Fast, Arbitrary BRDF Shading for Low-Frequency Lighting Using Spherical Harmonics

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Fast, Arbitrary BRDF Shading for Low-Frequency
Lighting Using Spherical Harmonics

• Jan Kautz, MPI Informatik
• Peter-Pike Sloan, Microsoft Research
• John Snyder, Microsoft Research

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Motivation BRDF vs. Light Complexity
Lighting
?
arealights
pointlights
BRDF Complexity
Phong diffuse
arbitraryaniso. BRDFs
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Motivation What we want

• What we want
• Illuminate objects with environment maps
• Use arbitrary BRDFs
• Change lighting on-the-fly
• Possibly include self-shadowing
  andinterreflections
• At real-time rates

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Related Work Interactive Techniques
Lighting
high-frequencyarea lighting
low-frequencyarea lighting
BRDF Complexity
point lights
diffuse
Phong
isotropic
anisotropic
Phong/Diffuse Prefiltered Environment
MapsMiller84 Greene86 Heidrich99
Arbitrary BRDFs with Point LightsKautz99
McCool01
BRDF Approximation for Environment MapsKautz99
Reflection Space RenderingCabral99
Diffuse Environment Maps using Spherical
HarmonicsRamamoorthi01
Homomorphic Factorization of Environment
MapsLatta02
Frequency Space Environment MappingRamamoorthi02

Precomputed Radiance TransferSloan02
Our Technique
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Related Work

• Previous use of Spherical Harmonics
• Cabral87 Bidirectional Reflection Functions
  from Surface Bump Maps
• Westin92 Predicting Reflectance Functions from
  Complex Surfaces

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Background Spherical Harmonics

• Spherical Harmonics
• Orthonormal basis over the sphere
• Analogous to Fourier transform over 1D circle
• Important properties
• Rotational invariance ? no aliasing artifacts
• Projection
• Integration
• Rotation linear xform on coefficients

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Background Spherical Harmonics

• Basis functions (examples)

i 1
i 2
i 3
i 4
i 8
i 12
i 15
i 19
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Background Spherical Harmonics

• Example projection of environment

n4
n9
n25
n262
original
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Environment Mapping Spherical Harmonics

• Rendering Equation (no shadows)
• Rewrite with
• Project Lighting and BRDF

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Evaluating the Integral

• The integralbecomes
• But BRDF defined in local frameRotate lighting
  (or BRDF) to match

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Preprocessing BRDF Texture

• Project BRDF into SH
• Put coefficients in texture map
• Use parabolic parameterization for

i1
i3
i4
i5
i6
i7
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Rendering
Project lighting
per object
per pixel/vertex
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Examples
Phong
Anisotropicbrushed in X
Anisotropicbrushed in Y
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Rendering Fixed Light
Project lighting
ONCE
Rotate lighting (local)
Compute integral
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Rendering Fixed View
Project lighting
Rotate BRDF (to global)


ONCE
Compute integral
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Example

• Bird model
• 48K vert.
• Measured Vinyl
• FPS
• 6.04 free light/view
• 28.4 fixed light
• 128 fixed view

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Precomputed Radiance Transfer
SIG02
Without PRT
PRT ShadowsInterrefl.SIG02 Phong only
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Precomputed Radiance Transfer Transfer Matrix
Precompute how global incident lighting ? local
incident

p1
p1
lighting
p2
p2

transfer matrices
transferred radiance
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Arbitrary BRDF with PRT
Project lighting
per object
Transfer rotate light
per pixel/vertex



Compute integral
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Example

• Stanfordbuddha
• 50K vert.
• Ashikhmin-BRDF
• FPS
• 4.05 no xfer
• 3.22 xfer
• 15.6 fixed light
• 127 fixed view

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Example 2PRT with different BRDFs

Measured Vinyl
Phong SIG02
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Results Different BRDFs

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Results Brushed Metal-Patch

Anisotropic ASbrushed radially
Anisotropic ASbrushed tangentally
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Results Spatially Varying BRDF
Varying Exponent
Varying Anisotropy
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Comparison of SH order vs. Glossiness
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Conclusions

• Pros
• Fast, arbitrary dynamic lighting
• Works for arbitrary BRDFs
• Combined with PRT includes shadows and
  interreflections
• Cons
• Works only for low-frequency lighting
• Not real-time (yet)

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• Thank you!
• Questions?
• Please visit us at www.mpi-sb.mpg.de

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Glossy Transfer Rendering
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Precomputation Transfer Matrix

• Glossy Transfer
• More difficult, but works similarly
• Have to compute matrix instead of vector
• Update matrices for interreflections
• Neighborhood Transfer
• Same as for glossy, just for points not on
  surface

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Precomputation Diffuse Transfer

• Visually

illuminate
result
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Rendering

• Project lighting into SH
• Per-vertex
• Project into local tangent frame
• Lookup
• Rotate lighting
• Compute dot-product

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Results
No Shadows/Inter Shadows
ShadowsInter

• Glossy object, 50K mesh
• Runs at 3.6/16/125fps on 2.2Ghz P4, ATI Radeon
  8500

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Dynamic Lighting

• Sample incident lighting on-the-fly
• Precompute textures for SH basis functions in
  cube map parameterization
• Render 6 cube map faces around p
• Read them back
• Projection simple dot-product between cube maps
• Results
• Low-resolution cube maps sufficient
  6x16x16Average error 0.2, worst-case 0.5
• Takes 1.16 ms on P3-933Mhz, ATI 8500

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Introduction Light Integration

• Integrate over all incoming light

Emitter 1
Emitter 2
Diffuse cosltn, sgt Glossy f(v, s)
cosltn, sgt
Receiver
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Background Spherical Harmonics

• Projection
• Reconstruction
• Integration
• Convolution/Rotation
• Simple and efficient formulas

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Overview

• Previous Work
• Background
• Environment Mapping
• Spherical Harmonics
• Fast Environment Mapping with SH
• Theory
• Rendering
• Combine with Precomputed Radiance Transfer
• Results
• Conclusions

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Comparison Size Light vs. SH Order
0
20
40
n2 n3 n4 n5
n6 n26 n26 RT
linear quadratic cubic quartic
quintic windowed
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Introduction Filtered Environment Maps

Environment map over sphere
Source
Target

• BRDF maps to
• Shift-variant radially symmetric kernel? 2D
  filtered environment map
• But
• General anisotropic BRDF? 5D filtered
  environment map

apply filter
Filter kernel
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Precomputed Radiance Transfer

• Precompute how global incident radiance is
  transferred to local incident radiance at points
  
• For self-shadowing and interreflections
• Transfer is represented as a
• Transfer Matrix

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Introduction Environment Maps

• Environment Map
• Approximate incident light field with a single
  sample at objects center

• Assumptions
• Environment at infinity
• No self-shadowing orinterreflections (concave
  object)

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Motivation BRDF Complexity

• HW rendering Increased BRDF complexity
• But only for point light sources!

Heidrich98
Kautz00
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Results Head in Various Environments

• Max Planck head
• 50K vertices
• Ashikhmin-BRDF
• FPS
• 5.24 no xfer
• 4.18 xfer
• 25.3 fixed light
• 130 fixed view

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Results Different BRDFs

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Motivation Environment Maps

• Environment Maps
• Store light incident at single position
• Prefilter to get glossy reflections
• Only limited Phong-like BRDFs
• Complex BRDFs require up to 5D table
• Dynamic lighting difficult, no self-shadowing

Miller Hoffmann84
filter