1. Spatial Directional Radiance Caching Václav Gassenbauer Czech Technical University in Prague Jaroslav Křivánek Cornell University Kadi Bouatouch IRISA / INRIA Rennes 1

2. Goal Acceleration of Global Illumination Computation on Glossy Surfaces 2 Adapt glossiness of surfaces

3. Previous Work Irradiance caching (IC) ◦ [Ward et al. 88], [Ward and Heckbert 92] ◦ Indirect illumination changes slowly → interpolate Variants of IC ◦ [Tabellion and Lamorlette 04], [Brouillat et al. 08], [Arikan et al. 05], … Radiance caching (SHRC) ◦ [Křivánek et al. 05] Other techniques ◦ [Hinkenjann and Roth 07, …] 3

4. Motivation Radiance caching limitation ◦ Uniform sampling of full hemisphere ◦ Low glossy surfaces ◦ Conversion of the scene BRDFs into the frequency domain in preprocess 4

5. SDRC – Overview Caching scheme Cache structure New record computation Spatial / Directional Interpolation Outgoing radiance computation 5

6. Spatial Cache Lookup Spatial Cache Miss! BRDF Importance Sampling Spatial Directional Caching Scheme Spatial Cache p2p2 p1p1 Project Sample onto Unit Square Store in cache Spatial Cache Lookup Spatial Cache Hit! Directional Cache HIT! Directional Cache MISS! Directional Cache Update 6 Directional Cache

7. Structure of the Two Caches 7 kD-tree (directional cache) Octree (spatial cache) Spatial Cache

8. New Record Computation Generate N samples using BRDF importance sampling p Compute incoming radiance using ray casting and photon map Transform samples onto 2D domain Build a k-D tree upon the samples L-tree 8

9. Spatial Interpolation p Collect L-trees that can be used for interpolation at p (borrowed from RC) 9 For all L-trees found compute the spatial weight Spatial Cache Spatial Cache Lookup p1p1 p2p2 p Spatial Cache Hit! L-tree(p 2 ) p2p2 L-tree(p 1 ) p1p1

10. Directional Interpolation p2p2 p L-tree(p 2 ) Generate M(M<<N) samples using BRDF importance sampling For all the samples try find nearby radiance samples in L- tree(p 2 ) in S(p) Transform samples onto unit domain Update L-tree(p 2 ) if necessary Radiance sample found Radiance not sample found → ray tracing 10 L-tree(p 2 )

11. Which Radiance Samples Are Nearby? i-th L-tree Compute search radius for each radiance sample Collect nearby radiance samples Compute directional weights 11

12. Incoming Radiance Interpolation Interpolate all collected radiance sample ◦ Sums run over all radiance samples from all contributing L-trees. 12 Product of spatial and directional weights k-th radiance sample stored in the i-th L-tree Interpolated incoming radiance

13. Outgoing Radiance Computation Evaluate Monte Carlo Estimator interpolated incoming radiance # render samples Sampling probability of Estimated outgoing radiance 13

14. Results SHRC vs. SDRC ◦ SHRC = Spherical harmonics caching ◦ SDRC = new Spatial-Directional caching MC vs. SHRC vs. SDRC vs. REF ◦ MC = Monte Carlo importance sampling ◦ REF = reference solution SDRC scalability Animation 14

15. SHRC vs. SDRC 15 SDRC adapts to the BRDF lobe exponent automatically

16. MC vs. SHRC vs. SDRC vs. REF 16 SDRC produce less noise than MC SDRC produce no ringing artifacts as SHRC. MCSDRC (new) SHRCREF

17. SDRC scalability 17 N=64 / t ≈6.2s N=128 / t ≈13.0s N=256 / t ≈23.6s SDRC MC Rendering time is O(N). indirect lighting compu- tation time of the detail

18. Animation 18 Without reusing cache record With reusing cache record - Flickering reduced Side-by-side comparison

19. Discussion 19 Interpolation ◦ MC performs better than SDRC for highly glossy materials Supported materials ◦ Spatially varying ones without sudden changes ◦ Availability of sampling procedure Memory consumption ◦≈ higher memory requirements than SHRC (N = 512 and SH order of 10)

20. Conclusion Indirect lighting computation on glossy surfaces PROS: + Exploits spatial / directional coherence + No blurry / banding artifacts + Adapts automatically to the glossiness + Less noisy than MC CONS − Higher memory requirements − Potentially difficult parallelization 20

21. Future Work Precise formalization of illumination coherence Decrease flickering in animation 21

22. Acknowledgements Chess pieces courtesy of T. Hachisuka Ray tracing system - PBRT Thank you for your attention 22

23. Cache Record Density Control 23