Volume Rendering

Volumetric rendering is an algorithm used for rendering radiance fields such as [[NeRFs]] and [[3D Gaussian Splats]] 1 2 . You start with some implicit or explicit scene representation that can be sampled at 3D positions along a ray in a scene, to return a color, $c$, and an opacity $\alpha$. $$ C = \sum_{i=1}^{N} T_i \alpha_i c_i ~\text{ where } T_i = \prod_{j=1}^{i-1} (1 - \alpha_i) $$ The…