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Normal Mapping for Precomputed Radiance Transfer

Develop techniques to decouple normal variation from parameterized lighting models for rigid objects. Explore Bi-Scale Radiance Transfer for efficient normal mapping. Inspired by HL2, aim to model normal variation without local GI, masking effects, or glossy materials.

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Normal Mapping for Precomputed Radiance Transfer

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  1. Normal Mapping for Precomputed Radiance Transfer Peter-Pike Sloan Microsoft

  2. Inspiration • [McTaggart04] Half-Life 2 “Radiosity Normal Mapping”

  3. 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”

  4. 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

  5. PRT

  6. PRT

  7. PRT

  8. Bi-Scale Radiance Transfer

  9. 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

  10. 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

  12. 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

  13. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Distant Lighting Environment

  14. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Distant Radiance to Transferred Incident Radiance In local frame

  15. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Diagonal Convolution Matrix Clamped cosine kernel

  16. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Irradiance Environment Map

  17. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Irradiance Environment Map

  18. Diffuse + Normal Maps • Quadratic SH [Ramamoorthi2001] Evaluate SH basis with normal

  19. 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

  20. Analytic Basis Project into new basis (fewer rows)

  21. Shifted Associated Legendre Polynomials [Gautron2005]

  22. Half-Life 2 Basis

  23. Comparison PRT Gold Standard HL2 SAL

  24. Comparison PRT Gold Standard HL2 SAL

  25. 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”

  26. Normal Mapping for PRT

  27. Normal Mapping for PRT • Compute SVD of A Nx9 matrix (each column is a “normal basis” texture) 9x9 diagonal matrix (singular values) 9x9 matrix

  28. Normal Mapping for PRT • Old equation • New equation

  29. Normal Mapping for PRT • Use first M singular values • MxO2 matrix • M channel “normal direction” texture

  30. Pixel Shader StandardSVDPS( VS_OUT In, out float3 rgb : COLOR ) { float2 Normal = tex2D(NormalSampler, In.TexCoord); float2 vTex = Normal*0.5 + 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); }

  31. Comparison

  32. Demo

  33. 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

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

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