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
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