cvtp
cvtp,
a FORTRAN90 code which
creates CVTP's, that is, Centroidal Voronoi Tessellations
of a periodic region.
A 2D unit logical torus is the unit square, but with "wraparound".
This is the connectivity frequently seen in video games, in which
a spaceship flies off the top of the screen and immediately reappears
at the bottom of the screen. In the general Mdimensional case,
the extreme minimum and maximum values of each coordinate are
identified, and modular arithmetic may be used to determine
distances.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
cvtp is available in
a FORTRAN90 version.
Related Data and Programs:
CVT,
a FORTRAN90 code which
computes a Centroidal Voronoi Tessellation.
CVTP,
a dataset directory which
contains examples of CVTP's, that is, Centroidal Voronoi Tessellations
on a periodic domain.
cvtp_test
Reference:

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

John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,
User Manual and Supporting Information for code 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, 1999, pages 637676.

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 15 June 2020.