table_quality
table_quality,
a FORTRAN90 code which
reads a data file containing
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:

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;

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
where

filename is the name of the file containing the point coordinates.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
table_quality is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
DIAPHONY,
a FORTRAN90 code which
reads a file of N points in M dimensions and computes its diaphony, a measure
of point dispersion.
QUALITY,
a FORTRAN90 code which
supplies the routines that compute the
quality measures needed by TABLE_QUALITY.
table_quality_test
TRIANGULATION_QUALITY,
a FORTRAN90 code which
can evaluate a triangulation of a given set of nodes.
Reference:

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

Douglas 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:
Last revised on 02 September 2020.