For each pixel on the display, you derive a (not necessarily integer) pixel coordinate on the original image. The top-left display pixel may be at (0, 0) on the image. The next pixel to the right is at (0, 0.333) on the image.
So say you're dealing with the pixel at (0, 1.333). You take the pixels at (0, 0), (0, 1), (0, 2), and (0, 3), and you run a cubic interpolation to find the value at 1.333. (You do this three times, for red, green, and blue).
If you're at non-integer coordinates in both directions, then you run an interpolation that is cubic in both directions (that is, a bi-cubic interpolation).
So say you're dealing with the pixel at (0, 1.333). You take the pixels at (0, 0), (0, 1), (0, 2), and (0, 3), and you run a cubic interpolation to find the value at 1.333. (You do this three times, for red, green, and blue).
If you're at non-integer coordinates in both directions, then you run an interpolation that is cubic in both directions (that is, a bi-cubic interpolation).