Global Illumination

CS 319

Advanced Topics in Computer Graphics

John C. Hart

Global Illumination

Accounts for all light in a sceneTechniques• The Rendering Equation

– theoretical basis forlight transport

• Path Tracing– attempts to trace

“all rays” in a scene• Photon Mapping

– deposits light energy on surfaces for later collection

• Radiosity– balances diffuse interreflection

The Rendering Equation

I(x,x’) – intensity at x from x’

g(x,x’) – geometry term (g)• % of light from x’ that reaches x

• e.g. shadows, occlusion

e(x,x’) – emissive term (e)• light emitted by x’ toward x

• e.g. light sources

(x,x’,x’’) – reflectivity• % of light incident at x’ from x’’

reflected in the x direction

xxxxxxxxxxxx dI,egI ),(),(),(),(),(

x’

xx”

g(x,x’)

I(x,x’

)

I(x’,x”)

Describing Paths

• I = ge + gR(I)

• R() – linear integral “reflection” operator

– R(cI) = cR(I)

– R(I1 + I2) = R(I1) + R(I2)

• Solve for intensity I

– (1 – gR)I = ge

– I = (1 – gR)-1 ge

– I = ge + gRge + gRgRge + gRgRgRge + ...

2

3

32

2

2

1

1

11AA

A

AA

A

AA

A

A

A

xxxxxxxxxxxx dI,egI ),(),(),(),(),(

Reflectance Categories• L – emitter (light source)

• E – receiver (eye)

• D – diffuse

– ideal

(x,x’,x”) = (,x’,x”)

– in general includes all diffusive reflection, e.g. Phong reflectance

• S – specular

– ideal

(x,x’,x”) = (arg(x,x’) – arg(x’,x’’))

– e.g. mirrors

– also includes refraction

Paths

• OpenGLLDE

LDSE (w/mirror or env. map)I = ge + gDe (no shadows)

I = ge + gDge (shadow buffer)

• Ray tracingLDS*E

I = ge + g(Sg)*Dge• Radiosity

LD*EI = g(Dg)*e

Energy Transport

• Radiance – power per unit projected area perpendicular to the ray, per unit solid angle in the direction of the ray

– Fundamental unit of light transport

– Invariant along ray

dA

d

dA

d

dAdL

AdLdd

Add

dL

cos

2

2

L1 L2

dA1 dA2

d1d2

d21 = L1d1dA1 = L2d2dA2 = d22

d1 = dA2/r2, d2 = dA1/r2

d1 dA1 = dA1 dA2/r2 = d2 dA2

L1 = L2

Radiance Form of Rendering Equation

AdLGfLL re ),(),(),,(),(),( xxxxxx

)(coscos

)( 2 xxxx

xx

,V,G

x

x’

’

V(x,x’) – visibility term

• 1 if visible

• 0 if occluded

’

Energy Conservation

• Energy remains contant

Out – In = Emitted – Absorbed

• Global conservation

– Total energy input must equal total energy output

– Where does it go? Mostly heat

– Closed environment

• Local conservation

– Incident energy must be reflected or absorbed

– Ratio controlled by Fresnel