CVT_DEMO is a directory of MATLAB programs which use interaction and graphics to demonstrate properties of the CVT (Centroidal Voronoi Tessellation) calculation.
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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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_DATASET, a MATLAB program which creates a CVT dataset.
DISCRETE_PDF_SAMPLE, 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.
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;
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 )
CVT_ELLIPSE_UNIFORM is a MATLAB function which works the same as the code for the square, except that we are now working in a more interesting region, namely, the ellipse defined by x'*A*x<=36 with A = [ 9, 6; 6, 20 ]; The only tricky thing we have to do is write a routine that returns sample points from the region. The calling sequence is:
[ p, t ] = cvt_ellipse_uniform ( n, sample_num, delaunay_display )
CVT_SQUARE_UNIFORM is a MATLAB function which works in a square with a uniform density. The function starts from a random initial configuration. Another step of the CVT iteration is carried out each time the user hits RETURN. The MATLAB routines trimesh and voronoi are used to simultaneously display the Voronoi diagram and Delaunay triangulation associated with the generators. Moreover, the nearest-neighbor search and centroid computation are carried out efficiently using MATLAB's Delaunay search and rapid array accumulation. The calling sequence is:
[ p, t ] = cvt_square_uniform ( n, sample_num, delaunay_display )
CVT_SQUARE_PDF_DISCRETE is a MATLAB function which works the same as the code for the uniform square, except that we are now working with 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 )
CVT_TRIANGLE_UNIFORM is a MATLAB function which generates a CVT in a triangle with a uniform density. The calling sequence is:
[ p, t ] = cvt_triangle_uniform ( n, sample_num, delaunay_display )
You can go up one level to the MATLAB source codes.
