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Precomputation aided GI on the GPU

Precomputation aided GI on the GPU. László Szirmay-Kalos. GI: light path generation . image. Virtual world. Path precomputation. Entry point. Exit point. Transfer factors: T ( y ,  i  x,  o ). Entry point y. Entry dir  i. Exit dir  o. Exit Point x.

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Precomputation aided GI on the GPU

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  1. Precomputation aided GI on the GPU László Szirmay-Kalos

  2. GI: light path generation image Virtual world

  3. Path precomputation Entry point Exit point

  4. Transfer factors: T(y,i x,o) Entry point y Entry dir i Exit dir o Exit Point x

  5. Having the transfer factors

  6. Having the Transfer factors L(x,o) =  S Lin(y,wi) T(y,ix,o) dwidy • Directional lights or Image Based Lighting: • Linis independent of y • Diffuse surfaces: L(x,o) =  Lin(wi) S T(y,ix,o) dydwi= =  Lin(wi) Tenv(ix,o) dwi L(x) =  S Lin(y) T(y,ix) dwidy

  7. Problems • Exit points: • Vertices of a highly tessellated mesh • Points corresponding to texel centers • Entry points: • Vertices of a highly tessellated mesh • Sampled randomly • No problem if directional lights or environment lighting • Exit directions: • no problem if the scene is diffuse • T is a 4-variate (8-dimensional) function: • how to store? • Simplification: diffuse surfaces + environment lighting requires just 2 variate functions

  8. Storing the Transfer factors • Finite element representation • Pros: compact, good for low frequency illumination • Cons: costly to update • Sampling + interpolation • Pros: easier to update, good for high frequency illumination • Cons: not as compact

  9. Finite-element representation Tenv(ix) T x(i) = NTn bn()

  10. How to computeTm • Find an adjoint basis function set:  bn(w) b*m(w) dw = 1 if m=n, and 0 otherwise T x(i) = NTn bn()// multiply by b*m() T x()b*m(w)dw =  NTnbn()b*m(w)dw = Tm Monte Carlo integration

  11. Monte Carlo preprocess i L b*n(wi) p(i, y,path) 1 K Tn +=  y x Number of samples

  12. Precomputed Radiance Transfer (Sloan02) • Transfer factors for directional illumination • Express directional illumination with adjoint basis functions • Thanks to orthogonality, the exit radiance is: • It requires N rgb transfer factors at each exit points Lin(w) N Ln b*n() L(x) =  Lin(wi) Tenv(ix) dwi = NLnb*n(i)NTmbm(i)dwi =NLn Tn

  13. Principal ComponentAnalysis • M is the mean of the dataset • Bs are the eigenvectors corresponding to the largest eigenvalues of the covariance matrix:  (Tm-M)T  (Tm-M)

  14. PRT results 1 bounce preproc: 12 sec 5 bounce preproc: 172 sec Run time: 466 FPS

  15. Sampling approach to precomputation aided GI • No finite-element representation • Entry-exit point samples are stored directly • Comparison to PRT: • It is easy to update • It does not assume low frequency environment map • Particularly good for point lights that can be close

  16. Preprocessing: Entry points Random sampling

  17. Preprocessing: Transfer from entry to exit points entry point with unit irradiance

  18. Preprocessing: Reference point illumination unit irrad Virtual lights

  19. Precomputed Radiance Map Item: (entry, exit, irrad) unit irrad irrad transfer

  20. PRM: 4D array Exit point Texcoord: (u,v) Entry point: r, g, b PRM item

  21. Real-time Rendering:Entry point visibility

  22. Rendering:PRM weighting

  23. Implementation CPU GPU Entry point sampling and Photon tracing Exit point illumination computation PRMs in textures Preprocessing Shadow mapping: Direct illum + Entry point visibility Camera rendering: Direct illum + PRM weighting Image Real-time rendering

  24. Tile in a single or few textures PRMs in textures: Tiling u u Exit point Exit point v v r, g, b r, g, b Etc. Pane of Entry point 1 Pane of Entry point 2

  25. Entry point clustering u u Exit point Exit point r, g, b r, g, b v v Pane of Entry point 2 Pane of Entry point 1 Close and have similar normals

  26. Resulting cluster u Exit point Pane of Entry point Cluster 1 r, g, b v

  27. Results 4096 entry points 256 – 32 clusters: 128 – 4Mb texture memory Preproc: 5 minutes Rendering: 40 FPS

  28. Results: Room with stairs 16K entries 32 clusters 4Mb per obj 50 FPS

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