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I'm confused on the actual definition of bilinear resampling.


Same question here... What does this series of pictures try to illustrate about bilinear sampling?


This figure illustrates the result of sampling texture maps at level 0 (highest resolution level) of the mip-map. Notice aliasing in the background due to high frequency detail.

Bilinear filtering (rather than trilinear filtering) of texel data is used to generate the value of the texture function at a given sample point.

The math of bilinear sampling (which forms part of trilinear sampling) is shown on slide 54 of this lecture.