Participating Media

Volume rendering equation
L(x, ⃗ω) = ∫ s
0 e−τ(x,x′) σ a (x′)L e (x′)dx′+
∫ s
0 e(−τ(x,x′) σ s (x′) ∫ Ω4π p(x′, ⃗ω′, ⃗ω)L i(x′, ⃗ω′)d⃗ω′dx′+
e −τ(x,x+s⃗ω) L(x + s⃗ω, ⃗ω)
where
τ(x, x′) = ∫ x′
x
σ t(t)dt
is the optical depth.
integrate over length of segment (s)
Must be numerically integrated
Costlier than rendering equation