Post on 21-Dec-2015
Everything onEverything onGlobal IlluminationGlobal Illumination
Xavier Granier - IMAGER/UBC
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OverviewOverview
Introduction Radiosity Methods Stochastic Methods Conclusion
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OverviewOverview
IntroductionLocal IlluminationGlobal Illumination EffectsRendering EquationLight Paths
Radiosity Methods Stochastic Methods Conclusion
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Local IlluminationLocal Illumination
Equation
Example:OpenGLSimple Ray-Tracing
ll la LioxLoxL ,,,
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Colour BleedingColour Bleeding
Debevec
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Indirect LightingIndirect Lighting
Granier
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Soft ShadowsSoft Shadows
Herf
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CausticsCaustics
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CausticsCaustics
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Rendering Equation Rendering Equation [Kajiya86][Kajiya86]
AssumptionsLight exchange equilibrium One wavelength
Emitted energy (W.m-2.sr-1)Self emittedReflected
dsLssLsL ip ,,,,,
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The Rendering Equation (2)The Rendering Equation (2)
Based on radiance value only
Sp sdsLssGssLsL ,),(,,,,
d’ds’
sdsLssGdsLi ,,,
dsLssLsL ip ,,,,,
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Light Paths Light Paths [Heckbert90][Heckbert90]
Regular expression : L = light source D = diffuse reflection S = directional reflection (specular) E = view-point
,,,, sss sd
ESDL*
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Diffuse assumption Diffuse assumption [Goral84][Goral84]
Independent of the direction of reflection Radiosity value (W.m-2)
New equation
sLdsLsB
,
Sdp sdsB
ssGssBsB
),(
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Matrix equationMatrix equation
Matrix equation [Goral84]
Form factor
jj
jidipii BFBB ,,,
jiji
S S
jijii
ji vfdsdsssGA
Fi j
,,, ,1
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Colour Bleeding Colour Bleeding
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GatheringGathering
Solve as an Ax=bMB = Bp
Jacobi Bi
(k+1) = Bpi – ji Mij Bj(k)
Gauss-Siedel Bi = Bpi – ji Mij Bj
np
p
p
nnnnn
n
n
B
B
B
B
B
B
FF
FF
FF
2
1
2
1
21
22212
11121
1
1
1
Bi
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Shooting/ProgressiveShooting/Progressive
Progressive refinement Distribute extra radiosity Bi
Bj(k+1) = Bj
(k) + jFji Bi
Extra “unshot” radiosityBi = Bj
(k) – Bj(k-1)
Energy starts at emitters Distributes “progressively” Ambiant term
Bi
[Cohen]
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Hierarchical Radiosity Hierarchical Radiosity [Hanrahan91][Hanrahan91]
Exchanges computed at different levels Clustering [Smith94,Silllion95,Christensen97,Willmot99]
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LinksLinks
Exchange representationStored on receptor
Stored informationVisibilityForm FactorEmitter
Exchanges partitionningF,V,S
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One IterationOne Iteration
RefinementLink Creation at “correct level”Visibility and Form factor computation
Energy transferFor each link
IRS = FRSVRSBS
Push-pull Hierarchical update
IRS
IR = IR + IRS
S
R
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Push-PullPush-Pull
Energy sum on leaves
Reflection
Hierarchical update
parentsp
pfeuille II
feuilledfeuillefeuille IB ,
ifilsf
ffi
i BAA
B1
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Advantages / DrawbacksAdvantages / Drawbacks
View-independent solution Deal with complex scenes Exchanges partitioning
Interactive updates [Shaw97,Drettakis97]
Memory cost (Links/Hierarchy) Only diffuse Mesh
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Probabilistic MethodsProbabilistic Methods
Based on the Rendering Equation [Kajiya86]
Estimations based on samplesLight paths, rays, particles
Probabilistic PropagationMaterial property probability density function
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From a viewpointFrom a viewpoint
N
k
d
iiip
i
l i
iiilji
i
sLp
n
NL
1 1 2 1
11, ,
,,1
[Kaj86, Shi90]
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PropagationPropagation
Choose p x cos Russian Roullette
Propability of non-reflection p(0)If(Ran#< p(0)) then stopElse reflect in direction ’ using p
)(
,,
p
nx
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Bi-directionalBi-directional
[Lafortune,Veach]
N
k
d
iiip
i
l i
iilji
i
sLpN
L1 1 2 1
1, ,
,,1
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Particle TracingParticle Tracing
[Walter,Jensen]
N
kkkkji xxKx
dyyxKL
1, )(,,
)(
1
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Particle TracingParticle Tracing
Emission : choose p Lp x cos
PropagationSame as previous
Reconstruction : Irradiance
),(
,
xpN
nxLp
N
kkkxxK
dyyxKxI
1
)()(
1
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Photon Map [Jensen]Photon Map [Jensen]
Photon generation stageEmit photons on light sourcesRandom walk (trace photons through scene)Store interactions (position x, power phi, …)
Rendering : Modified distribution ray tracingApproximate radiance by density estimationQuery k nearest photonsRadiance = sumOfEnergies/coveredArea
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Photon Map [Jensen]Photon Map [Jensen]
Separate particle emissionDiffuseCaustics
BSP-tree storage Efficient particule representation Simple Kernel (n=1-Cone n=2-Epanechnikov)
1,0)1( xxxKn
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Advantages / DrawbacksAdvantages / Drawbacks
Independent : geometry, materials High directional cases Simple Noise : slow convergence (diffuse) Dynamic case
Solution updates (moving objects)Temporal continuity
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BiblioBiblio
http://www.helios32.com/resources.htm Stochastic method
Bidirectionnal (Lafortune-Veach)Particle Tracing (Walter)Photon Map (Siggraph course 2001, book)
Radiosity MethodSillion/Puech Book
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SoftwareSoftware
http://radsite.lbl.gov/radiance/HOME.html http://www.cs.kuleuven.ac.be/cwis/
research/graphics/RENDERPARK/ blender (radiosity)/povray(photon-map) http://www.mentalimages.com/p101.html
Mental Ray (Maya)