Computing the Discrepancy with Applications to Supersampling Patterns
David P. Dobkin, David Eppstein, Don P. Mitchell
In ACM Transactions on Graphics, 15(4), October 1996.
Abstract: Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy--how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.
@article{Dobkin:1996:CTD,
  author = {David P. Dobkin and David Eppstein and Don P. Mitchell},
  title  = {Computing the Discrepancy with Applications to Supersampling Patterns},
  journal = {ACM Transactions on Graphics},
  volume = {15},
  number = {4},
  pages = {354--376},
  month = oct,
  year = {1996},
}
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