Everything on Global Illumination Xavier Granier - IMAGER/UBC

Everything onEverything onGlobal IlluminationGlobal Illumination

Xavier Granier - IMAGER/UBC

2 IMAGER /UBCEverything on Global Illumination

OverviewOverview

Introduction Radiosity Methods Stochastic Methods Conclusion


OverviewOverview

IntroductionLocal IlluminationGlobal Illumination EffectsRendering EquationLight Paths

Radiosity Methods Stochastic Methods Conclusion


Local IlluminationLocal Illumination

Equation

Example:OpenGLSimple Ray-Tracing

ll la LioxLoxL ,,,


Colour BleedingColour Bleeding

Debevec


Indirect LightingIndirect Lighting

Granier


Soft ShadowsSoft Shadows

Herf


CausticsCaustics


CausticsCaustics


Rendering Equation Rendering Equation [Kajiya86][Kajiya86]

AssumptionsLight exchange equilibrium One wavelength

Emitted energy (W.m-2.sr-1)Self emittedReflected

dsLssLsL ip ,,,,,


The Rendering Equation (2)The Rendering Equation (2)

Based on radiance value only

Sp sdsLssGssLsL ,),(,,,,

d’ds’

sdsLssGdsLi ,,,

dsLssLsL ip ,,,,,


Light Paths Light Paths [Heckbert90][Heckbert90]

Regular expression : L = light source D = diffuse reflection S = directional reflection (specular) E = view-point

,,,, sss sd

ESDL*


Diffuse assumption Diffuse assumption [Goral84][Goral84]

Independent of the direction of reflection Radiosity value (W.m-2)

New equation

sLdsLsB

,

Sdp sdsB

ssGssBsB

),(


Matrix equationMatrix equation

Matrix equation [Goral84]

Form factor

jj

jidipii BFBB ,,,

jiji

S S

jijii

ji vfdsdsssGA

Fi j

,,, ,1


Colour Bleeding Colour Bleeding


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


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]


Hierarchical Radiosity Hierarchical Radiosity [Hanrahan91][Hanrahan91]

Exchanges computed at different levels Clustering [Smith94,Silllion95,Christensen97,Willmot99]


LinksLinks

Exchange representationStored on receptor

Stored informationVisibilityForm FactorEmitter

Exchanges partitionningF,V,S


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


Push-PullPush-Pull

Energy sum on leaves

Reflection

Hierarchical update

parentsp

pfeuille II

feuilledfeuillefeuille IB ,

ifilsf

ffi

i BAA

B1


Advantages / DrawbacksAdvantages / Drawbacks

View-independent solution Deal with complex scenes Exchanges partitioning

Interactive updates [Shaw97,Drettakis97]

Memory cost (Links/Hierarchy) Only diffuse Mesh


Probabilistic MethodsProbabilistic Methods

Based on the Rendering Equation [Kajiya86]

Estimations based on samplesLight paths, rays, particles

Probabilistic PropagationMaterial property probability density function


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]


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


Bi-directionalBi-directional

[Lafortune,Veach]

N

k

d

iiip

i

l i

iilji

i

sLpN

L1 1 2 1

1, ,

,,1


Particle TracingParticle Tracing

[Walter,Jensen]

N

kkkkji xxKx

dyyxKL

1, )(,,

)(

1


Particle TracingParticle Tracing

Emission : choose p Lp x cos

PropagationSame as previous

Reconstruction : Irradiance

),(

,

xpN

nxLp

N

kkkxxK

dyyxKxI

1

)()(

1


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


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


Advantages / DrawbacksAdvantages / Drawbacks

Independent : geometry, materials High directional cases Simple Noise : slow convergence (diffuse) Dynamic case

Solution updates (moving objects)Temporal continuity


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


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)

Documents

Everything on Global Illumination Xavier Granier - IMAGER/UBC