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Real-Time Shading with Filtered Importance Sampling

Explore dynamic BRDF and lighting for gaming and production, using single GPU shader with minimal code. Implement filtered importance sampling for real-time glossy surface reflections.

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Real-Time Shading with Filtered Importance Sampling

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  1. Real-time Shading with Filtered Importance Sampling Mark Colbert University of Central Florida JaroslavKřivánek Czech Technical University in Prague

  2. Motivation • Dynamic BRDF and lighting • Applications • Material design • Gaming • Production pipeline friendly • Single GPU shader • No precomputation • Minimal code base

  3. Demo

  4. Our Approach BRDF proportional sampling Environment map filtering

  5. Related Work A Unified Approach to Prefiltered Environment Maps[ Kautz et al. 2000 ] Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions[ McAllister et al. 2002 ] Efficient Reflectance and Visibility Approximations for Environment Map Rendering [ Green et al. 2007 ] Interactive Illumination with Coherent Shadow Maps[ Ritschel et al. 2007 ]

  6. Illumination Integral Ignores visibility[ Kozlowski and Kautz 2007 ] Computationally expensive

  7. Importance Sampling Choose a few random samples Select according to the BRDF

  8. Importance Sampling Result 40 samples per pixel

  9. Random Numbers on the GPU • Relatively expensive • Random numbers per pixel (computation) • Random number textures (memory/indirection) • Quasi-random sequence • Good sample distribution (no clumping) • Use same sequence for each pixel

  10. Same Sequence Result 40 samples per pixel

  11. Filtered Importance Sampling • Filter environment mapbetween samples over hemisphere • Samples distributed by the BRDF • Support approximately equivalent to:

  12. Filtering Use MIP-maps Level proportional to log of filter size

  13. Implementation • Auto-generated MIP-map • Dual paraboloids • Single GPU Shader • Sum together filtered samples

  14. ResultsSphere – Grace Probe Stochastic No Filtering Our Result Reference

  15. ResultsBunny – Ennis Probe Stochastic No Filtering Our Result Reference

  16. Approximations Constant BRDF across filter Isotropic filter shape Tri-linear filtering

  17. RMS Error Phong Reflection - Ennis Light Probe n=10 n=100 n=1000

  18. Performance 512x512 Sphere

  19. Conclusions • Real-time glossy surface reflections • Signal Processing Theory • Practical • Affords new interfaces • For more information:GPU Gems 3 • Download the code now! • graphics.cs.ucf.edu/gpusampling/

  20. Questions

  21. Additional Slides

  22. Performance

  23. Which distribution? • Product of lighting and BRDF • Requires bookkeeping • Too expensive • Lighting • BRDF

  24. Which distribution? • Product of lighting and BRDF • Lighting • Too many samples for glossy surfaces • BRDF

  25. Which distribution? • Product of lighting and BRDF • Lighting • BRDF • Computationally efficient

  26. Environment Mapping Error Support Region • Dual Paraboloid

  27. Environment Mapping • Cube Maps • Low distortion • Accelerated by GPU • Decimation/reconstruction filters non-spherical • Introduces Seams

  28. Environment Mapping • Latitude/Longitude • Too much distortion at poles

  29. Measured BRDF Data Fast primitive distribution for illustration[ Secord et al. 2002 ] Efficient BRDF importance sampling using a factored representation[ Lawrence et al. 2004 ] Probability Trees[ McCool and Harwood 1997 ]

  30. Importance Sampling Random Samples on Unit Square PDF-Proportional Samples on Hemisphere 1 PDF Mapping 0 0 1

  31. Pseudocode float4FilteredIS(float3 viewing : TEXCOORD1 uniform sampler2Denv) : COLOR { float4 c = 0; // sample loop for (int k=0; k < N; k++) { float2 xi = quasi_random_seq(k); float3 u = sample_material(xi); floatpdf = p(u, viewing); floatlod = compute_lod(u, pdf); float3 L = tex2Dlod(env,float4(u, lod)); c += L*f(u,viewing)/pdf; } returnc/N; }

  32. Filter Support • Ideal • Isotropic approximation • Assume sample points are perfectly stratified • Implies area of 1 sample = 1 / N • Use Jacobian approximation for warping function (Inverted PDF) • Support region of sample  1 / p(i, o) N

  33. Ideal Sample Filter Design h – Filter function More expensive than illumination integral

  34. Approximate Sample Filter • Estimate for sample • BRDF  PDF • PDF is normalized BRDF • Near constant over single sample • Low frequency cosine approximation • Use multiple samples to estimate effect

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