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",
   year = "1996",
   month = oct,
   volume = "15",
   number = "4",
   pages = "354--376"
}