# CVT_SQUARE_PDF_DISCRETE Centroidal Voronoi Tessellation in Square, Discrete PDF Density

CVT_SQUARE_PDF_DISCRETE is a MATLAB program which iteratively computes a Centroidal Voronoi Tessellation (CVT) in a square, using a density determined by a discrete PDF.

As you watch the CVT develop, for instance, you will be able to guess something about the angle of intersection between the boundaries of the region, and the edges of Voronoi regions.

CVT_SQUARE_PDF_DISCRETE is a MATLAB function which uses a density function defined by discrete data. In this case, the density is defined by a 20 x 20 grid of sample density values. The calling sequence is:

[ p, t ] = cvt_square_pdf_discrete ( n, sample_num, delaunay_display )
• N, the number of generators.
• SAMPLE_NUM, the number of sample points per generator.
• DELAUNAY_DISPLAY, 0 to hide, 1 to show the Delaunay triangulation.

### Languages:

CVT_SQUARE_PDF_DISCRETE is available in a MATLAB version.

### Related Data and Programs:

CCVT_BOX, a MATLAB program which constructs a modified CVT in which some points are forced to lie on the boundary.

CCVT_REFLECT, a MATLAB program which tries to construct a modified CVT in which some points are forced to lie on the boundary, using a reflection idea.

CVT_1D_LLOYD, a MATLAB program which computes an N-point Centroidal Voronoi Tessellation (CVT) within the interval [0,1], under a uniform density.

CVT_1D_NONUNIFORM, a MATLAB library which allows the user to watch the evolution of a CVT computed over a 1D interval with a nonuniform density.

CVT_1D_SAMPLING, a MATLAB program 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.

CVT_2D_SAMPLING, a MATLAB program which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit square [0,1]x[0,1], under a uniform density, using sampling to estimate the Voronoi regions.

CVT_CIRCLE_NONUNIFORM, a MATLAB program which calculates a nonuniform Centroidal Voronoi Tessellation (CVT) over a circle.

CVT_CIRCLE_UNIFORM, a MATLAB program which calculates a Centroidal Voronoi Tessellation (CVT) over a circle with uniform density.

CVT_DATASET, a MATLAB program which creates a CVT dataset.

CVT_SQUARE_NONUNIFORM, a MATLAB program which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a nonuniform density.

CVTM_1D, a MATLAB program which estimates a mirror-periodic centroidal Voronoi Tessellation (CVTM) in the periodic interval [0,1], using a version of Lloyd's iteration.

CVTP_1D, a MATLAB program which estimates a periodic centroidal Voronoi Tessellation (CVTP) in the periodic interval [0,1], using a version of Lloyd's iteration.

DISCRETE_PDF_SAMPLE_2D, a MATLAB program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

FLORIDA_CVT_GEO, MATLAB programs which explore the creation of a centroidal Voronoi Tessellation (CVT) of the state of Florida, based solely on geometric considerations.

LCVT, a MATLAB library which computes a "Latinized" Centroidal Voronoi Tessellation.

TEST_TRIANGULATION, a MATLAB library which defines the geometry of a number of sample regions.

VORONOI_PLOT, a MATLAB program which plots the Voronoi neighborhoods of points using L1, L2, LInfinity or arbitrary LP norms;

### Reference:

1. Franz Aurenhammer,
Voronoi diagrams - a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, pages 345-405, September 1991.
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.

### Source Code:

You can go up one level to the MATLAB source codes.

Last revised on 06 June 2016.