Participating Media

Participating Media
Valerie Szudziejka

Outline
Light scattering
The volume rendering equation
Phase functions
Ray marching
Rendering specifics

Light scattering
Photon can continue through medium
unaffected
Or can be out-scattered (out of path of
light ray) or absorbed - reduced radiance
Or can be in-scattered (into path of light
ray) or medium can emit more light -
increased radiance

Light scattering
Reduced radiance due to out-scattering:
(⃗ω · ∇)L(x, ⃗ω) = −σ s (x)L(x, ⃗ω)
Reduced radiance due to absorption:
(⃗ω · ∇)L(x, ⃗ω) = −σ a (x)L(x, ⃗ω)

Light scattering
Increased radiance due to in-scattering:
(⃗ω · ∇)L(x, ⃗ω) = σ s (x) ∫ Ω4π p(x, ⃗ω′, ⃗ω)L i(x, ⃗ω′)d⃗ω′
integrate over all directions on a sphere
(surface area)
Increased radiance due to emission:
(⃗ω · ∇)L(x, ⃗ω) = σ a (x)L e (x, ⃗ω)

Light scattering
Change in radiance:
emission - out-scattering - absorption + inscattering
(⃗ω · ∇)L(x, ⃗ω) = σ a (x)L e (x, ⃗ω) − σ t (x)L(x, ⃗ω) + σ s (x) ∫ Ω4π p(x
x)L e (x, ⃗ω) − σ t (x)L(x, ⃗ω) + σ s (x) ∫ Ω4π p(x, ⃗ω′, ⃗ω)L i(x, ⃗ω′)d⃗ω′
where
σ t = σ s + σ a
is the extinction coefficient.

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

Phase functions
∫
Ω4π
p(x, ⃗ω′, ⃗ω)d⃗ω = 1
similar to BRDF - but unitless and
normalized

Phase Functions
anisotropic scattering: preferential
scattering direction
isotropic: no preference
anisotropic medium: phase function
depends on orientation of medium
isotropic: no dependence

Isotropic Phase function
scattering completely random
p(θ) = 1
4π

Raleigh Scattering
p(θ) = 3
16π (1 + cos2 θ)
shorter wavelengths scattered more
for particles smaller than a wavelength of
light
why the sky is blue

Henyey-Greenstein
p(θ) =
1−g 2
4π(1+g 2 −2g cos θ) 1.5
g in (-1, 1)
g < 0: backward scattering
g > 0: forward scattering
g = 0: isotropic scattering

Henyey-Greenstein
ellipsoid-shaped scattering
larger g = more preferential scattering
costly 1.5 exponent

Schlick Phase Function
accurate shape of phase function not so
important
use equation of ellipse to approximate
Henyey-Greenstein
p(θ) =
1−k 2
4π(1+k cos θ) 2
k is similar to g in Henyey-Greenstein

Ray marching
Solves volume rendering equation
Uniform steps through medium, making
local simplifications
Multiple scattering simulation can be
done with photon map
Multiple scattering needed for such things
as clouds

Adaptive ray marching
Better for non-homogeneous media -
change in extinction coefficient
Varies length of step size on the fly
Ideally little change of extinction
coefficient & density (albedo) within a
step

Photon Tracing
Requires photon map for participating
media and subsurface scattering
Volume (rather than surface) photon map
Exclude photons coming directly from
light source (separate out direct
illumination)

Rendering Fire
Emits light
Fluid flow equations
Bright enough for the eye to adapt to its
color

Rendering Smoke
Uses fluid flow equations
Random perturbation of the flow field to
simulate curling
Ideally won’t look alive & growing but
passive & natural

Rendering Volume Caustics
form in participating media

glass sphere, fog medium

Rendering Wet Materials
Can look darker, brighter, or more
specular
Primarily due to subsurface scattering
Two interactions: air-water and watersurface

Rendering Translucent Material
Can be estimated with diffuse lighting but
looks coarse and fake
Subsurface scattering looks much better
Pretty much same algorithm as for
participating media

Skim milk, whole milk, diffuse milk

References
Jensen:
Realistic Image Synthesis Using Photon Mapping
Rendering of Wet Materials
Visual Simulation of Smoke
Physically based Modeling and Animation of Fire
ATI:
Rendering Outdoor Light Scattering in Real Time