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<html>
<head>
<title>
CVT_2D_SAMPLING - Centroidal Voronoi Tessellation in the Unit Square
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_2D_SAMPLING <br> Centroidal Voronoi Tessellation in Unit Square
</h1>
<hr>
<p>
<b>CVT_2D_SAMPLING</b>
is a MATLAB program which
allows the user to carry out steps of Lloyd's iteration for
approximating a Centroidal Voronoi Tessellation (CVT) in the unit square.
</p>
<p>
The determination of the Voronoi regions is carried out using
sampling. This means that the convergence of the iteration is
influenced by the accuracy of the estimates provided by sampling.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>cvt_2d_sampling</b> ( <i>g_num</i>, <i>it_num</i>, <i>s_num</i> )
</blockquote>
where
<ul>
<li>
<i>g_num</i> is the number of generators;
</li>
<li>
<i>it_num</i> is the number of iterative steps to take.
</li>
<li>
<i>s_num</i> is the number of sample points in the unit square
used to estimate the Voronoi regions. A value between 1,000
and 100,000 is typical.
</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>CVT_2D_SAMPLING</b> is available in
<a href = "../../m_src/cvt_2d_sampling/cvt_2d_sampling.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
computes CVT's.
</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,
using exact techniques to determine the Voronoi regions.
</p>
<p>
<a href = "../../m_src/cvt_1d_nonuniform/cvt_1d_nonuniform.html">
CVT_1D_NONUNIFORM</a>,
a MATLAB program which
computes an N-point Centroidal
Voronoi Tessellation in 1 dimension, under a nonuniform density,
and plots the evolution of the locations of the generators
during the iteration;
</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_3d_sampling/cvt_3d_sampling.html">
CVT_3D_SAMPLING</a>,
a MATLAB program which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit cube [0,1]x[0,1]x[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
can create a CVT dataset.
</p>
<p>
<a href = "../../m_src/cvt_demo/cvt_demo.html">
CVT_DEMO</a>,
a MATLAB program which
demonstrates a CVT calculation.
</p>
<p>
<a href = "../../m_src/lcvt/lcvt.html">
LCVT</a> ,
a MATLAB library which
computes a "Latinized"
Centroidal Voronoi Tessellation.
</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>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cvt_2d_sampling.m">cvt_2d_sampling.m</a>
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cvt_2d_sampling.png">cvt_2d_sampling.png</a>
a PNG image of the Voronoi diagram and Delaunay triangulation
for a set of 35 points on the 10th step of an iteration.
</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 27 May 2011.
</i>
<!-- John Burkardt -->
</body>
</html>