Anisotropic filtering helps in rendering texture sharply, even at angles, whereas bi- and trilinear filtering assumes that the texture is viewed from directly above. As far as I know.
Trilinear is a square sampling method that samples four texels from each mipmap and another four that are weighted between the two mipmaps.
Anisotropic filtering is a non-square sampling method that samples either four or eight texels from up to 16 mipmaps and deals with texture distortion on angled polygons.
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