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<html>
<head>
<title>
CVT_DATASET - An Interactive Centroidal Voronoi Tessellation Program
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_DATASET <br> Generate CVT Datasets
</h1>
<hr>
<p>
<b>CVT_DATASET</b>
is a MATLAB program which
creates a CVT dataset and writes it to a file.
</p>
<p>
The program is interactive, and allows the user to choose the parameters
that define the dataset.
</p>
<p>
Normally, data is computed in the unit hypercube, with uniform
density. However, if you wish to work in a more interesting
geometry, or to control the density function, it is necessary
to modify the <b>USER</b> routine in the <b>CVT</b> library,
and then direct <b>CVT_DATASET</b> to use that routine for
initialization and sampling.
</p>
<p>
The data that the user may set includes:
<ul>
<li>
<b>DIM_NUM</b>, the spatial dimension,
</li>
<li>
<b>N</b>, the number of points to generate,
</li>
<li>
<b>SEED</b>, a seed to use for random number generation;
</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>'RANDOM'</i>, using FORTRAN RANDOM function;
</li>
<li>
<i>'UNIFORM'</i>, using a simple uniform RNG;
</li>
<li>
<i>'USER'</i>, by calling the "user" routine;
</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>'RANDOM'</i>, using FORTRAN RANDOM function;
</li>
<li>
<i>'UNIFORM'</i>, using a simple uniform RNG;
</li>
<li>
<i>'USER'</i>, by calling the "user" routine;
</li>
</ul>
</li>
<li>
<b>SAMPLE_NUM</b>, the number of sampling points;
</li>
<li>
<b>BATCH</b>, the number of sampling points to create
at one time (between 1 and <b>SAMPLE_NUM</b>);
</li>
<li>
<b>OUTPUT</b>, a file in which to store the data.
</li>
</ul>
</p>
<p>
A "CVT" is a Centroidal Voronoi Tessellation. Essentially, a
CVT is a set of sample points in a (finite) region with the
property that each point is the centroid of its Voronoi subregion.
A "random" set of sample points will not have this property.
However, it is possible to begin with a random set of sample
points, and drive it towards a CVT set, by applying an iterative
refinement process.
</p>
<p>
The generation of a CVT dataset is of necessity more complicated than
for a quasirandom sequence. An iteration is involved, so there
must be an initial assignment for the generators, and then a
number of iterations. Moreover, in each iteration, estimates must
be made of the volume and location of the Voronoi subregions. This is
typically done by Monte Carlo sampling. The accuracy of the resulting
CVT depends in part on the number of sampling points and the number
of iterations taken.
</p>
<p>
A reasonable set of input data might be:
<pre>
2 <i>spatial dimension is 2</i>
10 <i>compute 10 points</i>
123456789 <i>seed for random numbers</i>
'uniform' <i>initialize by UNIFORM</i>
40 <i>40 iterations</i>
0.0 <i>zero tolerance; won't stop early</i>
'uniform' <i>sample using UNIFORM</i>
10000 <i>use 10,000 sample points on each iteration</i>
1000 <i>create 1,000 sample points at a time</i>
-1 <i>stop; don't want to define another set.</i>
</pre>
</p>
<p>
Once these parameters are set, the program generates the data
and writes it to a file. The user may then specify another set of
input data, or terminate the program.
</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>CVT_DATASET</b> is available in
<a href = "../../cpp_src/cvt_dataset/cvt_dataset.html">a C++ version</a> and
<a href = "../../f_src/cvt_dataset/cvt_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/cvt_dataset/cvt_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/ccvt_box/ccvt_box.html">
CCVT_BOX</a>,
a MATLAB program which
constructs a modified CVT in which some points are forced to
lie on the boundary.
</p>
<p>
<a href = "../../m_src/ccvt_reflect/ccvt_reflect.html">
CCVT_REFLECT</a>,
a MATLAB program which
tries to construct a modified CVT in which some points are forced to
lie on the boundary, using a reflection idea.
</p>
<p>
<a href = "../../m_src/cvt/cvt.html">
CVT</a>,
a MATLAB library which
can compute a CVT.
</p>
<p>
<a href = "../../datasets/cvt/cvt.html">
CVT</a>,
a dataset directory which
contains a variety of examples of CVT datasets.
</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_nonuniform/cvt_1d_nonuniform.html">
CVT_1D_NONUNIFORM</a>,
a MATLAB program which
constructs a CVT in one dimension, under a nonuniform density function.
