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

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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