I looked at this and though of supersampling AA (yes I remembered it from video games) and read some descriptions of it. It turns out that we can supersample them with different patterns. The sampling points can be either uniformly distributed, randomly distributed, ...etc. In practice, how do we decide which pattern to use? Do we simply choose the one with the best visual fidelity?
I think random sampling is sometimes used because it can decrease artifacts like Moiré patterns
@hanliny We'll talk a bunch about sampling patterns (stratification, QMC, ...) in our lecture on variance reduction. For patterns used in rasterization engines, where you usually want to use a fixed sampling (for performance) there are lots of possibilities with funky names: N-queens, quincunx, N-rooks, etc., and Googling those terms will bring up some interesting stuff. As for which is the best it really depends on what you're trying to rasterize; for instance, a pattern that is great for hard edges might not be so good for high-frequency textures and so on.
@HelloWorld Yes, random sampling is in some sense "safe" because it avoids the adversarial worst case. I.e., if I know what your sampling pattern is ahead of time, then I can construct a signal that is very badly sampled (i.e., aliased) by your pattern. But if you sample randomly, the expected signal will look pretty good. On the flip side, random sampling only starts to work well for a large number of samples; if I randomly pick just one or two or three sample locations, then what I get is a crappy sampling pattern! :-). (For instance, all my sample points could land very close to each other.)