3c9cae0d6b18ed895165edc568a9a773.ppt

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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 § 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 2 sr) emission change along w in-scattering absorption out-scattering

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 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 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 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 § 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 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 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 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 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 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 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 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 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 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 - 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 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)

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

Thanks!

Results In scenes with variable s, indirect light travels straight

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