Limitations
Bilinear filtering is rather accurate until the scaling of the texture gets below half or above double the original size of the texture - that is, if the texture was 256 pixels in each direction, scaling it to below 128 or above 512 pixels can make the texture look bad, because of missing pixels or too much smoothness. Often, mipmapping is used to provide a scaled-down version of the texture for better performance; however, the transition between two differently-sized mipmaps on a texture in perspective using bilinear filtering can be very abrupt. Trilinear filtering, though somewhat more complex, can make this transition smooth throughout.
For a quick demonstration of how a texel can be missing from a filtered texture, here's a list of numbers representing the centers of boxes from an 8-texel-wide texture (in red and black), intermingled with the numbers from the centers of boxes from a 3-texel-wide down-sampled texture (in blue). The red numbers represent texels that would not be used in calculating the 3-texel texture at all.
0.0625, 0.1667, 0.1875, 0.3125, 0.4375, 0.5000, 0.5625, 0.6875, 0.8125, 0.8333, 0.9375
Read more about this topic: Bilinear Filtering
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