cvt_1d_lloyd, a MATLAB code which allows the user to carry out Lloyd's algorithm for a Centroidal Voronoi Tessellation (CVT) in the interval [0,1].
The determination of the Voronoi regions is carried out using exact techniques.
For n generators, the solution is known in advance:
x(i) = ( 2 * i - 1 ) / ( 2 * n )Lloyd's iterative algorithm starts from an arbitrary vector x, however, so it is interesting to see how the approximate solution evolves toward the correct answer.
cvt_1d_lloyd ( n, it_num, init )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
cvt_1d_lloyd is available in a MATLAB version and a Python version.
ccvt_reflect, a MATLAB code which tries to construct a constrained Centroidal Voronoi Tessellation (CCVT) in which some points are forced to lie on the boundary, using a reflection idea.
cvt, a MATLAB code which computes a Centroidal Voronoi Tessellation (CVT).
cvt, a dataset directory which contains a variety of examples of Centroidal Voronoi Tessellations (CVT).
cvt_1d_nonuniform, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) in 1 dimension, under a nonuniform density, and plots the evolution of the locations of the generators during the iteration;
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_3d_sampling, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit cube [0,1]x[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.
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.