Computing the Discrepancy with Applicaitons to Supersampling Patterns

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.

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.