A Simple Layered RGB BRDF Model Xavier Granier - Wolfgang Heidrich IMAGER / University of British...

A Simple LayeredA Simple LayeredRGB BRDF ModelRGB BRDF Model

Xavier Granier - Wolfgang HeidrichIMAGER / University of British Columbia

2 IMAGER / UBCA Simple layered RGB BRDF

MotivationsMotivations

Increase the range of possible effects For graphic content creation

Work in Color Space RBG - XYZ - LMSCurrently limited to linear reflection

Convincing and simple modelNot a full simulationEffect as realistic as possible


MotivationsMotivations

Wavelength effectsInterferenceColour dispersion

Investigation Framework


OverviewOverview

Previous Work General Configuration Glossy Case Diffuse Case Results Conclusion


OverviewOverview



Uniform BRDFUniform BRDF

Phong models [Phong75,Lafortune94-97,…]Most commonly used

Simplified models [Ward92,Schlick94,…]Faster / Better for Global illumination

Micro-facet [Torrance67,Ashikhmin00,…]

Physically based [He91,Hanrahan93,…]

No wavelength dependent effects


Wavelength effectsWavelength effects

Diffraction [Stam99,Sun00,…]

InterferencesRecursive Ray-Tracing [Hirayama00-01,…]Full model [Icart99-00,…]

Fine Spectral representation RGB based BRDF Interferences + Colour dispersion


OverviewOverview



Approach Approach

Semi-transparent layerInterferences effects

Local prism configurationOne refraction index by colour componentNon-parallel layer interfacesColour dispersion

RGB colour spaceCommonly used in image production


Layer configurationLayer configuration

0

1

20n

1n

d

i

o

ir

it

tirot

Air

Layer

Support


Interference : Phase ChangeInterference : Phase Change

0

1 , nttdr

oi

Uncorrelated layers

Resulting energy from interferences trtr IIIII 2cos2

0

1 ,2 ntdr

i

Parallel layers


Color dispersion : AssumptionColor dispersion : Assumption

i o

o

i

i o


BRDF BRDF general general expressionexpression

k{r,g,b} R (reflected BRDF)

3 (RGB) lobe-like models T (transmitted BRDF)

3 (RGB) lobe-like models Ex: using Phong models

koiTkoiRkoi

koiTkoiRkoi

,,,,,,2cos2

,,,,,,


OverviewOverview



Reflected partReflected part

Phong 0,,,,e

i orkifkoiR

0n

1n

i o

ir


Transmitted partTransmitted part

Assumption No absorption Only one reflection

1,,,,,e

otio trkttkitkoiT

Transmitted term

d

i

it

tirot

kvfkvt ,1,

i

ot


Main ParametersMain Parameters

Normally r0(k) 1 (air/vacuum) Local geometric configuration : layer-normal Material properties : exponents - indices Fully determined by 4-12 parameters

2-6 Exponents (control transition smoothness)1-3 RGB refraction indices (rB rG rR)1 Layer size 0-2 Normal variation (colour dispersion)


OverviewOverview



AssumptionsAssumptions

kTkRkkTkRk dddddd 2cos2

Similar expression

kRTkTkRk 2cos2

Diffuse case Average along direction

Rd average reflected energy

No colour dispersion


Diffuse componentDiffuse component

kTkTk

dkrk ddd

1

)(4cos21 1

Phase change for orthogonal incidence

)(4 1

k

dkr

Final expression

No absorption at the interface kRkT dd 1


OverviewOverview



Diffuse componentDiffuse component

1 - 30 nm67 - 73 nm 1 - 210 nm


Layer Size ChangeLayer Size Change

1-30 nm 79-106 nm 148-200 nm

Constant normal deviation


Constant deviationConstant deviation

Parallel Interfaces Constant deviation


Size / Normal correlationSize / Normal correlation

1-10 nm 1-90 nmrR = 1.5 rG = 1.7 rB = 1.8


OverviewOverview



ConclusionConclusion

RGB ModelInterferences and colour dispersionContinuous along direction

Two modelsPhong - like for specularityDiffuse

ValidationSuch effects are possible in colour space


Future WorkFuture Work

With current modelHardware acceleration (shader)Try to fit some measured BRDF

Investigate otherIncrease accuracy / More physicalInvestigate colour spacesKeep simplicity

Multi-layer


AcknowledgementsAcknowledgements

IMAGER / University of British ColumbiaPost-doctoral position

PIMS Post-doctoral Fellowship

Wolfgang Heidrich & Lionel BastardUseful comments and support


The EndThe End


Reflected partReflected part

Phong reflection

0,,,,e

i orkifkoiR

2

10

10

5

0,11,

krr

krrkF

nvkFFkvf Fresnel term (Schlick approximation)

A Simple Layered RGB BRDF Model Xavier Granier - Wolfgang Heidrich IMAGER / University of British...

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