In order to get the sort of images the we expect, we must prefilter the texture to remove the high frequencies that show up as artifacts in the final rendering. The prefiltering required in the undersampling case is basically a spatail integration over the extent of the sample.

We could perform this filtering while texture mapping (during rasterization), by keeping track of the area enclosed by sequential samples and performing the integration as required. However, this would be expensive. The most common solution to undersampling is to perform prefiltering prior to rendering.