Implicit Visibility and Antiradiance for Interactive Global Illumination

1. Implicit Visibility and Antiradiance for Interactive Global Illumination Carsten Dachsbacher1, Marc Stamminger2, George Drettakis1, Frédo Durand3 1 REVES/INRIA Sophia-Antipolis, 2 University of Erlangen, 3 MIT CSAIL

2. Motivation • global illumination • important for realistic image synthesis • interactivity is desirable • visibility is expensive direct illumination global illumination

3. Previous Work • off-line vs. precomputed vs. real-time • radiosity / finite element methods • amount of transport: form factors • computation involves visibility, most expensive part • dynamic scenes make global updates necessary [Sloan02] [Keller97] [Cohen88]

4. Previous Work - negative light • still using visibility • incremental updates for dynamic radiosity [Chen90] • complex data structures, “negative light” • photon mapping (shadow photons) [Jensen95] • alleviating visibility • ambient occlusion [Bunnell05] • “how to avoid explicit visibility” [Pellegrini99] • purely theoretical discussion • does not address directional discretization, iterative solutions

5. Light Transport rendering equation [Kajiya86] BRDF incident radiance geometry term visibility function

6. Rendering Equation • linear operators [Arvo94] • global transport operator G • computes incident radiance from other surfaces • determines visibility G transport with occlusion

7. Rendering Equation • reflection operator K • local operator, computes reflected radiance • rendering equation radiance L emission E G K transport with occlusion reflection

8. Goal: alleviate visibility computation • replace G • use operator U for unoccluded transport • problem: excessive light transport • solution: compensate with “negative light” U transport without occlusion generate negative light

9. New operator • additional local operator • go-through operator J • lets radiance pass through surface • no change in direction or magnitude K reflection U J transport without occlusion go-through operator

10. From occluded to unoccluded transport unoccluded problem: negative occluded input go-through radiance transport extraneous operator J light transport light L GL UL A=JGL UA Antiradiance what we want what we can do cheaply what we need to remove

11. unoccluded negative occluded transport light transport GL UL UA From occluded to unoccluded transport = -

12. occluded and unoccluded transport antiradiance radiance GL UA UL Antiradiance

13. Occluded vs. unoccluded transport UL: transport A to B GL: light is blocked at C, no transport A to B antiradiance generated at C A UL antiradiance exchange from C to B GL C B

14. Recap • new rendering equation • avoids explicit visibility • new quantity antiradiance • propagate K U reflection J transport without occlusion go-through operator

15. Practical implementation • finite element approach • iterative strategies and convergence • using the GPU • implicit visibility makes is feasible

16. Finite Elements • spatial and directional discretization • hierarchical radiosity with clustering • energy transport over links • form factors: energy transport between two patches • directional quantities: uniform discretization

17. Computation K reflection U J transport without occlusion go-through operator

18. global pass propagate energy hierarchical solver: links Computation U transport without occlusion

19. local pass transform incident energy into new exitant energy Computation K reflection J go-through operator

20. Iterative Solution • symmetric iteration

21. Symmetric Iteration 1st iteration 2nd iteration 3rd iteration path tracing 4th iteration 8th iteration reference

22. Iterative Solution • symmetric iteration • shadows are one step behind • fast convergence • it can diverge in contrived scenes • converged in allscenes tested

23. Iterative Solution • asymmetric iteration • one step of radiance propagation • multiple steps for antiradiance • #iterations = depth complexity • “emulate” one step of GL UL UA

24. Convergence • office scene • symmetric: faster in the beginning • asymmetric: better >90 steps • visually: 10 iterations suffice

25. spatial and directional discretization simple 2D data structures textures/render targets on GPUs each table stores L and A K and J operate on separate hemispheres Data structures exitant energy incident energy emission+total reflection elements directions

26. Data structures (global pass) link table cheap, because no visibility Q FPQ P direction mask * sender patch form factor receiver patch * exitant energy incident energy emission+total reflection directions

27. Data structures (local pass) store radiance and antiradiance for next iteration accumulate reflected radiance for display apply local operators to incident energy of each patch new antiradiance new radiance J K exitant energy incident energy emission+total reflection

28. Results • separate direct and indirect illumination • initialize from environment maps • evaluate direct light with shadow maps

29. Results • glossy materials • comparison to path tracing GPU (11 fps) path tracing

30. Dynamic Scenes • moving or deforming objects • only update directly affected links • optimal link hierarchy changes

31. Discussion • meshing and linking • excessive subdivision for dynamic scenes • directional quantities • memory • accuracy, main approximation

32. Conclusion • rendering equation with implicit visibility • directional quantity antiradiance • reorganized global illumination computation • interactive updates • moving objects, lights • glossy surfaces

33. Thank you for your attention! Questions? Acknowledgements: DFG (project “Interaktive Visualisierung Prozeduraler Modelle”) Marie-Curie Postdoctoral Fellowship “Scalable-GlobIllum” (MEIF-CT-2006-041306) Microsoft Research New Faculty Fellowship, Sloan Fellowship NSF CAREER award 0447561 Autodesk, A. Olivier, F. Firsching, P. Richard, P. Green