Blurb::
Design of Computer Experiments - Centroidal Voronoi Tessellation 
Description::
The FSU Centroidal Voronoi Tessellation method (\c fsu_cvt) 
produces a set of sample points that are 
(approximately) a Centroidal Voronoi Tessellation. The primary feature of 
such a set of points is that they have good volumetric spacing; the points 
tend to arrange themselves in a pattern of cells that are roughly the 
same shape. 

To produce this set of points, an almost arbitrary set of
initial points is chosen, and then an internal set of 
iterations is carried out. These iterations repeatedly replace 
the current set of sample points by an estimate 
of the centroids of the corresponding Voronoi subregions.
\cite Du99.

The user may generally ignore the details of this internal iteration. If 
control is desired, however, there are a few variables with which the user
can influence the iteration. 
The user may specify: 
\li \ref method-fsu_cvt-max_iterations, the number of iterations carried out
\li \ref method-fsu_cvt-num_trials, the number of secondary sample points generated to adjust the location of the primary sample points
\li \ref method-fsu_cvt-trial_type, which controls how these secondary sample points are generated

This method generates sets of uniform random variables on the 
interval [0,1]. If the user specifies lower and upper bounds for a 
variable, the [0,1] samples are mapped to the [lower, upper] interval.


Topics::	package_fsudace, design_and_analysis_of_computer_experiments
Examples::
Theory::
This method is designed to generate samples with the goal of low discrepancy.
Discrepancy refers to the nonuniformity of the sample points 
within the hypercube. 

Discrepancy is defined as the difference between 
the actual number and the expected number of points one would expect 
in a particular set B (such as a hyper-rectangle within the unit 
hypercube), maximized over all such sets. 
Low discrepancy sequences tend to cover the 
unit hypercube reasonably uniformly. 

Centroidal Voronoi Tessellation 
does very well volumetrically: it spaces the points fairly 
equally throughout the space, so that the points cover the region 
and are isotropically distributed with no directional bias in the 
point placement. There are various measures of volumetric 
uniformity which take into account the distances between 
pairs of points, regularity measures, etc. 
Note that Centroidal Voronoi Tessellation does not produce low-discrepancy sequences 
in lower dimensions. The lower-dimension (such as 1-D) 
projections of Centroidal Voronoi Tessellation can have high discrepancy. 

Faq::
See_Also::	method-dace, method-fsu_quasi_mc, method-psuade_moat