</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_2d_sampling/cvt_2d_sampling.html">
CVT_2D_SAMPLING</a>,
a MATLAB program which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit square [0,1]x[0,1], under a uniform density,
using sampling to estimate the Voronoi regions.
</p>
<p>
<a href = "../../m_src/cvt_demo/cvt_demo.html">
CVT_DEMO</a>,
a MATLAB program which
is an interactive graphic demonstration of a CVT calculation.
</p>
<p>
<a href = "../../m_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a MATLAB program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../m_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a MATLAB program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../m_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a MATLAB program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../m_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a MATLAB program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../m_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a MATLAB program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../m_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a MATLAB program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../m_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a MATLAB program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../m_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a MATLAB program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../m_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a MATLAB program which
generates a dataset of uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../m_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a MATLAB program which
creates a van der Corput quasirandom sequence and writes it to a file.
</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,<br>
Volume 41, 1999, pages 637-676.
</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 = "cvt_dataset.m">cvt_dataset.m</a>,
the main program;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>Test 1</b> computes 85 CVT points in 2 dimensions, using uniform
initialization, a seed of 123456789, 40 iterations, a zero tolerance,
uniform sampling, 10,000 sample points in batches of 1000:
<ul>
<li>
<a href = "input01.txt">input01.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output01.txt">output01.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt01.txt">cvt01.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt01.png">cvt01.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 2</b> repeats test 1, but with 80 iterations:
<ul>
<li>
<a href = "input02.txt">input02.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output02.txt">output02.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt02.txt">cvt02.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt02.png">cvt02.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 3</b> repeats test 1, but with 1,000,000 sample points:
<ul>
<li>
<a href = "input03.txt">input03.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output03.txt">output03.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt03.txt">cvt03.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt03.png">cvt03.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 4</b> repeats test 1, but with Halton sampling:
<ul>
<li>
<a href = "input04.txt">input04.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output04.txt">output04.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt04.txt">cvt04.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt04.png">cvt04.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 5</b> repeats test 1, but with Grid sampling:
<ul>
<li>
<a href = "input05.txt">input05.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output05.txt">output05.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt05.txt">cvt05.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt05.png">cvt05.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 6</b> repeats test 1, but with Random sampling:
<ul>
<li>
<a href = "input06.txt">input06.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output06.txt">output06.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt06.txt">cvt06.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt06.png">cvt06.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 7</b> repeats test 1, but with a seed of 987654321:
<ul>
<li>
<a href = "input07.txt">input07.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output07.txt">output07.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt07.txt">cvt07.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt07.png">cvt07.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 8</b> repeats test 1, but with a batch size of 5:
<ul>
<li>
<a href = "input08.txt">input08.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output08.txt">output08.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt08.txt">cvt08.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt08.png">cvt08.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 9</b> computes 100 CVT points in 3 dimensions, using uniform
initialization, a seed of 123456789, 40 iterations, a tolerance
of 0.000001, uniform sampling, 10,000 sample points in batches of 1000:
<ul>
<li>
<a href = "input09.txt">input09.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output09.txt">output09.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt09.txt">cvt09.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 10</b> investigates the unstable CVT formed by a Cartesian
grid of 100 points in 2D. Starting from this unstable solution,
the iteration proceeds towards a more "hexagonal" pattern :
<ul>
<li>
<a href = "input10.txt">input10.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output10.txt">output10.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt10.txt">cvt10.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt10.png">cvt10.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 11</b> shows how the user may specify the initial point locations
in a file. 15 points are specified in 2D:
<ul>
<li>
<a href = "input11.txt">input11.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output11.txt">output11.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "initial11.txt">initial11.txt</a>,
the initial dataset, created by the user;
</li>
<li>
<a href = "initial11.png">initial11.png</a>,
a PNG image of
the initial dataset;
</li>
<li>
<a href = "cvt11.txt">cvt11.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt11.png">cvt11.png</a>,
a PNG image of the dataset;
</li>
</ul>
</p>
<p>
<b>Test 12</b>:
<ul>
<li>
<a href = "input12.txt">input12.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output12.txt">output12.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt12.txt">cvt12.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 13</b>:
<ul>
<li>
<a href = "input13.txt">input13.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output13.txt">output13.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt13.txt">cvt13.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 14</b> shows how the user may refer to the USER routine
for a different geometry. The default USER routine is set up
to sample the unit circle in 2D. 100 points are requested:
<ul>
<li>
<a href = "input14.txt">input14.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output14.txt">output14.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt14.txt">cvt14.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt14.png">cvt14.png</a>,
a PNG image of the dataset;
</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 17 September 2005.
</i>
<!-- John Burkardt -->
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