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/m2sr)
emission
change along w
in-scattering
absorption
out-scattering
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
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
1st order
2nd 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 2D Light Propagation Maps (LPM) and not use DOM
stationary grid
eqns. in 3D 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,
2D 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
2D
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, Ifields
wasn’t(zero
replaced
by L
Approx.
using discrete
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 3D)
‫‏‬
‫‏‬
‫‏‬
‫‏‬
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
o
o
o
o
For 643 with 9x9x6=54
o
LPM
angular bins DOM requires
510MBs
9x9 angles in LPM, 1+6 in grid
Less memory for
stationary grid!
Using LPM of 9x9 requires
< 1MB and grid 6MB
Results
DOM with 54 ordinates on 1283
spurious light ray
9x9 ordinates in LPM
on 1283
Same coarse grid res.
(6 dirs. isotropic sct.)
Results
First-order upwind
Second-order upwind
High-res. 2nd-order upwind
LPM parametric advection
Results
Comparison with Monte Carlo
MC with 106 particles,
3.5 mins.
MC with 5x106
particles, 17.6 mins
9x9 LPM,3.7 mins
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 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