Spherical Harmonic Lighting of Spherical Harmonic Lighting of Wavelength-dependent Wavelength-dependent PhenomenaPhenomenaClifford Lindsay, Emmanuel AguClifford Lindsay, Emmanuel AguWorcester Polytechnic Institute Worcester Polytechnic Institute (USA)(USA)

Introduction

Modeling of Light Interference As A BRDFModeling of Light Interference As A BRDF

Compactly Store Surface Response and Compactly Store Surface Response and Hemispheric Light Contribution In Terms Of Hemispheric Light Contribution In Terms Of Spherical Harmonic CoefficientsSpherical Harmonic Coefficients

Evaluation of Light And Reflection Is Done on GPUEvaluation of Light And Reflection Is Done on GPU

Working With Spectral Color Space Instead of RGBWorking With Spectral Color Space Instead of RGB

Spherical Harmonics

xBcN

iii

1

,mly

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jjiji xyxf

Nc

1

4

We can then use We can then use these coefficients to these coefficients to reconstruct an reconstruct an approximation to the approximation to the original signaloriginal signal

We can use spherical We can use spherical harmonics to approximate the harmonics to approximate the original, where original, where ccii is a vector of is a vector of SH coefficientSH coefficient

Spherical harmonics is a set of Spherical harmonics is a set of basis functions defined in basis functions defined in spherical coordinatesspherical coordinates

InterferenceInterferenceFactors that Affect Light InterferenceFactors that Affect Light Interference::

Refractive index and thickness of the thin filmRefractive index and thickness of the thin film Refractive indices of the media 1 & 2Refractive indices of the media 1 & 2 Incident Angle Incident Angle and incident SPD (Spectral Power and incident SPD (Spectral Power

Distribution)Distribution)

Spectral BRDFSpectral BRDF

Just Like Regular BRDFs (but different)Just Like Regular BRDFs (but different) Rendering equationRendering equation Function of 4 angles (incident, reflection)Function of 4 angles (incident, reflection) ConservativeConservative

What’s Different?What’s Different? Different Color InteractionDifferent Color Interaction Different Material InteractionDifferent Material Interaction Different Viewer Interaction (non-reciprocalDifferent Viewer Interaction (non-reciprocal))

)cos2(sin),(4),( 2t

sf wRsf

Previous Work in S.H.Previous Work in S.H.

Diffuse Reflection Maps, Hanrahan, Ramamoorthi, 2001Diffuse Reflection Maps, Hanrahan, Ramamoorthi, 2001

Physically Based BRDFs, Westin 1992Physically Based BRDFs, Westin 1992

Isotropic BRDFs with SH Maps, Hanrahan, Ramamoorthi, 2002Isotropic BRDFs with SH Maps, Hanrahan, Ramamoorthi, 2002

Arbitrary BRDFs, Kautz et al, 2002Arbitrary BRDFs, Kautz et al, 2002

Radiance Transfer, Glossy Surfaces, Self-shadow, Radiance Transfer, Glossy Surfaces, Self-shadow, and Interreflection, Sloan et al, 2002and Interreflection, Sloan et al, 2002

Our ApproachOur Approach

Two Stage ApproachTwo Stage Approach::1. Pre-computation1. Pre-computation

2. Render2. Render

is LL

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0),(

2

0

n

iii fL

Pre-computation

V

ini

n

cc

ccsf

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0,0,0

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Total Light Contribution:Total Light Contribution:

BRDF Response:BRDF Response: Texture map based all possible view vectorsTexture map based all possible view vectors

i

s

L

LL

0

Set of coefficients approximating total light contributionSet of coefficients approximating total light contribution

GPU

V,T,BV,T,B

Vertex Processor

Fragment Processor

Texture Map, Texture Map, ffii

2

0

n

iii fLUniform Var, Li

Rendering:Rendering:

Index Texture Map Based on view Index Texture Map Based on view VV

Summing the coefficients for Summing the coefficients for final contributionfinal contribution

Add ambient, diffuse, Fresnel Add ambient, diffuse, Fresnel for additional realismfor additional realism

ConclusionConclusion

Real-time rendering of complex materials Real-time rendering of complex materials previously available to offline renderers (ray previously available to offline renderers (ray tracers)tracers)

Data and Data structures that are GPU friendlyData and Data structures that are GPU friendly

Evaluation of Spherical Harmonics is a linear Evaluation of Spherical Harmonics is a linear operationoperation

Increased realism with Image Based Lighting and Increased realism with Image Based Lighting and accurate BRDFs with GPU accelerationaccurate BRDFs with GPU acceleration

Results