Couldn't we also say something similar for garden variety bi- or trilinear then?
Absolutely. It's just a tradeoff of complexity VS quality. In the Lance Williams paper that introduced MIP mapping and "trilinear" (amongst other things), Williams does point out the compromises made to the quality in order to achieve speed.
I'm trying to understand what you mean here: if a signal (texture) has been correctly prefiltered and if the mip map selection scheme is also correctly implemented then AF shouldn't be regarded as an AA process, right?
IMHO, AA is either preventing high-frequency data, that cannot be represented in a sampled represenation of a signal, causing incorrect results in that sampled represention (or at least masking them so that they are not distracting
). I would therefore feel that filtering of the input signal counts as a valid (in fact, the best) technique. However, completely correct signak filtering is exceedingly difficult. AF is of course implementation dependent, but let's assume we are talking about a "fast" method that builds on top of (predetermined) pre-filtering techniques.
The "correct" pre-filtering for a
particular MIP level will assume a fixed projection. Generally this will have equal, power of 2 compression in X and Y. Furthermore, it
might only use a simple Box filter which does not correctly pre-filter the data. Of course, Fourier analysis can be used to do correct generation of the smaller maps but it is more expensive.
The problem then lies in the fact that the sample region of the texture that corresponds to the pixel is going to be vaguely elliptical or, better, a distorted Gaussian. This means that we have to approximate this sample region by constructing it from the smaller building blocks available in the MIP levels. If you don't do this correctly, you will still end up with illegally high frequencies creeping in and ruining the result. In this sense, I feel completely justified in saying it is AA.