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.

This technical report has been published as

Computing the Discrepancy with Applicaitons to Supersampling Patterns. David P. Dobkin, David Eppstein, Don P. Mitchell, ACM TOGS vol. 15, no. 4, 354-376, October 1996.