Normal Mapping for Precomputed Radiance Transfer

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Normal Mapping for Precomputed Radiance Transfer

• Peter-Pike Sloan
• Microsoft

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Inspiration

• McTaggart04 Half-Life 2 Radiosity Normal
  Mapping

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Related Work

• Willmott99 Vector irradiance formulation of
  radiosity (for accelerating computation)
• Tabellion04 Lighting model similar to above
  (dominant light direction)
• Good2005 Spherical Harmonic Light Maps

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Goal

• Develop lightweight techniques to decouple normal
  variation (ala HL2)
• From parameterized models of lighting (PRT)
• For rigid objects
• Non goals
• Modeling local GI of the bumps Sig05
• Masking effects
• Glossy materials

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PRT
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PRT
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PRT
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Bi-Scale Radiance Transfer
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Bi-Scale Radiance Transfer

• l vector source radiance spherical function
• Mp 25x25 transfer matrix at point p (source ?
  transferred incident)
• q(xp) ID map (2D ? 2D, maps RTT patch over
  surface)
• b(x,v) RTT (4D ? 25D, tabulated over small
  spatial patch)

applies macro-scale transferred radiance to
meso-scale RTT
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Bi-Scale Radiance Transfer

• l vector source radiance spherical function
• Mp 25x25 transfer matrix at point p (source ?
  transferred incident)
• q(xp) ID map (2D ? 2D, maps RTT patch over
  surface)
• b(x,v) RTT (4D ? 25D, tabulated over small
  spatial patch)

applies macro-scale transferred radiance to
meso-scale RTT
11
Bi-Scale Radiance Transfer

• l vector source radiance spherical function
• Mp 25x25 transfer matrix at point p (source ?
  transferred incident)
• q(xp) ID map (2D ? 2D, maps RTT patch over
  surface)
• b(x,v) RTT (4D ? 25D, tabulated over small
  spatial patch)

applies macro-scale transferred radiance to
meso-scale RTT
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Limitations

• Expensive
• Stores 64 response vectors that are 9-36D (x3
  for spectral)
• Parallax mapping cheaper way of getting masking
• Local radiance is too much data (9 36 x 3) for
  low res textures/per-vertex
• Add constraints
• Just model normal variation
• Diffuse only

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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Distant Lighting Environment
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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Distant Radiance to Transferred Incident
Radiance In local frame
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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Diagonal Convolution Matrix Clamped cosine kernel
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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Irradiance Environment Map
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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Irradiance Environment Map
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Diffuse Normal Maps

• Quadratic SH Ramamoorthi2001

Evaluate SH basis with normal
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Concerns

• Lot of data at low res
• 9xO2 matrices (x3 with color bleeding)
• Can compress using CPCA Sig03
• Too much data passed from low res to high res
• Irradiance emap (27 numbers, 7 interpolators)
• Alternatives
• Project into analytic basis
• Separable approximation

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Analytic Basis
Project into new basis (fewer rows)
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Shifted Associated Legendre Polynomials
Gautron2005
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Half-Life 2 Basis
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Comparison
Gold Standard
HL2
SAL
PRT
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Comparison
Gold Standard
HL2
SAL
PRT
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Normal Mapping for PRT

• Use same ideas as BRDF factorization Kautz and
  McCool1999

Bi-linear basis functions over hemisphere (4
non-zero)
Matrix, rows normal directions columns
quadratic SH light Aij equals evaluating
convolved light basis function j in normal
direction i
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Normal Mapping for PRT
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Normal Mapping for PRT

• Compute SVD of A

Nx9 matrix (each column is a normal basis
texture)
9x9 diagonal matrix (singular values)
9x9 matrix
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Normal Mapping for PRT

• Old equation
• New equation

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Normal Mapping for PRT

• Use first M singular values
• MxO2 matrix
• M channel normal direction texture

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Pixel Shader
StandardSVDPS( VS_OUT In, out float3 rgb COLOR
) float2 Normal tex2D(NormalSampler,
In.TexCoord) float2 vTex Normal0.5
float2(0.5,0.5) float4 vU tex2D(USampler,vTex
) rgb.r dot(In.cR,vU) rgb.g
dot(In.cG,vU) rgb.b dot(In.cB,vU) rgb
tex2D(AlbedoSampler, In.TexCoord)
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Comparison
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Demo
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Conclusions

• Lightweight form of normal mapping for PRT
• Inspired by Half-Life 2
• For static objects, diffuse only
• HL2 basis and separable basis seem to be best
• Experiment with CPCA more Sig03
• Integrate with other techniques
• Parallax mapping for masking
• Ambient Occlusion for local effects

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Acknowledgments

• Gary McTaggart for HL2 images
• Shanon Drone for Models
• Paul Debevec for Light Probes