CVT
Centroidal Voronoi Tessellations
CVT
is a C++ library which
creates Centroidal Voronoi Tessellation (CVT) datasets.
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.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
CVT is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
BOX_BEHNKEN,
a C++ library which
computes a BoxBehnken design,
that is, a set of arguments to sample the behavior
of a function of multiple parameters;
CCVT_BOX,
a C++ program which
computes a CVT with some points
forced to lie on the boundary.
CVT,
a dataset directory which
contains files describing a number of CVT's.
CVT_DATASET,
a C++ program which
creates a CVT dataset.
FAURE,
a C++ library which
computes Faure sequences.
GRID,
a C++ library which
computes points on a grid.
HALTON,
a C++ library which
computes Halton
sequences.
HAMMERSLEY,
a C++ library which
computes Hammersley
sequences.
HEX_GRID,
a C++ library which
computes sets of points in a 2D hexagonal grid.
IHS,
a C++ library which
computes improved Latin Hypercube datasets.
LATIN_CENTER,
a C++ library which
computes Latin square data choosing the center value.
LATIN_EDGE,
a C++ library which
computes Latin square data choosing the edge value.
LATIN_RANDOM,
a C++ library which
computes Latin square data choosing a random value in the square.
NIEDERREITER2,
a C++ library which
computes Niederreiter sequences with base 2.
NORMAL,
a C++ library which
computes elements of a
sequence of pseudorandom normally distributed values.
SOBOL,
a C++ library which
computes Sobol sequences.
UNIFORM,
a C++ library which
computes uniform random values.
VAN_DER_CORPUT,
a C++ library which
computes van der Corput sequences.
Reference:

Franz Aurenhammer,
Voronoi diagrams 
a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, pages 345405, September 1991.

Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Springer Verlag, pages 201202, 1983.

John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,
Sandia National Laboratories Technical Report SAND20020099,
February 2002.

Qiang Du, Vance Faber, Max Gunzburger,
Centroidal Voronoi Tessellations: Applications and Algorithms,
SIAM Review,
Volume 41, 1999, pages 637676.

Bennett Fox,
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, pages 362376, 1986.

John Halton,
On the efficiency of certain quasirandom sequences of points
in evaluating multidimensional integrals,
Numerische Mathematik,
Volume 2, pages 8490, 1960.

Lili Ju, Qiang Du, Max Gunzburger,
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,
Parallel Computing,
Volume 28, 2002, pages 14771500.
Source Code:
Examples and Tests:
List of Routines:

CH_CAP capitalizes a single character.

CH_EQI is true if two characters are equal, disregarding case.

CH_TO_DIGIT returns the integer value of a base 10 digit.

CVT computes a Centroidal Voronoi Tessellation.

CVT_ENERGY computes the CVT energy of a dataset.

CVT_ITERATE takes one step of the CVT iteration.

CVT_SAMPLE returns sample points.

CVT_WRITE writes a CVT dataset to a file.

DATA_READ reads generator coordinate data from a file.

DIGIT_TO_CH returns the base 10 digit character corresponding to a digit.

FIND_CLOSEST finds the nearest R point to each S point.

GET_SEED returns a random seed for the random number generator.

HALHAM_LEAP_CHECK checks LEAP for a Halton or Hammersley sequence.

HALHAM_N_CHECK checks N for a Halton or Hammersley sequence.

HALHAM_DIM_NUM_CHECK checks DIM_NUM for a Halton or Hammersley sequence.

HALHAM_SEED_CHECK checks SEED for a Halton or Hammersley sequence.

HALHAM_STEP_CHECK checks STEP for a Halton or Hammersley sequence.

HALTON_BASE_CHECK checks BASE for a Halton sequence.

I4_LOG_10 returns the whole part of the logarithm base 10 of an integer.

I4_MAX returns the maximum of two integers.

I4_MIN returns the smaller of two integers.

I4_TO_HALTON_SEQUENCE computes N elements of a leaped Halton subsequence.

I4_TO_S converts an integer to a string.

PRIME returns any of the first PRIME_MAX prime numbers.

R8_EPSILON returns the R8 round off unit.

R8_HUGE returns a "huge" R8.

R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.

R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.

R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.

RANDOM_INITIALIZE initializes the RANDOM random number generator.

S_EQI reports whether two strings are equal, ignoring case.

S_LEN_TRIM returns the length of a string to the last nonblank.

S_TO_R8 reads an R8 from a string.

S_TO_R8VEC reads an R8VEC from a string.

TIMESTAMP prints the current YMDHMS date as a time stamp.

TIMESTRING returns the current YMDHMS date as a string.

TUPLE_NEXT_FAST computes the next element of a tuple space, "fast".

USER samples points in a userspecified region with given density.
You can go up one level to
the C++ source codes.
Last revised on 10 November 2006.