That has some interesting notes on anti-aliasing:
It seems like the best solution that you’d want would be getting a sort of uniform grey that
represented the average color of the black and white lines in the right proportions. That just cannot
happen with normal uniform sampling and standard reconstruction. There is no way to force the
samples to hit the lines and hit the background with exactly the right percentages everywhere. They
land where they land, and you’re stuck with it.
One approach would be to look at small regions of the floor, and analyze how much black
and how much white are in that region, and return the appropriate grey. This technique is called
area sampling. It is very appropriate if you can choose the size of the regions wisely (such as,
the amount of the floor that all is visible in the same pixel), and if your model of the lines lends
itself to calculating the areas of the intersections of the pattern pieces with the region.
for mathematical procedural textures:
Another popular technique is known as prefiltering. In this technique, whatever function is
generating the pattern is simply not allowed to create a pattern with frequencies that are too high.
For example, the black and white strips might not be allowed to be thinner than a certain width,
and as they go back in distance they are forced to become thicker and thicker to compensate for the
shrinking in perspective.
The final popular technique is to remove the restriction that the sampling happens at a pre-
dictable, regular interval. Instead, take the same number of samples, but spray them all over the
place at random and see what they hit. This technique is called stochastic sampling, and was de-
veloped by Pixar in the mid 1980s. The idea is that if there is no way to force uniform samples
to hit the black and the white with the right percentages everywhere, just fire at random and you’ll
get something close to the right answer. You’ll never get exactly the right answer, but since there is
no pattern to your sampling, there will be no pattern to your errors either. You won’t get a Moire
pattern, but rather you’ll get a jumble of noise.
Doing antialiasing well is what separates the
men from the boys.
I think the Renderman documents are extremely informative for all areas of computer graphics in general. They really help you understand the technical aspects behind 3D software.