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 built-in 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:

The program also prints:


table_quality filename


The computer code and data files described and made available on this web page are distributed under the MIT license


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.


TRIANGULATION_QUALITY, a FORTRAN90 code which can evaluate a triangulation of a given set of nodes.


  1. David Field,
    Qualitative Measures for Initial Meshes,
    International Journal of Numerical Methods in Engineering,
    Volume 47, 2000, pages 887-906.
  2. Douglas Hardin, Edward Saff,
    Discretizing Manifolds via Minimum Energy Points,
    Notices of the AMS,
    Volume 51, Number 10, November 2004, pages 1186-1194.
  3. Per-Olof Persson, Gilbert Strang,
    A Simple Mesh Generator in MATLAB,
    SIAM Review,
    Volume 46, Number 2, pages 329-345, June 2004.
  4. 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 3-4, 2007, pages 729-743,

Source Code:

Last revised on 02 September 2020.