Fast, Arbitrary BRDF Shading for Fast, Arbitrary BRDF Shading for Low-Frequency Lighting Using Low-Frequency Lighting Using
Spherical HarmonicsSpherical Harmonics
Jan Kautz, MPI InformatikJan Kautz, MPI Informatik
Peter-Pike Sloan, Microsoft ResearchPeter-Pike Sloan, Microsoft Research
John Snyder, Microsoft ResearchJohn Snyder, Microsoft Research
Motivation –Motivation –BRDF vs. Light ComplexityBRDF vs. Light Complexity
BRDF BRDF ComplexityComplexity
LightingLighting
Phong +Phong +diffusediffuse
arbitraryarbitraryaniso. BRDFsaniso. BRDFs
pointpointlightslights
areaarealightslights ??
Motivation – Motivation – What we wantWhat we want
• What we want:What we want:• Illuminate objects with Illuminate objects with
environment mapsenvironment maps
• Use Use arbitraryarbitrary BRDFs BRDFs
• Change lighting Change lighting on-the-flyon-the-fly
• Possibly include Possibly include self-shadowing andself-shadowing andinterreflectionsinterreflections
• At real-time ratesAt real-time rates
Ph
on
gP
hon
gA
nis
otro
pic
An
isotro
pic
Related Work –Related Work –Interactive TechniquesInteractive Techniques
BRDF BRDF ComplexityComplexity
LightingLighting
PhoDiffPhoDiff
RefSpaceRefSpace
ApproxEnvApproxEnv HomEnvHomEnv
DiffSHDiffSH
FreqSpace FreqSpace
Our TechniqueOur Technique
ArbBRDFArbBRDF
PRTPRT
diffusediffuse PhongPhong isotropicisotropic anisotropicanisotropic
Phong/Diffuse Prefiltered Environment MapsPhong/Diffuse Prefiltered Environment Maps[Miller84] [Greene86] [Heidrich99][Miller84] [Greene86] [Heidrich99]Arbitrary BRDFs with Point LightsArbitrary BRDFs with Point Lights[Kautz99] [McCool01][Kautz99] [McCool01]BRDF Approximation for Environment MapsBRDF Approximation for Environment Maps[Kautz99][Kautz99]Reflection Space RenderingReflection Space Rendering[Cabral99][Cabral99]Diffuse Environment Maps using Spherical HarmonicsDiffuse Environment Maps using Spherical Harmonics[Ramamoorthi01][Ramamoorthi01]Homomorphic Factorization of Environment MapsHomomorphic Factorization of Environment Maps[Latta02][Latta02]Frequency Space Environment MappingFrequency Space Environment Mapping[Ramamoorthi02][Ramamoorthi02]Precomputed Radiance TransferPrecomputed Radiance Transfer[Sloan02][Sloan02]Our TechniqueOur Technique
point lightspoint lights
low-frequencylow-frequencyarea lightingarea lighting
high-frequencyhigh-frequencyarea lightingarea lighting
Related WorkRelated Work
• Previous use of Spherical HarmonicsPrevious use of Spherical Harmonics• [Cabral87] Bidirectional Reflection Functions [Cabral87] Bidirectional Reflection Functions
from Surface Bump Mapsfrom Surface Bump Maps
• [Westin92] Predicting Reflectance Functions [Westin92] Predicting Reflectance Functions from Complex Surfaces from Complex Surfaces
Background – Background – Spherical HarmonicsSpherical Harmonics
• Spherical Harmonics : Spherical Harmonics : • Orthonormal basis over the sphereOrthonormal basis over the sphere
• Analogous to Fourier transform over 1D circleAnalogous to Fourier transform over 1D circle
• Important properties:Important properties:• Rotational invariance Rotational invariance no aliasing artifacts no aliasing artifacts
• Projection:Projection:
• Integration:Integration:
• Rotation: linear xform on coefficientsRotation: linear xform on coefficients
sdsysff ii
)()( sdsysff ii
)()(
n
iiibasdsbsa
1
)(~)(~
n
iiibasdsbsa
1
)(~)(~
)(syi)(syi
Background –Background –Spherical HarmonicsSpherical Harmonics
• Basis functions (examples)Basis functions (examples)
i = 1i = 1 i = 2i = 2 i = 3i = 3 i = 4i = 4
i = 8i = 8 i = 12i = 12 i = 15i = 15 i = 19i = 19
Background –Background –Spherical HarmonicsSpherical Harmonics
• Example: projection of environmentExample: projection of environment
n=4n=4 n=9n=9 n=25n=25
n=26n=2622 originaloriginal
sdsfsLvL vinout
p
)()()( * sdsfsLvL v
inoutp
)()()( *
Environment Mapping + Environment Mapping + Spherical HarmonicsSpherical Harmonics
• Rendering Equation (no shadows):Rendering Equation (no shadows):
• Rewrite with Rewrite with
• Project Lighting and BRDFProject Lighting and BRDF
sdnsvsfsLvL pinout
p
)0,max(),()()( sdnsvsfsLvL p
inoutp
)0,max(),()()(
)0,max(),()(* pv nsvsfsf
)0,max(),()(* pv nsvsfsf
light function:light function:
