Ray differentials estimate how much of a pixel's footprint overlaps SDF geometry to produce smooth antialiased edges

Standard raymarching fires one ray per pixel, producing aliased (jagged) edges at geometry boundaries. Ray differentials track how the ray varies across the pixel, letting the marcher estimate how much of the pixel’s footprint (its frustum) approximately intersects the surface at each step. Since the SDF gives the distance to the nearest surface at each step, this is used to compute partial coverage per near-intersection, which is then composited front-to-back to give a smooth image without edge pixelization. This is more expensive than single-ray marching but cheaper than heavy supersampling. IQ demonstrated the technique in ‘Antialias, sort of’ (2014).

Examples

At each march step near an edge, use the ray differential to estimate pixel-footprint size, compare it with the SDF value (remaining distance), and blend partial coverage when the footprint is comparable to the distance to the surface.

Assessment

Explain what information ray differentials provide that a single ray does not, and describe how it is used to compute partial pixel coverage in a raymarched scene.