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

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

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

Solving the RTE – Previous Work In 3 D, the RTE involves 5 -dimensional Solving the RTE – Previous Work In 3 D, 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]

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

Previous Work Monte Carlo Methods: Photon tracing techniques [Pattanaik et al. 1993, Jensen et 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 Pattanaik et al. 1993 Jensen et al. 1998 Lafortune et al. 1996 Noise requires many paths per a pixel Unique motion many computations per a photon

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

Discrete Ordinates ‘Numerical smearing’ (or ‘false scattering’) Discrete flux approx. involves successive interpolations § Discrete Ordinates ‘Numerical smearing’ (or ‘false scattering’) Discrete flux approx. involves successive interpolations § smear intensity profile or § generate oscillations 1 st order 2 nd order (showing ray’s cross section) Analog of numerical dissipation/diffusion in CFD

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

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

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

New Method - Derivation Next: derive the eqns. for and their relation to Plug 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 Approx. using discrete fields (zero order) Introduce an unpropagated light field U instead of sources stationary grid single light ray in LPM

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

New Method – an Iteration Rays integrate U – emptying relevant bins stationary grid New Method – an Iteration Rays integrate U – emptying relevant bins stationary grid Light scattered from rays added to U, I Proceed to next layer - repeat Sweep along other directions (6 in 3 D) 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

Results DOM with 54 angular bins o o o o For 643 with 9 Results DOM with 54 angular bins o o o o For 643 with 9 x 9 x 6=54 o LPM angular bins DOM requires 510 MBs 9 x 9 angles in LPM, 1+6 in grid Less memory for stationary grid! Using LPM of 9 x 9 requires < 1 MB and grid 6 MB

Results DOM with 54 ordinates on 1283 spurious light ray 9 x 9 ordinates Results DOM with 54 ordinates on 1283 spurious light ray 9 x 9 ordinates in LPM on 1283 Same coarse grid res. (6 dirs. isotropic sct. )

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

Results Comparison with Monte Carlo MC with 106 particles, 3. 5 mins. MC with Results Comparison with Monte Carlo MC with 106 particles, 3. 5 mins. MC with 5 x 106 particles, 17. 6 mins 9 x 9 LPM, 3. 7 mins

Results – Clouds Scenes Back lit Top lit Results – Clouds Scenes Back lit Top lit

Results - Marble Constant scattering Perturbed absorption (isotropic, 52 x 1283) Perturbed scattering Zero Results - Marble Constant scattering Perturbed absorption (isotropic, 52 x 1283) Perturbed scattering Zero absorption (isotropic, 52 x 1283)

Results – Two “wavelengths” Two simulations combined (isotropic, 52 x 1283) Results – Two “wavelengths” Two simulations combined (isotropic, 52 x 1283)

Results Hygia, Model courtesy of: Image-based 3 D Models Archive, Telecom Paris (isotropic, 52 Results Hygia, Model courtesy of: Image-based 3 D Models Archive, Telecom Paris (isotropic, 52 x 2563)

Results - Smoke CFD smoke animation (isotropic, 72 x 643) Results - Smoke CFD smoke animation (isotropic, 72 x 643)

Summary Running times (3 scat. generations x 6 sweeps): § 643 (isotropic), LPM of Summary Running times (3 scat. generations x 6 sweeps): § 643 (isotropic), LPM of 5 x 5 – 17 seconds § 643 (isotropic), LPM of 9 x 9 – 125 seconds § 643 3 x 3(x 6), LPM of 6 x 6 – 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

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Results In scenes with variable s, indirect light travels straight Results In scenes with variable s, indirect light travels straight

Discrete Ordinates In CFD, advected flux is treated via Flux Limiters § high-order stencils 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