[1][2] Bilinear filtering has several weaknesses that make it an unattractive choice in many cases: using it on a full-detail texture when scaling to a very small size causes accuracy problems from missed texels, and compensating for this by using multiple mipmaps throughout the polygon leads to abrupt changes in blurriness, which is most pronounced in polygons that are steeply angled relative to the camera.
The first step in this process is to determine how big in terms of the texture the pixel in question is.
Since it uses both larger and smaller mipmaps, trilinear filtering cannot be used in places where the pixel is smaller than a texel on the original texture, because mipmaps larger than the original texture are not defined.
Bilinear filtering still works, and can be used in these situations without worrying too much about abruptness because bilinear and trilinear filtering provide the same result when the pixel size is exactly the same as the size of a texel on the appropriate mipmap.
Trilinear filtering still has weaknesses, because the pixel is still assumed to take up a square area on the texture.