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<html>
<head>
<title>
CCVT_BOX - Animated Constrained CVT Algorithm
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CCVT_BOX <br> Animated Constrained CVT Algorithm
</h1>
<hr>
<p>
<b>CCVT_BOX</b>
is a MATLAB program which
allows the user to specify certain parameters, and then
creates and animates a Centroidal Voronoi Tessellation
of points in a 2D box. After each iteration, points near
the boundary are projected onto the boundary.
</p>
<p>
The data that the user may set includes:
<ul>
<li>
<b>N</b>, the number of points to generate,
</li>
<li>
<b>NPP</b>, the number of (equally spaced) sample points
to be used along the boundary of the box;
</li>
<li>
<b>INIT</b>, initialize the points:
<ul>
<li>
<i>file</i>, by reading data from file;
</li>
<li>
<i>'GRID'</i>, picking points from a grid;
</li>
<li>
<i>'HALTON'</i>, from a Halton sequence;
</li>
<li>
<i>'RAND'</i>, using MATLAB's RAND function;
</li>
<li>
<i>'UNIFORM'</i>, using a simple uniform RNG;
</li>
</ul>
</li>
<li>
<b>IT_MAX</b>, the maximum number of iterations;
</li>
<li>
<b>IT_FIXED</b>, the number of iterations for which each
set of sample points should be used (between 1 and <b>IT_MAX</b>);
</li>
<li>
<b>SAMPLE</b>, how to conduct the sampling:
<ul>
<li>
<i>'GRID'</i>, picking points from a grid;
</li>
<li>
<i>'HALTON'</i>, from a Halton sequence;
</li>
<li>
<i>'RAND'</i>, using MATLAB's RAND function;
</li>
<li>
<i>'UNIFORM'</i>, using a simple uniform RNG;
</li>
</ul>
</li>
<li>
<b>SAMPLE_NUM</b>, the number of sampling points:
</li>
<li>
<b>MOVIE_NAME</b>, the number the animation file to be created.
</li>
</ul>
</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 = "../../data/avi/avi.html">
AVI</a>,
a data directory which
contains an animation of the behavior of the generator points
during the iteration, as computed by CCVT_BOX.
</p>
<p>
<a href = "../../m_src/ccvt_reflect/ccvt_reflect.html">
CCVT_REFLECT</a>,
a MATLAB program which
tries to achieve the same results
as <b>CCVT_BOX</b> but using a "reflection" idea to force points
onto the boundary of the region.
</p>
<p>
<a href = "../../m_src/cvt/cvt.html">
CVT</a>,
a MATLAB library which
can create 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 = "../../m_src/cvt_1d_lloyd/cvt_1d_lloyd.html">
CVT_1D_LLOYD</a>,
a MATLAB program which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density.
</p>
<p>
<a href = "../../m_src/cvt_1d_sampling/cvt_1d_sampling.html">
CVT_1D_SAMPLING</a>,
a MATLAB program which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using sampling to estimate the Voronoi regions.
</p>
<p>
<a href = "../../m_src/cvt_dataset/cvt_dataset.html">
CVT_DATASET</a>,
a MATLAB program which
creates a CVT dataset.
</p>
<h3 align = "center">
Author:
</h3>
<p>
The FORTRAN version of <b>CCVT_BOX</b> was written by Lili Ju.
</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, September 1991, pages 345-405.
</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,<br>
Volume 41, Number 4, December 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,<br>
Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ccvt_box.m">ccvt_box.m</a>
gets information from the user, creates the CVT and
saves the animation.
</li>
<li>
<a href = "ch_cap.m">ch_cap.m</a>
capitalizes a single character.
</li>
<li>
<a href = "cvt_energy.m">cvt_energy.m</a>
estimates the CVT energy of a given pointset.
</li>
<li>
<a href = "cvt_sample.m">cvt_sample.m</a>
returns sample points.
</li>
<li>
<a href = "cvt_write.m">cvt_write.m</a>
writes a CVT dataset to a file.
</li>
<li>
<a href = "data_read.m">data_read.m</a>
reads data from a file.
</li>
<li>
<a href = "file_exist.m">file_exist.m</a>
is true if a file exists.
</li>
<li>
<a href = "file_delete.m">file_delete.m</a>
deletes a file.
</li>
<li>
<a href = "find_closest.m">find_closest.m</a>
finds the Voronoi cell generator closest to a point X.
</li>
<li>
<a href = "get_seed.m">get_seed.m</a>
returns a seed for the random number generator.
</li>
<li>
<a href = "halham_leap_check.m">halham_leap_check.m</a>
checks LEAP for a Halton or Hammersley sequence.
</li>
<li>
<a href = "halham_n_check.m">halham_n_check.m</a>
checks N for a Halton or Hammersley sequence.
</li>
<li>
<a href = "halham_dim_num_check.m">halham_dim_num_check.m</a>
checks NDIM for a Halton or Hammersley sequence.
</li>
<li>
<a href = "halham_seed_check.m">halham_seed_check.m</a>
checks SEED for a Halton or Hammersley sequence.
</li>
<li>
<a href = "halham_step_check.m">halham_step_check.m</a>
checks STEP for a Halton or Hammersley sequence.
</li>
<li>
<a href = "halton_base_check.m">halton_base_check.m</a>
checks BASE for a Halton sequence.
</li>
<li>
<a href = "i4_to_halton_sequence.m">i4_to_halton_sequence.m</a>
next N elements of an NDIM-dimensional Halton sequence
</li>
<li>
<a href = "points_eps.m">points_eps.m</a>
creates a PostScript image of a set of points.
</li>
<li>
<a href = "prime.m">prime.m</a>
returns the N-th prime number.
</li>
<li>
<a href = "r8_huge.m">r8_huge.m</a>
returns a very large R8 value.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>
prints the transpose of an R8MAT, with an optional title.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">
r8mat_transpose_print_some.m</a>
prints the transpose of some of an R8MAT, with an optional title.
</li>
<li>
<a href = "r8mat_uniform_01.m">r8mat_uniform_01.m</a>
returns a unit pseudorandom R8MAT.
</li>
<li>
<a href = "random_initialize.m">random_initialize.m</a>
initializes the MATLAB random number seed.
</li>
<li>
<a href = "s_eqi.m">s_eqi.m</a>
is TRUE if two strings are equal, ignoring case.
</li>
<li>
<a href = "s_len_trim.m">s_len_trim.m</a>
returns the length of a string to the last nonblank.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a timestamp.
</li>
<li>
<a href = "timestring.m">timestring.m</a>
prints the current YMDHMS date into a string.
</li>
<li>
<a href = "tuple_next_fast.m">tuple_next_fast.m</a>
computes the next element of a tuple space, "fast".
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ccvt_box_output.txt">ccvt_box_output.txt</a>,
the output file.
</li>
<li>
<a href = "initial.txt">initial.txt</a>,
a <a href = "../../data/table/table.html">TABLE file</a>
containing the initial CVT generators.
</li>
<li>
<a href = "initial.png">initial.png</a>,
a <a href = "../../data/png/png.html">PNG</a>
image of the initial CVT generators.
</li>
<li>
<a href = "final.txt">final.txt</a>,
a <a href = "../../data/table/table.html">TABLE file</a>
containing the final CVT generators.
</li>
<li>
<a href = "final.png">final.png</a>,
a <a href = "../../data/png/png.html">PNG</a>
image of the final CVT generators.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 08 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>