CVTP
CVT Datasets on a Logical Torus

CVTP is a dataset directory which contains examples of CVTP's, that is, Centroidal Voronoi Tessellations defined on a periodic domain, usually a rectangle or hyperrectangle.

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 within one cell of a periodically repeating region.

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:

TABLE, a file format which is used to store the data.

PLOT_POINTS, a FORTRAN90 program which was used to make images of some of the 2D datasets.

TABLE_TOP, a FORTRAN90 program which was used to make pairwise coordinate plots of some of the higher dimensional datasets

Example dataset:

A typical (but small) dataset looks like this:

  0.378753  0.919641
  0.725977  0.572210
  0.551973  0.246525
  0.264802  0.248364
  0.052727  0.745158
  0.057432  0.457647
  0.395623  0.587517
  0.710814  0.904034
  0.839889  0.240473
  0.046507  0.033340
      

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, Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.

Datasets:

There is a family of datasets in M = 2 dimensions. At least for the lower values of N, it is useful to look at plots of this data.

• cvtp_02_00010.txt, is the computed dataset;
• cvtp_02_00010.png
• cvtp_02_00100.txt, is the computed dataset;
• cvtp_02_00100.png
• cvtp_02_01000.txt, is the computed dataset;
• cvtp_02_01000.png
• cvtp_02_10000.txt, is the computed dataset;

There is a family of datasets in M = 7 dimensions.

• cvtp_07_00010.txt, is the computed dataset;
• cvtp_07_00100.txt, is the computed dataset;
• cvtp_07_01000.txt, is the computed dataset;
• cvtp_07_10000.txt, is the computed dataset;

There is a family of datasets in M = 16 dimensions.

• cvtp_16_00010.txt, is the computed dataset;
• cvtp_16_00100.txt, is the computed dataset;
• cvtp_16_01000.txt, is the computed dataset;
• cvtp_16_10000.txt, is the computed dataset;

You can go up one level to the DATASETS directory.