Distance & height fog

How it works

Air is never perfectly clear. Over a long enough stretch, dust and water droplets absorb and scatter part of the light coming from a distant object, and scatter some of the sky’s light toward you instead. Far mountains look paler and bluer than near ones for that reason, and painters call it aerial perspective. Fog in a shader fakes it with two numbers per pixel: how far the surface is, and how much of its light survives that distance.

The survival part follows the Beer–Lambert law: every unit of fog lets the same fraction of the light through, so the transmittance falls exponentially with distance, exp(-density * distance). The pixel then mixes from its own color toward the fog color by whatever didn’t get through. That exponential is a shaping curve: it never quite reaches full fog, and its density says how fast it closes in.

Where the distance comes from decides the stage:

• Screen-post. A full-screen pass reads the finished frame and the depth buffer, turns each pixel’s depth into a distance and fogs the whole image at once. One pass covers every material in the scene, which is why engines do it this way. Exponential fog is this version.
• Surface. Each material computes its own fog from the world position of the fragment and the camera position, at the end of its fragment shader. It needs no depth texture and works on transparent surfaces, which a depth pass misses, but every shader in the scene has to include it.

Height fog swaps the even medium for one that is thicker near the ground: the density falls exponentially with altitude, and the fog along a ray still has a closed form. It needs the world position of each pixel, so in a post pass it also needs the camera’s matrices to rebuild that position from depth.

Most engines ship distance fog, and many height fog too, in their environment settings, and they are usually the right choice. Write your own when the look has to differ: a fog color that changes with the view direction, fog that only fills a valley, or fog in a stylized pipeline where the built-in one doesn’t run.