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Does it seem that if the sample rate is low, it is not a good strategy to put the sample in the random position of sub-pixels? And if the sample rate is high it would get a better result than just putting the sample in the centers of sub-pixels...


At pretty much any sampling rate it is a good idea to do this kind of stratified sampling where you subdivide a pixel into equal regions and sample randomly in each region. The initial subdivision helps guard against bad random number pulls, which could lump samples in a single part of the pixel by chance, and the "jittering" within each subregion helps guard against aliasing which may occur at this finer level (e.g., imagine a high frequency checkerboard where sampling in the centers of each region pulls out only the whites and skips the blacks).