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1 2 3 – – – – – Dynamic lighting Changeable viewpoint All-frequency effects Dynamic, editable, and spatially-varying materials Dynamic, deformable scenes 4 • Modeling the complex reflectance of real world materials • Integration over the whole hemisphere (cannot afford especially when environment maps are used) • Interreflection, shadows, …etc 5 Precomputed Radiance Transfer Real-time Ray-tracing Wang et al. SIGGRAPH ‘09 Programmable Graphics Hardware Ritschel Dachsbacher et al. SIGGRAPH et al. SIGGRAPH Asia ‘08 ‘07 6 – The term comes from – Precompute L( x, o ) 4 L(i )V ( x, i )[ (i , o ) max( i n( x),0)]di – Compress by (SH, Wavelet, SRBF…) – The computation of rendering equation reduces to in the run time 7 Triple Product Ng et al. SIGGRAPH ‘03 Zhou et al. SIGGRAPH ‘05 Ng et al. SIGGRAPH ‘04 Wavelet Dynamic Scenes 02 03 04 05 Sloan et al. SIGGRAPH ‘05 Sloan et al. SIGGRAPH ‘02 Pioneer, SH Sloan et al. SIGGRAPH ‘03 Wang et al. EGSR ‘04 In-Out Fac. CPCA Lui et al. EGSR ‘04 8 BRDF-Editing With G.I. SVBRDF, BRDF-Editing Wang et al. SIGGRAPH Asia ‘09 Ben-Artzi et al. ACMTOG ‘08 Green et al. EGSR ‘07 Green et al. I3D ‘06 BRDF-Editing Ben-Artzi et al. SIGGRAPH ‘06 SRBF 06 07 08 Ramamoorthi CG&V ‘09 Wang et al. ACMTOG ‘06 Sun et al. SIGGRAPH ‘07 BRDF-Editing With G.I. 09 Xu et al. TVCG ‘08 Survey CTA Tsai et al. SIGGRAPH ‘06 9 – Compression • PCA, Clustered PCA (CPCA), Clustered Tensor Approximation (CTA) … – Basis • • • • Spherical harmonics (SH) Wavelets Zonal harmonics (ZH) Spherical Radial Basis Function (SRBF) 10 – How to choose good basis for representation? • • • • Can model all-frequency effects Rotational invariant Accuracy Compact Fit clamped cosine term to basis Wang et al. SIGGRAPH Asia ‘09 – supplement materials 11 – A type of SRBF, symmetric around a specific lobe axis G(v; p, , ) e (v p 1) lobe axis lobe amplitude lobe sharpness – All advantages in the previous page – Inner product & cross product can be efficiently computed 12 Single Lobe Two Lobes Multiple Lobes n F (v) G (v; pi , i , i ) * i 1 n RF (v) G (v; Rpi , i , i ) * Rotated version i 1 13 14 • Real-time (editable, change with time), BRDFs • All-frequency effects from both environmental and local point lights 15 • Propose two new representations for and to compact the size of data • Accurate and compact • Parametric BRDFs can be fit on-the-fly • Fast rotation, warping, and products in run time • Ghost-free, per-pixel interpolation • Dynamic local point lights 17 • Decoupling BRDF from visibility Represent 6D SVBRDF Fit into SGs 4D NDF Mixture of SGs (Microfacet) (Spherical Gaussians) Map PCA Visibility SSDF (binary) (Spherical Signed Distance Functions) EigenVectors 18 19 • Microfacet Model (i , o ) D(h )G (i , o ) F (i , h ) 4 cos i cos o Normal Geometry Distribution Term Function Fresnel Term • Why use microfacet model? – General 20 • Reflectance representation using SGs (o, i) M o (i) D(h) remaining factor (shadowing+Fresnel) Very Smooth NDF High-Frequency Fit into SGs – Example: Cook-Torrance Model M o (i) FCT (o, i) SCT (o, i) (n i)( n o) D(h) e (arccos(hn ) / m) 2 G(h; n,2 / m2 ,1) 21 Cook-Torrance m=0.1 Cook-Torrance m=0.045 64-term 16-term ground truth single-lobe SG 256-term (this paper) BRDF factorization 22 Ashikhmin-Shirley nu=8,nv=128 Ashikhmin-Shirley nu=25,nv=400 Ashikhmin-Shirley nu=75,nv=1200 ground truth 7-lobe SG (this paper) 256-term 64-term BRDF factorization 23 – Parametric isotropic models 24 – Parametric anisotropic models 25 • Reflectance representation using SGs • Using shadowing factor S at each surface point • Compress shadowing function by PCA (8D) • Fit NDF with a small number of SGs and 26 fabric green delrin phenolic yellow albm bronze violet acrylic steel ground truth 1SG 2SG 3SG 256-Term Fac. 64-Term Fac. 27 – Measured BRDFs 28 29 • Spatially-varying visibility is represented with – Directly interpolate binary visibilities will produce ghost effects – SSDF maps binary visibility to continuous function 30 – Positive: visible; negative: occluded – Value: the to the nearest direction t on the shadow boundary min arccos(t i), if V (i) 1; V (i ) V ( t ) 0 min arccos(t i), if V (i) 0. V ( t ) 1 31 Reconstructed Visibility V ' (i ) 1, if (i) 2 - d 0, otherwise δ: elevation angle Inner product / vector product of SGs and V’(i) can be efficiently evaluated in the run time! 32 • Compression – Using PCA Nv Vx (i) V j (i)wVx, j j 1 PCA eigenvectors PCA coefficients • PCA coefficients are stored as and Interpolated to each pixel during rasterization • Eigenvectors are encoded in multiple textures 33 • Compression results Ray-Traced Uncompressed SSDF SSDF/PCA 384 Terms SSDF/PCA 144 Terms SSDF/PCA 48 Terms SSDF/PCA 16 Terms 34 35 – Approximated with a single-lobe SG – Yielding a lx 2r 2 s l: 3D light position 1 L (i) G(i; , fa ( ), ) s: intensity || l x || || l x ||2 || l x ||2 * x L* (i ) G (i; I , f a1 (2r 2 ), s ) 36 • Distant environmental lighting – Apply to diffuse component • [Tsai. et al. SIGGRAPH 2006] – Apply to specular component • Preconvolve environmental radiance with SG kernels • The run-time inner product is reduced to a MIPMAP texture fetch • [Kautz et al. EGWR 2000], [McAllister et al. GH 2002], [Green et al. I3D 2006] 37 38 – Position, texture coordinates, local coordinate frame, PCA coefficient for SSDF • BRDF parameters, tabulated SG lobes (for measured BRDFs), and PCA-compressed shadow factors are stored in textures 39 R(o) kd Rd ks Rs (o) Rd 2 L(i)V (i) max( 0, i n)di Rs (o) 2 L(i) s (o, i)V (i) max( 0, i n)di S S Cosine Approximation C * (i; nx ) G (i; nx , c , c ), c 2.133, c 1.170 Lighting Approximation L* (i ) BRDF Approximation SGs for NDF Visibility Approximation PCA coefficients of SSDFs Rd (C * (i; nx ) L* (i )) Vxd (i ) Spherical Warp Multiplied remaining factor D* (h) W * (i) s* (i; o) M o (i ) W * (i ) Uncompressed on GPU Rs (o) (C* (i; nx ) s*, x (i, o) Vxd (i)) L* (i) 40 41 42 • Per-vertex vs. per-pixel wireframe per-vertex shading per-pixel shading 43 • Distant environmental light + nearby point light 44 • Results for isotropic BRDFs 45 • Results for anisotropic BRDFs 46 • Video 47 • Solution for highly-specular, spatially varying, dynamic materials, natural lighting, changeable viewpoints realistic rendering • Accurate and compact • Fast rotation, warping, and products in run time • Ghost-free, per-pixel interpolation • Allow sparse set of per-vertex visibility samples 48 49 50 • Algorithm (diffuse) – Express lighting as L(i ) j 1 jY j (i ) ( l *1) 2 – Reflection Equation becomes L ( x) Y ( )V ( x, ) max( n,0)d o j j 4 j i – Define i i i and project to SH T j ( x) 4 Y j (i )V ( x, i ) max( i n,0)di Transfer vector (diffuse) Transfer Matrix (glossy) – Rendering reduces to Lo ( x ) j 1 jT j (i ) 51 52 T ( x, ) V ( x, ) (, o ( x)) max( i n( x),0) Lo ( x ) iT ( x, i )L(i ) Lo TL Column: Lighting direction Lo = Li Row: Pixel or Vertex 53 • The dimension of – 300000 x 25000 for a 512x512 image and 6 x 64 x 64 environment map (How to preserve high-frequency shadow?) are enough to generate high-quality results (compared to 20000 with SH) 54 55 • Changeable view makes a • Factor the BRDF and visibility, reduce 6D function into – For each spatial location and outgoing direction, store 3 functions in cubemaps (Light, Visibility, BRDF) – Calculate in run time B ( x, o ) 4 L ( ) V ( x) ( ) (n( x), ) ( )d j j j i k k k i l l o l i i j k l L jVk l j (i ) k (i ) l (i )di 4 j k l C jkl L jVk l 56 57 58 • Factor the BRDF into terms which depend only on incident / outgoing angles (i , o ) k 1 k hk (o ) g k (i ) K • We can then define and precompute a viewindependent transport function Tk ( x, i ) V ( x, i ) g k (i ) max( i n( x),0) • Thus, rendering is reduced to B( x, o ) k 1 k hk (o ) K 4 L(i )Tk ( x, i )di 59 – Triple product • Pros: support true all-frequency effects • Cons: performance – BRDF in-out factorization • Pros: speed and simple • Cons: k can not be large, make it only suit for glossy or broad specular lobes 60 61 62 • Real-Time BRDF Editing in Complex Lighting – Ben-Artzi, Overbeck, Ramamoorthi – SIGGRAPH 2006 63 • Fixed the scene, lighting, and viewpoint • Write the BRDF as an expansion in terms of basis functions, instead of lighting (i , o ) q (i , o ) f ( (i , o )) q (i , o ) j 1 c j b j ( ) J Fixed part Editable part 64 65