STEP for a Halton or Hammersley sequence.
</li>
<li>
<b>HALTON_BASE_CHECK</b> checks BASE for a Halton sequence.
</li>
<li>
<b>I4_LOG_10</b> returns the whole part of the logarithm base 10 of an integer.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two integers.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two integers.
</li>
<li>
<b>I4_TO_HALTON_SEQUENCE</b> computes N elements of a leaped Halton subsequence.
</li>
<li>
<b>I4_TO_S</b> converts an integer to a string.
</li>
<li>
<b>MPB</b> projects generators onto the boundary of the region.
</li>
<li>
<b>POINTS_EPS</b> creates an EPS file image of a set of points.
</li>
<li>
<b>PRIME</b> returns any of the first PRIME_MAX prime numbers.
</li>
<li>
<b>R8_EPSILON</b> returns the round off unit for double precision arithmetic.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" real value, usually the largest legal real.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two double precision values.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two double precision values.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> fills a double precision array with pseudorandom values.
</li>
<li>
<b>RANDOM_INITIALIZE</b> initializes the RANDOM random number generator.
</li>
<li>
<b>S_EQI</b> reports whether two strings are equal, ignoring case.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</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>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> returns the current YMDHMS date as 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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 02 December 2006.
</i>
<!-- John Burkardt -->
</body>
</html>