While the "Bi" in "Bilinear Filtering" implied filtering over 2 dimensions, trilinear filtering's third dimension is related to blending two bilinear results! :O Crazy content
I think it's really interesting how important and often linear interpolation shows up for sampling in graphics. We use barycentric coordinates, where alpha, beta, and gamma are proportions between the three points of a triangle. We also use interpolation for bilinear filtering, where s and t are distance ratios between the four points, and then again for trilinear filtering between mipmap level results.