cvt_box

cvt_box, an Octave 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 information on this web page is distributed under the MIT license.

Languages:

cvt_box is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

cvt_box_test

avi, a data directory which contains an animation of the behavior of the generator points during the iteration, as computed by CCVT_BOX().

cvt, an Octave code which can create a Centroidal Voronoi Tessellation (CVT).

cvt, a dataset directory which contains files describing a Centroidal Voronoi Tessellation (CVT).

cvt_1d_lloyd, an Octave code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the interval [0,1], under a uniform density.

cvt_1d_sampling, an Octave code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the interval [0,1], under a uniform density, using sampling to estimate the Voronoi regions.

florida_cvt_geo, an Octave code which explores the creation of a centroidal Voronoi Tessellation (CVT) of the state of Florida, based solely on geometric considerations.

Author:

Original FORTRAN version by Lili Ju. This version by John Burkardt.

Reference:

1. Franz Aurenhammer,
   Voronoi diagrams - a study of a fundamental geometric data structure,
   ACM Computing Surveys,
   Volume 23, Number 3, September 1991, pages 345-405.
2. 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.
3. Qiang Du, Vance Faber, Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review,
   Volume 41, Number 4, December 1999, pages 637-676.
4. 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 1349-1366.
5. 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:

• ch_cap.m capitalizes a single character.
• cvt_box.m gets information from the user, creates the CVT and saves the animation.
• cvt_energy.m estimates the CVT energy of a given pointset.
• cvt_iterate.m takes one step of the CVT iteration.
• cvt_sample.m returns sample points.
• cvt_write.m writes a CVT dataset to a file.
• data_read.m reads data from a file.
• file_delete.m deletes a file.
• file_exist.m is true if a file exists.
• find_closest.m finds the Voronoi cell generator closest to a point X.
• r8mat_transpose_print.m prints the transpose of an R8MAT, with an optional title.
• r8mat_transpose_print_some.m prints the transpose of some of an R8MAT, with an optional title.
• s_eqi.m is TRUE if two strings are equal, ignoring case.
• s_len_trim.m returns the length of a string to the last nonblank.
• tuple_next_fast.m computes the next element of a tuple space, "fast".