cvtp
cvtp,
an Octave code which
creates a periodic Centroidal Voronoi Tessellation (CVTP).
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 M-dimensional 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 and
a MATLAB version and
an Octave version.
Related Data and Programs:
cvtp_test
cvt,
an Octave code which
computes a Centroidal Voronoi Tessellation (CVT).
cvtm_1d,
an Octave code which
estimates a mirror-periodic centroidal Voronoi Tessellation (CVTM) in the
periodic interval [0,1], using a version of Lloyd's iteration.
cvtp,
a dataset directory which
contains examples of CVTP's, that is, Centroidal Voronoi Tessellations
on a periodic domain.
cvtp_1d,
an Octave code which
estimates a periodic centroidal Voronoi Tessellation (CVTP) in the
periodic interval [0,1], using a version of Lloyd's iteration.
Reference:
-
Franz Aurenhammer,
Voronoi diagrams -
a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, pages 345-405, September 1991.
-
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 SAND2002-0099,
February 2002.
-
Qiang Du, Vance Faber, Max Gunzburger,
Centroidal Voronoi Tessellations: Applications and Algorithms,
SIAM Review, Volume 41, 1999, pages 637-676.
-
Lili Ju, Qiang Du, Max Gunzburger,
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,
Parallel Computing,
Volume 28, 2002, pages 1477-1500.
Source Code:
-
cvtp_find_closest.m,
returns the closest generator to a sample point or a periodic
image of that sample point.
-
cvtp_iteration.m,
carries out one step of the CVT iteration, replacing each generator
by the average of the sample points nearest them.
-
cvtp_region_sampler.m,
returns sample points from a region.
-
l4_to_s.m,
converts a logical value to the string 'True' or 'False'.
Last revised on 21 July 2023.