This post explores a technique for rendering fog with varying density using volumetric primitives. The author begins by reviewing basic fog rendering principles, focusing on absorption and the Beer-Lambert Law, which describes how light loses energy passing through a medium. The simplest approach uses constant density fog, but this limits visual complexity.

By constraining fog within bounded regions like spheres, boxes, or planes, developers gain more flexibility in creating realistic atmospheric effects. Ray-primitive intersection algorithms determine how light rays pass through these volumes. The article notes that real-world fog and smoke rarely have constant density, making heterogeneous volumes more challenging to render accurately.

For heterogeneous volumes, numerical methods like ray-marching approximate the integral of density along a ray by sampling at multiple points. While flexible, this approach can cause aliasing artifacts. The author presents an alternative using radial functions - mathematical expressions that depend on distance from a center point. By finding analytic antiderivatives for different density functions like linear and quadratic, developers can calculate fog density more efficiently without sacrificing quality.