2. Volume Integration

Discretized Volume Rendering and Transmittance

Moving toward more abstract concepts, we introduce the physics of light transport in semi-transparent media, the foundational theory for Neural Radiance Fields.

The Emission-Absorption Model describes how radiance L accumulates along a ray path through a cloud of particles.

Variable Definition Role in Rendering
σ(x) Volume Density Probability of light hitting a particle at point x
c(x, d) Radiance (Color) Light emitted from point x in direction d
T(t) Transmittance Cumulative occlusion from camera to distance t
α_i Alpha (Opacity) Discretized opacity of a single ray segment

Use the simulator on the right to "paint" density into a 3D grid and observe how the transmittance curve drops as the ray passes through dense regions.