cvt_box
cvt_box,
a MATLAB code which
allows the user to specify certain parameters, and then
creates and animates a Constrained Centroidal Voronoi Tessellation (CCVT)
of points in a 2D box. After each iteration, points near
the boundary are projected onto the boundary.
The data that the user may set includes:

N, the number of points to generate,

NPP, the number of (equally spaced) sample points
to be used along the boundary of the box;

INIT, initialize the points:

file, by reading data from file;

'GRID', picking points from a grid;

'HALTON', from a Halton sequence;

'RAND', using MATLAB's RAND function;

'UNIFORM', using a simple uniform RNG;

IT_MAX, the maximum number of iterations;

IT_FIXED, the number of iterations for which each
set of sample points should be used (between 1 and IT_MAX);

SAMPLE, how to conduct the sampling:

'GRID', picking points from a grid;

'HALTON', from a Halton sequence;

'RAND', using MATLAB's RAND function;

'UNIFORM', using a simple uniform RNG;

SAMPLE_NUM, the number of sampling points:

MOVIE_NAME, the number the animation file to be created.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
cvt_box is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
avi,
a data directory which
contains an animation of the behavior of the generator points
during the iteration, as computed by CCVT_BOX.
cvt_box_test
cvt,
a MATLAB code which
can create CVT's.
cvt,
a dataset directory which
contains files describing a number of CVT's.
cvt_1d_lloyd,
a MATLAB code which
computes an Npoint Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density.
cvt_1d_sampling,
a MATLAB code which
computes an Npoint Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using sampling to estimate the Voronoi regions.
florida_cvt_geo,
a MATLAB code which
explores the creation of a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based solely on geometric considerations.
Author:
The FORTRAN version was written by Lili Ju.
Reference:

Franz Aurenhammer,
Voronoi diagrams 
a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, September 1991, pages 345405.

John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,
Sandia National Laboratories Technical Report SAND20020099,
February 2002.

Qiang Du, Vance Faber, Max Gunzburger,
Centroidal Voronoi Tessellations: Applications and Algorithms,
SIAM Review,
Volume 41, Number 4, December 1999, pages 637676.

Qiang Du, Max Gunzburger, Lili Ju,
Meshfree, Probabilistic Determination of Point Sets and Support
Regions for Meshfree Computing,
Computer Methods in Applied Mechanics in Engineering,
Volume 191, 2002, pages 13491366.

Lili Ju, Qiang Du, Max Gunzburger,
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,
Parallel Computing,
Volume 28, 2002, pages 14771500.
Source Code:
Last revised on 22 December 2018.