TABLE_QUALITY
Interactive Program for
Point Dispersion Quality
TABLE_QUALITY
is a C++ program which
reads a data file contains
the coordinates of N points in an M dimensional region,
and computes some measures of the quality of dispersion
of the points.
The program assumes that the pointset lies in the unit hypercube.
However, it is easy to modify the program to handle other regions.
A single routine, named sample_routine, is required to return
sample points in the region. To handle a different region,
simply modify this routine, and rebuild the program. One other
builtin routine is already available, for sampling the unit sphere.
The unit hypercube in M dimensional space is simply the set of
all vectors whose entries are between 0 and 1. It is
a natural abstraction of the unit line segment, the unit square,
and the unit cube, and represents a very simple chunk of M
dimensional space.
The quality measures computed include:

Alpha, the minimum angle measure
(for triangulated 2D datasets only);

Beta, the standard deviation of the minimum spacing
between nodes, normalized by the average spacing;

Chi, the regularity measure;

D, the second moment determinant measure;

E, the Voronoi energy measure;

Gamma, the mesh ratio;

H, the point distribution norm;

Lambda, the COV measure;

Mu, the point distribution ratio;

Nu, the cell volume deviation;

Q, the triangle shape uniformity measure
(for triangulated 2D datasets only);

R0, the Riesz S=0 energy;

S, the sphere volume measure
(unit hypercube datasets only).

Tau, the second moment trace measure;
The program also prints:

Gamma_min, the minimum spacing between nodes;

Gamma_ave, the average spacing between nodes;

Gamma_max, the maximum spacing between nodes;

Gamma_std, the standard deviation of the spacing
between nodes;
Usage:

table_quality filename

reads the data in filename, computes the quality
measures, and prints them out.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
TABLE_QUALITY is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
DIAPHONY,
a C++ program which
reads a file of N points in M dimensions and computes its diaphony, a measure
of point dispersion.
QUALITY,
a C++ library which
makes the computations needed
by TABLE_QUALITY. To build a copy of TABLE_QUALITY,
a compiled copy of the QUALITY library must be available.
STAR_DISCREPANCY,
a C++ program which
reads a TABLE file of M points in N dimensions (presumed to lie in the
unit hypercube) and computes bounds on the star discrepancy,
a measure of dispersion, by Eric Thiemard.
TABLE_LATINIZE,
a C++ program which
can read a TABLE file
and write out a "latinized" version.
Reference:

David Field,
Qualitative Measures for Initial Meshes,
International Journal of Numerical Methods in Engineering,
Volume 47, 2000, pages 887906.

D P Hardin, Edward Saff,
Discretizing Manifolds via Minimum Energy Points,
Notices of the AMS,
Volume 51, Number 10, November 2004, pages 11861194.

PerOlof Persson, Gilbert Strang,
A Simple Mesh Generator in MATLAB,
SIAM Review,
Volume 46, Number 2, pages 329345, June 2004.

Yuki Saka, Max Gunzburger, John Burkardt,
Latinized, Improved LHS, and CVT Point Sets in Hypercubes,
International Journal of Numerical Analysis and Modeling,
Volume 4, Number 34, 2007, pages 729743,
Source Code:
Examples and Tests:
List of Routines:

MAIN is the main program for TABLE_QUALITY.
You can go up one level to
the C++ source codes.
Last revised on 31 August 2005.