# CVT_CIRCLE_NONUNIFORM Nonuniform Centroidal Voronoi Tessellation on Circle

CVT_CIRCLE_NONUNIFORM is a MATLAB program which demonstrates the computation of a centroidal Voronoi Tessellation (CVT) over a circular region, using a nonuniform density.

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.

### Usage:

CVT_CIRCLE_NONUNIFORM is a MATLAB function for computing a CVT in a circle with a nonuniform density. The spatial region is the unit circle, but a nonuniform density is applied to that region. The density is implicitly defined by the sampling routine, which returns many more points near the circumference than near the center of the circle. The result is that, during the CVT iteration, the generators arrange themselves more densely towards the outer part of the circle.

[ p, t ] = cvt_circle_nonuniform ( 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_CIRCLE_NONUNIFORM 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 Centroidal Voronoi Tessellation (CVT) over a circle with nonuniform density.

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_DEMO, a MATLAB program which interactively, graphically demonstrates a Centroidal Voronoi Tessellation (CVT) calculation;

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;

### Source Code:

Last revised on 24 December 2018.