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                        psa - Point Set Analysis

A tool for the analysis of two-dimensional point sets with applications in


psa is a command line tool that takes two-dimensional point sets as input
and analyzes these point sets with respect to several spatial and spectral
statistics important for sampling problems in computer graphics. These 
statistics include:

- Global minimum distance (smallest separation between any two points)
- Average minimum distance (average nearest-neighbor distance)
- Bond-orientational order (similarity to the hexagonal lattice)
- Effective Nyquist frequency (equivalent to Nyq. freq. in uniform sampling)
- Oscillations (metric for potential aliasing caused by the point set)

- Radial power spectrum
- Radial distribution function
- Anisotropy
- Fourier amplitude/power spectrum

For more information regarding these measures, consult our papers:

  Daniel Heck, Thomas Schl\"omer, Oliver Deussen:
  Blue Noise Sampling with Controlled Aliasing.
  ACM Trans. Graph., 32(3):25:1-25:12, 2013.

  Thomas Schl\"omer, Oliver Deussen:
  Accurate Spectral Analysis of Two-Dimensional Point Sets.
  Journal of Graphics, GPU, and Game Tools, 15:3, 152-160, 2011.

The latest version of psa can always be found at
Any suggestions regarding the concepts or the implementation of psa are very
welcome. Feel free to contact us via


- cairo ( for PDF and PNG output
- CGAL ( for the bond-orientational order

The CGAL dependency is not strict and can be removed by setting HAVE_CGAL to 0
in the accompanying Makefile. The computation of the bond-orientational order
is then omitted. psa also makes use of OpenMP if available.



  ./psa filename [options]

to analyze the given file(s). When called without any parameters, psa
generates a single PDF containing all measures. Use --avg if you want to
average all measures over the given files, e.g.

  ./psa --avg points/mypoints*.txt


  ./psa --help

for a list of available options.

                                File Formats

Point set files are supported in three flavors:

- TXT: plain text files with a pair of coordinates for each point
- RPS: raw single-precision floating point data
- EPS: coordinate pairs for each point with a basic EPS header that is
       understood by most EPS viewers

An example for each format is included in /points. Use --convert to convert
files between the three formats. Note that psa cannot read arbitrary EPS

                       License and Acknowledgements

psa is free software and published under the GNU GPL. For further information
see the file COPYING. This software has been partially funded by DFG, German
Research Foundation, and the PhD Program 'Explorative Analysis and
Visualization of Large Information Spaces'.

Copyright (C) 2011-2015
  Thomas Schl\"omer
  Daniel Heck

                              Version History
- Fixed some Linux/gcc compile issues

- Made oscillations metric independent of effective Nyquist frequency; the metric is now in line with the upcoming ACM TOG paper

- psa has been totally rewritten
- Added new statistics: effective Nyquist frequency, oscillations metric, and
  orientational order (the latter needs CGAL)
- Added new 1D measure next to radial power spectrum and anisotropy: radial
  distribution function
- Added option --raw to write the raw data of all 1D measures for better
  post-processing using external tools
- 1D measures are now written as TEX source files based on the TIKZ package
  for cleaner integration into larger documents and potential final touches
- Added options to generate every measure separately
- Added configuration file 'common/psa.cfg' for most important variables
- Can now directly read points from certain EPS files next to TXT and RPS
- Added option --convert to convert points between these formats
- Dropped need for fftw-library
- Dropped computation of star discrepancy

- Added average mindist measure
- Removed non-toroidal distance measure
- Normalized radius is now called normalized mindist
- Changed default plot colors to black
- Improved code readability

- Bug fixes with respect to cairo version >1.10.0
- Fixed some MS VS compilation issues

- Integrated an optional DFT using the fftw-library
- Non-spectral measurements are now also rendered into summary files
- Added non-toroidal minimum distance computation
- Support for more arbitrarily many point sets in a single directory
- Bug fixes

- Initial release