What would happen if d is negative?
When the texture is smaller than the image, which I think would be the most common case, won't L be smaller than 1?
Presumably, if d is negative, we should sample at level 0 since we don't have a higher-res layer to sample from. (Unless it's common to have negative-level maps to support higher resolutions for close viewing distances?)
It seems like L should only be smaller than 1 if the triangle being mapped onto is both mostly parallel to and very close to the near side of the frustum (since L is the distance, in pixels on the level 0 map, between sample points), so with a texture of appropriate resolution on a triangle viewed from a reasonable distance it seems like this shouldn't be an issue in most cases.
Just to clarify, the du/dx and dv/dx on the right picture have nothing to do with the du/dx and dv/dx on the left, correct?
Nevertheless, we are taking max between the stretching out Lx and Ly, why are they different and why are we taking the max but not the min. Don't we overstretch the other one when we take the max?