into SHinto SH
BRDF:BRDF:
into SHinto SH
*,ivf *,ivf
iniLiniL
Evaluating the IntegralEvaluating the Integral
• The integralThe integral
becomesbecomes
• But BRDF defined in local frameBut BRDF defined in local frameRotate lighting (or BRDF) to match:Rotate lighting (or BRDF) to match:
sdsfsLvL vinout
p
)()()( * sdsfsLvL v
inoutp
)()()( *
n
iiv
ini
outp fLvL *
,)(
n
iiv
ini
outp fLvL *
,)(
n
iiv
inip
outp fLRvL *
,)(
n
iiv
inip
outp fLRvL *
,)(
pRpR
Preprocessing –Preprocessing –BRDF TextureBRDF Texture
• Project BRDF into SH:Project BRDF into SH:
• Put coefficients in texture mapPut coefficients in texture map
• Use parabolic parameterization for Use parabolic parameterization for
sdsysff iviv
)()(**
, sdsysff iviv
)()(**
,
vv
i=1i=1 i=3i=3 i=4i=4 i=5i=5 i=6i=6 i=7i=7
……
)1,0,0(v
)1,0,0(v
)0,1,0(v
)0,1,0(v
RenderingRendering
Project lightingProject lighting
……
Lookup (local )Lookup (local )*,ivf *,ivf v
v
* * = =
Rotate lighting (to local)Rotate lighting (to local)
= =
Compute integralCompute integral
sdsfsLvL vinout
p
)()()( * sdsfsLvL v
inoutp
)()()( *
per per objectobject
per per pixel/vertexpixel/vertex
ExamplesExamples
PhongPhong AnisotropicAnisotropicbrushed in Xbrushed in X
AnisotropicAnisotropicbrushed in Ybrushed in Y
Rendering – Rendering – Fixed LightFixed Light
……
* * = =
= =
Project lightingProject lighting Lookup (local )Lookup (local )*,ivf *,ivf v
v
Rotate lighting (local)Rotate lighting (local)
Compute integralCompute integral
sdsfsLvL vinout
p
)()()( * sdsfsLvL v
inoutp
)()()( *
ONCEONCE
Rendering – Rendering – Fixed ViewFixed View
……
* * = =
= =
Project lightingProject lighting Lookup (local )Lookup (local )*,ivf *,ivf v
v
Rotate BRDF (to global)Rotate BRDF (to global)
Compute integralCompute integral
sdsfsLvL vinout
p
)()()( * sdsfsLvL v
inoutp
)()()( *
ONCEONCE
ExampleExample
• Bird modelBird model
• 48K vert.48K vert.
• Measured VinylMeasured Vinyl
• FPS:FPS:• 6.04 free light/view6.04 free light/view
• 28.4 fixed light28.4 fixed light
• 128 fixed view128 fixed view
Precomputed Radiance Precomputed Radiance TransferTransfer
Without PRTWithout PRT PRT: Shadows+Interrefl.PRT: Shadows+Interrefl.SIG02: Phong onlySIG02: Phong only
[SIG02][SIG02]
Precomputed Radiance Precomputed Radiance Transfer – Transfer MatrixTransfer – Transfer Matrix
**
**
lig
hti
ng
lig
hti
ng
transfer matricestransfer matrices transferred radiancetransferred radiance
pp11
pp22
pp11
pp22
Precompute how global incident lighting Precompute how global incident lighting local incident local incident
Arbitrary BRDF with PRTArbitrary BRDF with PRT
……
* * = =
= =
Project lightingProject lighting Lookup (local )Lookup (local )*,ivf *,ivf v
v
Transfer & rotate lightTransfer & rotate light
Compute integralCompute integral
sdsfsVsLvL vpinout
p
)()()()( * sdsfsVsLvL vp
inoutp
)()()()( *
per per objectobject
per per pixel/vertexpixel/vertex* *
ExampleExample
• StanfordStanfordbuddhabuddha
• 50K vert.50K vert.
• Ashikhmin-Ashikhmin-BRDFBRDF
• FPS:FPS:• 4.05 no xfer4.05 no xfer
• 3.22 xfer3.22 xfer
• 15.6 fixed light15.6 fixed light
• 127 fixed view127 fixed view
Example 2:Example 2:PRT with different BRDFsPRT with different BRDFs
Phong [SIG02]Phong [SIG02] Measured VinylMeasured Vinyl
Results –Results –Different BRDFsDifferent BRDFs
Results –Results –Brushed Metal-PatchBrushed Metal-Patch
Anisotropic ASAnisotropic ASbrushed radiallybrushed radially
Anisotropic ASAnisotropic ASbrushed tangentallybrushed tangentally
Results – Results – Spatially Varying BRDFSpatially Varying BRDF
Varying ExponentVarying Exponent Varying Varying AnisotropyAnisotropy
Comparison of SH order Comparison of SH order vs. Glossinessvs. Glossiness
ConclusionsConclusions
Pros:Pros:
• Fast, arbitrary dynamic lightingFast, arbitrary dynamic lighting
• Works for Works for arbitraryarbitrary BRDFs BRDFs
• Combined with PRT: includes Combined with PRT: includes shadows and interreflectionsshadows and interreflections
Cons:Cons:
• Works only for low-frequency Works only for low-frequency lightinglighting
• Not real-time (yet)Not real-time (yet)
Thank you!Thank you!
Questions?Questions?
Please visit us at Please visit us at www.mpi-sb.mpg.dewww.mpi-sb.mpg.de
