Participating Media Illumination using Light Propagation Maps

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Participating Media Illumination using Light
Propagation Maps

• Raanan Fattal
• Hebrew University of Jerusalem, Israel

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Introduction

• In media like fog, smoke and marble light is
• Scattered
• Absorbed
• Emitted
• Realistic rendering by accounting such phenomena

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Introduction

• The Radiative Transport Eqn. models these events

I(x,w) radiation intensity (W/m2sr)
emission
out-scattering
absorption
change along w
in-scattering
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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

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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

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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
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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

cell volume
angular index
spatial indices
Discrete light directions inside a spatial voxel
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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 rays cross section)
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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

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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

stationary grid
Offer a practical remedy to the ray effect
No interpolations needed for light flux, false
scattering is eliminated
Light Propagation Maps, 2D grids of rays, each
covering different set of directions
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New Method - Setup

• Variables
• average scattered light (unlike DOM)
• (need only 1 angular bin for isotropic
  scattering!)
• - rays intensity
• - rays position
• 
  Goal compute

stationary grid
light propagation map LPM
2D indexing
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New Method - Derivation

• Next derive the eqns. for and
  their relation to

Plug in L instead of I, and R rays pos.
instead of x
Note in the in-scattering term, I wasnt
replaced by L
Introduce an unpropagated light field U instead
of sources
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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,w)
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New Method an Iteration

• Rays integrate U emptying relevant bins

• Light scattered from rays added to U, I

stationary grid

• Proceed to next layer - repeat

• LPM rays dirs. must be included in Us
• Coarse bins of I, U contain scattered light,
  filtered by phase func.
• Linear light motion inadequate to simulate
  Caustics

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Results
DOM with 54 angular bins
For 643 with 9x9x654 angular bins DOM requires
510MBs Using LPM of 9x9 requires lt 1MB and grid
6MB
LPM
9x9 angles in LPM, 16 in grid
Less memory for stationary grid!
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Results
DOM with 54 ordinates on 1283
9x9 ordinates in LPM on 1283
Same coarse grid res. (6 dirs. isotropic sct.)
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Results
First-order upwind
Second-order upwind
High-res. 2nd-order upwind
LPM parametric advection
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Results
Comparison with Monte Carlo
MC with 5x106 particles, 17.6 mins
MC with 106 particles, 3.5 mins.
9x9 LPM,3.7 mins
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Results Clouds Scenes
Back lit
Top lit
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Results - Marble
Constant scattering Perturbed absorption
(isotropic, 52x1283)
Perturbed scattering Zero absorption (isotropic,
52x1283)
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Results Two wavelengths
Two simulations combined (isotropic, 52x1283)
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Results
Hygia, Model courtesy of Image-based 3D Models
Archive, Telecom Paris (isotropic, 52x2563)
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Results - Smoke
CFD smoke animation (isotropic, 72x643)
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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

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• Thanks!

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Results

• In scenes with variable s, indirect light travels
  straight

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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