cvt, a MATLAB code which creates Centroidal Voronoi Tessellations (CVT).
The generation of a CVT dataset is of necessity more complicated than for a quasirandom sequence. An iteration is involved, so there must be an initial assignment for the generators, and then a number of iterations. Moreover, in each iteration, estimates must be made of the volume and location of the Voronoi cells. This is typically done by Monte Carlo sampling. The accuracy of the resulting CVT depends in part on the number of sampling points and the number of iterations taken.
The library is mostly used to generate a dataset of points uniformly distributed in the unit hypersquare. However, a user may be interested in computations with other geometries or point densities. To do this, the user needs to replace the USER() routine in the CVT library, and then specify the appropriate values init=3 and sample=3.
The USER routine returns a set of sample points from the region of interest. The default USER routine samples points uniformly from the unit circle. But other geometries are easy to set up. Changing the point density simply requires weighting the sampling in the region.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
cvt is available in a C++ version and a FORTRAN90 version and a MATLAB version.
cvt_box, a MATLAB code which constructs a modified cvt in which some points are forced to lie on the boundary.
ccvt_reflect, a MATLAB code which tries to construct a modified cvt in which some points are forced to lie on the boundary, using a reflection idea.
cvt, a dataset directory which contains a variety of examples of cvt datasets.
cvt_1d_lloyd, a MATLAB code which computes an n-point centroidal voronoi tessellation (cvt) within the interval [0,1], under a uniform density.
cvt_1d_nonuniform, a MATLAB code which constructs a cvt in one dimension, under a nonuniform density function.
cvt_1d_sampling, a MATLAB 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.
cvt_2d_sampling, a MATLAB code 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_uniform, a MATLAB code which calculates a centroidal voronoi tessellation (cvt) over a circle with uniform density.
cvt_square_nonuniform, a MATLAB code which iteratively calculates a centroidal voronoi tessellation (cvt) over a square, with a nonuniform density.
cvtm_1d, a MATLAB code 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 code which estimates a periodic centroidal voronoi tessellation (cvtp) in the periodic interval [0,1], using a version of lloyd's iteration.
florida_cvt_geo, MATLAB codes which explore the creation of a centroidal voronoi tessellation (cvt) of the state of florida, based solely on geometric considerations.
halton, a MATLAB code which computes elements of a halton quasirandom sequence.
hammersley, a MATLAB code which computes elements of a hammersley quasirandom sequence.
latin_center, a MATLAB code which computes elements of a latin hypercube dataset, choosing center points.
latin_edge, a MATLAB code which computes elements of a latin hypercube dataset, choosing edge points.
latin_random, a MATLAB code which computes elements of a latin hypercube dataset, choosing points at random.
niederreiter2, a MATLAB code which computes elements of a niederreiter quasirandom sequence with base 2.
sobol, a MATLAB code which computes elements of a sobol quasirandom sequence.
uniform, a MATLAB code which computes elements of a uniform pseudorandom sequence.
van_der_corput, a MATLAB code which computes elements of a van der corput quasirandom sequence.