participating media illumination using light propagation maps
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
change along change along
emissionemission out-scatteringout-scattering
absorptionabsorption
in-scatteringin-scattering
I(x,) – radiation intensity (W/m2sr)
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]
Previous Work
The Zonal Method [Hottel & Sarofim 1967, Rushmeier 1988]
Compute exchange factor between every volume pair
In 3D , involves O(n7/3) 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
Noise requires many paths per a pixel
Unique motion many computations per a photon
Pattanaik et al. 1993
Lafortune et al. 1996
Jensen et al. 1998
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 indexangular index
spatial indicesspatial indices
cell volumecell volume
Discrete light directionsinside a spatial voxel
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)
1st order 2nd order
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
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’
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
No interpolations needed for light flux, ‘false scattering’ is eliminated
stationary grid
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
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 xNote: in the in-scattering term, I wasn’t replaced by LIntroduce an unpropagated light field U instead of sources
Approx. using discrete fields (zero order)
stationary grid
single light ray in LPM
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,)=
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)
Results
o
o
oo
o
o
o
o
o
DOM with 54 angular bins
9x9 angles in LPM, 1+6 in grid
For 643 with 9x9x6=54
angular bins DOM requires 510MBs
Using LPM of 9x9 requires < 1MB and grid 6MB
For 643 with 9x9x6=54
angular bins DOM requires 510MBs
Using LPM of 9x9 requires < 1MB and grid 6MB
Less memory for stationary grid!
LPM
Results
Same coarse grid res.(6 dirs. isotropic sct.)
DOM with 54 ordinates on 1283
9x9 ordinates in LPM on 1283
spurious light ray
Results
First-order upwind
High-res. 2nd-order upwind LPM parametric advection
Second-order upwind
Results
MC with 106 particles, 3.5 mins.
MC with 5x106 particles, 17.6 mins
9x9 LPM,3.7 mins
Comparison with Monte Carlo
Results – Clouds Scenes
Back lit Top lit
Results - Marble
Constant scattering Perturbed absorption (isotropic, 52x1283)
Perturbed scattering Zero absorption (isotropic, 52x1283)
Results – Two “wavelengths”
Two simulations combined (isotropic, 52x1283)
Results
Hygia, Model courtesy of: Image-based 3D Models Archive, Telecom Paris (isotropic, 52x2563)
Results - Smoke
CFD smoke animation (isotropic, 72x643)
Summary
Running times (3 scat. generations x 6 sweeps): 643 (isotropic), LPM of 5x5 – 17 seconds 643 (isotropic), LPM of 9x9 – 125 seconds 643 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
Thanks!
Results
In scenes with variable , 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