# xkcd’s cloud viewer, binocular vision and telestereoscopes

A recent xkcd comic illustrated a really neat idea: enhancing binocular vision artificially to view distant objects in “true” 3d. Binocular disparity, the mismatch between the position of objects between the two eyes, is a particularly strong 3d cue. It’s  really only well useful for objects which are physically close to the observer.

You can show using projective geometry that the relative disparity between two objects, where the first is at depth z, the second $\Delta$ behind that,  is proportional to $\frac{d\Delta}{z(z+\Delta)}$, where d is the distance between the eyes. Mike Langer has relevant lecture notes on this subject if you’re interested. So disparity diminishes as the square of distance, and things like clouds appear flat in part because they’re so far away. You have to take advantage of other (monocular) cues to get a sense of depth from far away objects: parallax, lighting, size, occlusion, etc.