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Fog rendering

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Nicholas Chapman

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Fog rendering is a March 2026 technical note by Nicholas Chapman on Forward Scattering deriving classic fog blending and exponential height fog from volumetric transport.

It starts from a participating-media integral with constant incoming radiance, shows how transmittance yields a lerp between fog color and surface color when the scattering-to-extinction ratio is constant, then derives optical depth for extinction that falls off exponentially with height, including the horizontal-ray case.

It is for intermediate to advanced graphics programmers implementing height fog or reviewing why simple fog lerps are justified under stated assumptions.

The page is a free self-contained math write-up with before/after fog images and closed-form expressions.

It is useful when you need exponential height-fog transmittance formulas without digging through engine source.