CVT
Centroidal Voronoi Tessellation Datasets

CVT is a dataset directory which contains points generated by an M-dimensional Centroidal Voronoi Tessellation.

Each dataset contains N points in M-dimensions, with the points having the property that they are (approximately) the centroids of the Voronoi regions that they generate.

The datasets are distinguished by the values of the following parameters:

The values of M and N are specified in the dataset file names.

The dataset also lists CHANGE, the L2 norm of the dataset change on the last step, that is the square root of the sum of the squares of the differences between the coordinates of the points before and after the last iterative step.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

CVT, a C++ library which computes elements of a Centroidal Voronoi Tessellation (CVT).

CVT_DATASET, a C++ program which computes a Centroidal Voronoi Tessellation (CVT) and writes it to a file.

PLOT_POINTS, a FORTRAN90 program which can plot two dimensional datasets, making Encapsulated PostScript images.

TABLE_TOP, a FORTRAN90 program which can be used to analyze datasets of any dimension, by creating images of pairwise coordinates.

Example dataset:

A typical (but small) CVT dataset looks like this: 

# cvt_02_00010.txt
# created by CVT_DATASET
# at April 11 2003  12:04:56.303 PM
#
#  Spatial dimension M =   2
#  Number of points N =  10
#
#  Initial SEED =    123456789
#  Initialization by UNIFORM.
#  Sampling by UNIFORM.
#  Number of sample points =       500000
#  Number of sampling iterations =    100
#  L2 norm of dataset change on last step =   0.001501
#
   0.168259       0.878328    
   0.834417       0.833004    
   0.521361       0.499896    
   0.506248       0.165244    
   0.180542       0.627410    
   0.179467       0.372410    
   0.505360       0.833925    
   0.834464       0.166314    
   0.841834       0.499935    
   0.169745       0.122347

Reference:

  1. John Burkardt, Max Gunzburger, Janet Peterson and 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 SAND2002-0099,
    February 2002.
  2. Qiang Du, Vance Faber, and Max Gunzburger,
    Centroidal Voronoi Tessellations: Applications and Algorithms,
    SIAM Review, Volume 41, 1999, pages 637-676.

Datasets:

CVT_02_00100_CIRCLE is a set of 100 points generated in a circle:

CVT_NONUNI_01, CVT_NONUNI_02, and CVT_NONUNI_03 are a set of CVT's using nonuniform density function. The three sets are distinguished by different starting data for the CVT iteration, generated by a Monte Carlo process.

CVT_NONUNI_04, CVT_NONUNI_05, and CVT_NONUNI_06 are a set of CVT's using nonuniform density function. The three sets are distinguished by different starting data for the CVT iteration, generated by a Latin hypercube process.

CVT_02_00010, CVT_02_00100, CVT_02_01000 and CVT_02_10000 are a family of datasets in M = 2 dimensions:

CVT_02_00010_a, CVT_02_00100_a, and CVT_02_01000_a are a second family of datasets in M = 2 dimensions, with 50 iterations, and 100 times as many sampling points as family 1:

CVT_07_00010, CVT_07_00100, CVT_07_01000 and CVT_07_10000 is a family of datasets in M = 7 dimensions:

CVT_07_00010_a, CVT_07_00100_a and CVT_07_01000_a is a second family of datasets in M = 7 dimensions, with 50 iterations, and 100 times as many sampling points as family 1:

CVT_16_00010, CVT_16_00100, CVT_16_01000 and CVT_16_10000 is a family of datasets in M = 16 dimensions:

CVT_16_00010_a and CVT_16_00100_a is a second family of datasets in M = 16 dimensions, with 50 iterations, and 100 times as many sampling points as family 1:

CVT_16_00010_b, CVT_16_00100_b and CVT_16_01000_b is a third family of datasets in M = 16 dimensions, with 200 iterations:

CVT_07_00010_c, CVT_07_00100_c and CVT_07_01000_c is a fourth family of datasets in M = 16 dimensions, which uses the idea of GRID sampling rather than Monte Carlo:

CVT_16_00010_d, CVT_16_00100_d and CVT_16_01000_d is a fifth family of datasets in M = 16 dimensions, which uses a different initial seed for the random number generator, includes:

CVT_16_00010_e, CVT_16_00100_e and CVT_16_01000_e is a sixth family of datasets in M = 16 dimensions, which uses double precision arithmetic:

You can go up one level to the DATASETS directory.

Last revised on 23 February 2006.