1. Participating Media Illumination using Light Propagation Maps Raanan Fattal Hebrew University of Jerusalem, Israel

2. Introduction ‏ In media like fog, smoke and marble light is:  Scattered  Absorbed  Emitted ‏ Realistic rendering by accounting such phenomena Images by H. W. Jensen

3. Introduction ‏ The Radiative Transport Eqn. models these events change along  emission out-scattering absorption in-scattering I(x,  ) – radiation intensity ( W/m 2 sr )

4. Solving the RTE – Previous Work ‏ In 3D, the RTE involves 5-dimensional variables, ‏ Much work put into calculating the solution ‏ Common approaches are:  volume-to-volume energy exchange  stochastic path tracing  Discrete Ordinates methods ‏ Methods survey [Perez, Pueyo, and Sillion 1997]

5. Previous Work ‏ The Zonal Method [Hottel & Sarofim 1967, Rushmeier 1988] ‏ Compute exchange factor between every volume pair ‏ In 3D, involves O(n 7/3 ) relations for isotropic scattering ‏ Hierarchical clustering strategy [Sillion 1995] reduce complexity

6. Previous Work ‏ Monte Carlo Methods: ‏Photon tracing techniques [Pattanaik et al. 1993, Jensen et al. 1998] ‏Path tracing techniques [Lafortune et al. 1996] ‏ Light particles are tracked within the media ‏ Noise requires many paths per a pixel ‏ Unique motion many computations per a photon Pattanaik et al. 1993Lafortune et al. 1996Jensen et al. 1998

7. Previous Work ‏ Discrete Ordinates [Chandrasekhar 60, Liu and Pollard 96, Jessee and Fiveland 97, Coelho 02,04] ‏ Both space and orientation are discretized ‏ Derive discrete eqns. and solve ‏ The DOM suffers two error types angular index spatial indices cell volume Discrete light directions inside a spatial voxel

8. Discrete Ordinates ‏ ‘Numerical smearing’ (or ‘false scattering’) ‏ Discrete flux approx. involves successive interpolations  smear intensity profile or  generate oscillations ‏ Analog of numerical dissipation/diffusion in CFD (showing ray’s cross section) 1 st order2 nd order

9. Discrete Ordinates ‏ ‘Ray effect’ ‏ Light propagates in (finite) discrete directions ‏ Spurious light streaks from concentrated light areas ‏ New method can be viewed as a form of DOM Jet color scheme

10. New Method - Overview ‏ Iterative solvers Progressive Radiosity & Zonal propagate light [Gortler et al. 94] Idea: propagate light using 2D Light Propagation Maps (LPM) and not use DOM eqns. in 3D stationary grid  One physical dimension less  Partial set of directions stored Allow higher angular resolution  Unattached to stationary grid Advected parametrically Offer a practical remedy to the ‘ray effect’ Light Propagation Maps, 2D grids of rays, each covering different set of directions No interpolations needed for light flux, ‘false scattering’ is eliminated stationary grid

11. New Method - Setup Variables: - average scattered light (unlike DOM) (need only 1 angular bin for isotropic scattering!) - ray’s intensity - ray’s position Goal: compute stationary grid light propagation map LPM 2D indexing

12. New Method - Derivation ‏ Next: derive the eqns. for and their relation to Plug in L instead of I, and R – ray’s pos. instead of x Note: in the in-scattering term, I wasn’t replaced by L Introduce an unpropagated light field U instead of sources Approx. using discrete fields (zero order) stationary grid single light ray in LPM

13. New Method - Derivation ‏ As done in Progressive Radiosity, the solution ‏ is constructed by accumulating light from LPMs ‏ (A -discrete surface areas, F – phase func. weights) ‏ This is also added to the unpropagated light field U I(x,  )=

14. New Method – an Iteration ‏ LPM ray’s dirs. must be included in U’s ‏ Coarse bins of I, U contain scattered light, filtered by phase func. ‏ Linear light motion: inadequate to simulate Caustics ‏ Rays integrate U – emptying relevant bins ‏ Proceed to next layer - repeat ‏ Light scattered from rays added to U, I stationary grid ‏ Sweep along other directions (6 in 3D)

15. Results o o o o o o o o o DOM with 54 angular bins 9x9 angles in LPM, 1+6 in grid For 64 3 with 9x9x6=54 angular bins DOM requires 510MBs Using LPM of 9x9 requires < 1MB and grid 6MB For 64 3 with 9x9x6=54 angular bins DOM requires 510MBs Using LPM of 9x9 requires < 1MB and grid 6MB Less memory for stationary grid! LPM

16. Results Same coarse grid res. (6 dirs. isotropic sct.) DOM with 54 ordinates on 128 3 9x9 ordinates in LPM on 128 3 spurious light ray

17. Results First-order upwind High-res. 2 nd -order upwind LPM parametric advection Second-order upwind

18. Results MC with 10 6 particles, 3.5 mins. MC with 5x10 6 particles, 17.6 mins 9x9 LPM,3.7 mins Comparison with Monte Carlo

19. Results – Clouds Scenes Back litTop lit

20. Results - Marble Constant scattering Perturbed absorption (isotropic, 5 2 x128 3 ) Perturbed scattering Zero absorption (isotropic, 5 2 x128 3 )

21. Results – Two “wavelengths” Two simulations combined (isotropic, 5 2 x128 3 )

22. Results Hygia, Model courtesy of: Image-based 3D Models Archive, Telecom Paris (isotropic, 5 2 x256 3 )

23. Results - Smoke CFD smoke animation (isotropic, 7 2 x64 3 )

24. Summary ‏ Running times (3 scat. generations x 6 sweeps):  64 3 (isotropic), LPM of 5x5 – 17 seconds  64 3 (isotropic), LPM of 9x9 – 125 seconds  64 3 3x3(x6), LPM of 6x6 – 60 seconds (2.7 GHz Pentium IV) ‏ Light rays advected collectively and independently  Avoids grid truncation errors - No numerical smearing  Less memory more ordinates – Reduced ray effect

25. Thanks!

26. Results ‏ In scenes with variable , indirect light travels straight

27. Discrete Ordinates ‏ In CFD, advected flux is treated via Flux Limiters  high-order stencils on smooth regions  switch to low-order near discontinuities ‏ For the RTE such ‘High res.’ methods suffer from:  still, some amount of initial smearing is produced  limiters are not linear, yielding a non-linear system of eqns.  offers no remedy to the ‘ray effect’ discussed next