CVT\
Centroidal Voronoi Tessellations {#cvt-centroidal-voronoi-tessellations align=”center”}
================================
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: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
CVT is available in a C++ version and
a FORTRAN90 version and a MATLAB
version.
BOX_BEHNKEN, a C++
library which computes a Box-Behnken 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: {#reference align=”center”}
- Franz Aurenhammer,\
Voronoi diagrams - a study of a fundamental geometric data
structure,\
ACM Computing Surveys,\
Volume 23, Number 3, pages 345-405, September 1991.
- Paul Bratley, Bennett Fox, Linus Schrage,\
A Guide to Simulation,\
Springer Verlag, pages 201-202, 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 SAND2002-0099,\
February 2002.
- Qiang Du, Vance Faber, Max Gunzburger,\
Centroidal Voronoi Tessellations: Applications and Algorithms,\
SIAM Review,\
Volume 41, 1999, pages 637-676.
- Bennett Fox,\
Algorithm 647:\
Implementation and Relative Efficiency of Quasirandom Sequence
Generators,\
ACM Transactions on Mathematical Software,\
Volume 12, Number 4, pages 362-376, 1986.
- John Halton,\
On the efficiency of certain quasi-random sequences of points in
evaluating multi-dimensional integrals,\
Numerische Mathematik,\
Volume 2, pages 84-90, 1960.
- Lili Ju, Qiang Du, Max Gunzburger,\
Probabilistic methods for centroidal Voronoi tessellations and their
parallel implementations,\
Parallel Computing,\
Volume 28, 2002, pages 1477-1500.
Source Code: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
List of Routines: {#list-of-routines align=”center”}
- 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 user-specified region with given
density.
You can go up one level to the C++ source codes.
Last revised on 10 November 2006.