1Blurb:: 2Design of Computer Experiments - Centroidal Voronoi Tessellation 3Description:: 4The FSU Centroidal Voronoi Tessellation method (\c fsu_cvt) 5produces a set of sample points that are 6(approximately) a Centroidal Voronoi Tessellation. The primary feature of 7such a set of points is that they have good volumetric spacing; the points 8tend to arrange themselves in a pattern of cells that are roughly the 9same shape. 10 11To produce this set of points, an almost arbitrary set of 12initial points is chosen, and then an internal set of 13iterations is carried out. These iterations repeatedly replace 14the current set of sample points by an estimate 15of the centroids of the corresponding Voronoi subregions. 16\cite Du99. 17 18The user may generally ignore the details of this internal iteration. If 19control is desired, however, there are a few variables with which the user 20can influence the iteration. 21The user may specify: 22\li \ref method-fsu_cvt-max_iterations, the number of iterations carried out 23\li \ref method-fsu_cvt-num_trials, the number of secondary sample points generated to adjust the location of the primary sample points 24\li \ref method-fsu_cvt-trial_type, which controls how these secondary sample points are generated 25 26This method generates sets of uniform random variables on the 27interval [0,1]. If the user specifies lower and upper bounds for a 28variable, the [0,1] samples are mapped to the [lower, upper] interval. 29 30 31Topics:: package_fsudace, design_and_analysis_of_computer_experiments 32Examples:: 33Theory:: 34This method is designed to generate samples with the goal of low discrepancy. 35Discrepancy refers to the nonuniformity of the sample points 36within the hypercube. 37 38Discrepancy is defined as the difference between 39the actual number and the expected number of points one would expect 40in a particular set B (such as a hyper-rectangle within the unit 41hypercube), maximized over all such sets. 42Low discrepancy sequences tend to cover the 43unit hypercube reasonably uniformly. 44 45Centroidal Voronoi Tessellation 46does very well volumetrically: it spaces the points fairly 47equally throughout the space, so that the points cover the region 48and are isotropically distributed with no directional bias in the 49point placement. There are various measures of volumetric 50uniformity which take into account the distances between 51pairs of points, regularity measures, etc. 52Note that Centroidal Voronoi Tessellation does not produce low-discrepancy sequences 53in lower dimensions. The lower-dimension (such as 1-D) 54projections of Centroidal Voronoi Tessellation can have high discrepancy. 55 56Faq:: 57See_Also:: method-dace, method-fsu_quasi_mc, method-psuade_moat 58