TABLE_QUALITY
Interactive Program for
Point Dispersion Quality

TABLE_QUALITY is an executable C++ program, using double precision arithmetic, which reads a data file containg 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:

• 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.

Related Data and Programs:

QUALITY is a C++ library of routines which is used to make the computations needed by TABLE_QUALITY. To build a copy of TABLE_QUALITY, a compiled copy of the QUALITY library must be available.

TABLE is a file format which is used for the input file.

TABLE_BORDER is a C++ program that can read a TABLE file and add zero entries corresponding to a single layer of boundary data.

TABLE_DELAUNAY is an executable C++ program that reads a file of 2d point coordinates and computes the Delaunay triangulation.

TABLE_DISCREPANCY is a C++ program that bounds the star discrepancy of a point set.

TABLE_IO is a C++ library of routines that can read or write a TABLE file.

TABLE_LATINIZE is a C++ program that can read a TABLE file and write out a "latinized" version.

TABLE_QUALITY is also available in a FORTRAN90 version and a MATLAB version.

TABLE_UNBORDER is a C++ program can be used to remove the border from a table file.

TABLE_VORONOI is a C++ program that can read a TABLE file describing a set of 2D points, and print out information describing the Voronoi diagram of those points.

Reference:

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

Source Code:

• table_quality.C, the source code.
• table_quality.csh, commands to compile, link and load the source code.

Examples and Tests:

• cvt_02_00100.txt, a set of 100 CVT points in 2D.
• cvt_02_00100_quality.txt, the quality analysis.
• cvt_07_00010.txt, a set of 10 CVT points in 7D.
• cvt_07_00010_quality.txt, the quality analysis.
• halton_02_00100.txt, a set of 100 Halton points in 2D.
• halton_02_00100_quality.txt, the quality analysis.
• degen_02_00130.txt, a set of 130 points in 2D, which involve a degenerate triangulation.
• degen_02_00130_quality.txt, the quality analysis.

List of Routines:

• MAIN is the main program for TABLE_QUALITY.

You can go up one level to the C++ source codes.