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Real-time Ray-tracing Real-time Ray-tracing Programmable Graphics Hardware Programmable Graphics Hardware Precomputed Radiance Transfer Precomputed Radiance Transfer Wang et al. SIGGRAPH 09Dachsbacher et al. SIGGRAPH 07 6 Ritschel et al. SIGGRAPH Asia 08

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02 03 04 05 Sloan et al. SIGGRAPH 02 Ng et al. SIGGRAPH 03 Sloan et al. SIGGRAPH 03 Ng et al. SIGGRAPH 04 Wang et al. EGSR 04 Lui et al. EGSR 04 Sloan et al. SIGGRAPH 05 Zhou et al. SIGGRAPH 05 8 Pioneer, SH CPCA Wavelet Triple Product In-Out Fac. In-Out Fac. Dynamic Scenes Dynamic Scenes

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07 08 09 Wang et al. ACMTOG 06 Green et al. I3D 06 Green et al. EGSR 07 Sun et al. SIGGRAPH 07 Ben-Artzi et al. ACMTOG 08 Ramamoorthi CG&V 09 Wang et al. SIGGRAPH Asia 09 9 06 Xu et al. TVCG 08 Ben-Artzi et al. SIGGRAPH 06 Tsai et al. SIGGRAPH 06 SRBF BRDF-Editing CTA SVBRDF, BRDF-Editing Survey BRDF-Editing With G.I. BRDF-Editing With G.I. BRDF-Editing With G.I. BRDF-Editing With G.I.

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11 Fit clamped cosine term to basis Wang et al. SIGGRAPH Asia 09 supplement materials

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12 lobe axis lobe sharpness lobe amplitude

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13 Rotated version Single Lobe Two LobesMultiple Lobes

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Decoupling BRDF from visibility 6D SVBRDF Represent 4D NDF (Microfacet) Visibility (binary) SSDF (Spherical Signed Distance Functions) Fit into SGs Map PCA Mixture of SGs (Spherical Gaussians) 18 Eigen- Vectors Eigen- Vectors

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20 Fresnel Term Geometry Term Normal Distribution Function

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remaining factor (shadowing+Fresnel) NDF Very Smooth High-Frequency Fit into SGs 21

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ground truth single-lobe SG (this paper) 256-term 64-term 16-term BRDF factorization Cook-Torrance m=0.1 Cook-Torrance m=0.045 22

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ground truth 7-lobe SG (this paper) 256-term 64-term BRDF factorization Ashikhmin-Shirley n u =8,n v =128 Ashikhmin-Shirley n u =25,n v =400 Ashikhmin-Shirley n u =75,n v =1200 23

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fabric green delrinsteel phenolic yellow albm bronze violet acrylic ground truth 1SG 2SG 3SG 256-Term Fac. 64-Term Fac. 27

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32 Reconstructed Visibility : elevation angle Inner product / vector product of SGs and V(i) can be efficiently evaluated in the run time!

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PCA coefficientsPCA eigenvectors 33

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Compression results Ray-TracedUncompressed SSDFSSDF/PCA 384 Terms SSDF/PCA 144 TermsSSDF/PCA 48 TermsSSDF/PCA 16 Terms 34

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36 l: 3D light position s: intensity

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40 Cosine Approximation Lighting Approximation BRDF Approximation Visibility Approximation SGs for NDF Spherical WarpMultiplied remaining factor PCA coefficients of SSDFs Uncompressed on GPU

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Per-vertex vs. per-pixel wireframe per-vertex shadingper-pixel shading 43

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Distant environmental light + nearby point light 44

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Results for isotropic BRDFs 45

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Results for anisotropic BRDFs 46

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Video 47

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51 Transfer vector (diffuse) Transfer Matrix (glossy)

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53 = LoLo LiLi Column: Lighting direction Row: Pixel or Vertex

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Factor the BRDF into terms which depend only on incident / outgoing angles We can then define and precompute a view- independent transport function Thus, rendering is reduced to 59

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Real-Time BRDF Editing in Complex Lighting Ben-Artzi, Overbeck, Ramamoorthi SIGGRAPH 2006 63

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Fixed the scene, lighting, and viewpoint Write the BRDF as an expansion in terms of basis functions, instead of lighting 64 Fixed partEditable part

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