cvtp_1d, an Octave code which estimates a periodic centroidal Voronoi Tessellation (CVTP) in the periodic interval [0,1], using a version of Lloyd's iteration.
The determination of the Voronoi regions is carried out using sampling. This means that the convergence of the iteration is influenced by the accuracy of the estimates provided by sampling.
For n generators, a solution set is known in advance:
x(i) = i / n, i = 1 : nas is any periodic translate of this set. Lloyd's algorithm starts from an arbitrary vector x, however, so it is interesting to see how the approximate solution evolves toward a correct solution, whose fundamental property is that the generators are equally spaced within the periodic domain.
cvtp_1d ( g_num, it_num, sample_num )where
The computer code and data files described and made available on this web page are distributed under the MIT license
cvtp_1d is available in a MATLAB version and an Octave version.
cvt_box, an Octave code which constructs a modified cvt in which some points are forced to lie on the boundary.
ccvt_reflect, an Octave code which tries to construct a modified cvt in which some points are forced to lie on the boundary, using a reflection idea.
cvt, an Octave code which computes cvt's.
cvt, a dataset directory which contains a variety of examples of cvt datasets.
cvt_1d_lloyd, an Octave code which computes an n-point centroidal voronoi tessellation (cvt) within the interval [0,1], under a uniform density, using lloyd's method to compute the voronoi regions exactly.
cvt_1d_nonuniform, an Octave code which computes an n-point centroidal voronoi tessellation in 1 dimension, under a nonuniform density, and plots the evolution of the locations of the generators during the iteration;
cvt_1d_sampling, an Octave 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, an Octave 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, an Octave 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_nonuniform, an Octave code which calculates a nonuniform centroidal voronoi tessellation (cvt) over a circle.
cvt_circle_uniform, an Octave code which calculates a centroidal voronoi tessellation (cvt) over a circle with uniform density.
cvt_corn, an Octave code which studies a 2d model of the growth of a corn kernel, by treating the surface and interior biological cells as points to be organized by a centroidal voronoi tessellation (cvt) with a nonuniform density; during a sequence of growth steps, new biological cells are randomly added to the surface and interior.
cvt_ellipse_uniform, an Octave code which iteratively calculates a centroidal voronoi tessellation (cvt) over an ellipse, with a uniform density.
cvt_metric, an Octave code which computes a centroidal voronoi tessellation (cvt) under a spatially varying metric;
cvtm_1d, an Octave code which estimates a mirror-periodic centroidal voronoi tessellation (cvtm) in the periodic interval [0,1], using a version of lloyd's iteration.
cvtp, an Octave code which creates a cvtp, that is, a centroidal voronoi tessellation on a periodic domain.
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.