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Spatial Directional Radiance Caching

Václav GassenbauerCzech Technical University in Prague

Jaroslav KřivánekCornell University

Kadi BouatouchIRISA / INRIA Rennes

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GoalAcceleration of Global Illumination

Computation on Glossy Surfaces

Adapt glossiness of surfaces

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Previous WorkIrradiance caching (IC)

◦[Ward et al. 88], [Ward and Heckbert 92]◦ Indirect illumination changes slowly →

interpolateVariants of IC

◦[Tabellion and Lamorlette 04], [Brouillat et al. 08], [Arikan et al. 05], …

Radiance caching (SHRC) ◦[Křivánek et al. 05]

Other techniques ◦[Hinkenjann and Roth 07, …]

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MotivationRadiance caching limitation

◦Uniform sampling of full hemisphere◦Low glossy surfaces◦Conversion of the scene BRDFs into the

frequency domain in preprocess

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SDRC – OverviewCaching schemeCache structureNew record computationSpatial / Directional InterpolationOutgoing radiance computation

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Spatial Cache Lookup

SpatialCacheMiss!

BRDFImportanceSampling

Spatial Directional Caching SchemeSpatialCache

p2

iL

p1

Project Sample onto Unit Square

Store incache

iLiL

N

i

oL1

/pdfoL

Spatial Cache Lookup

iL

SpatialCache

Hit!

DirectionalCache HIT!

DirectionalCache MISS!

Directional

CacheUpdate

M

i

oL1

/pdfoL

Directional Cache

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Structure of the Two Caches

kD-tree(directional cache)

Octree (spati

al cache)

SpatialCache

iL

iL

iL

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New Record ComputationGenerate N

samples using BRDF importance sampling

pCompute incoming radiance using ray casting and photon mapTransform samples onto 2D domain

Build a k-D tree upon the samples

L-tree

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Spatial Interpolation

p

Collect L-trees that can be used for interpolation at p (borrowed from RC)

For all L-trees found compute the spatial weight

1

1

i

i

isi Rw nn

ppp

Spatial

Cache

Spatial Cache Lookup

p1

p2p

SpatialCache

Hit!L-tree(p2)

p2

L-tree(p1)p1

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Directional Interpolation

p2

p

L-tree(p2)

Generate M(M<<N) samples using BRDF importance sampling

For all the samples try find nearby radiance samples in L-tree(p2) in S(p)

Transform samples onto unit domain

Update L-tree(p2) if necessary

Radiance sample found

Radiance not sample found→ ray tracing

L-tree(p2)

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Which Radiance Samples Are Nearby?

i-th L-tree

dr

2d

2

1,0maxr

w jikj

dik

ininin

Compute search radius for each radiance sample

Collect nearby radiance samples

Compute directional weights

dr inj

inik

inik

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Incoming Radiance InterpolationInterpolate all collected radiance sample

◦Sums run over all radiance samples from all contributing L-trees.

Product of spatial and directional

weights

k-th radiance sample stored in

the i-th L-treeInterpolate

d incoming radiance

Si Tkj

dik

si

Si Tkikj

dik

si

j

i

i

ww

LwwL in

inin

inin

p

pp

,~

Outgoing Radiance ComputationEvaluate Monte Carlo Estimator

interpolated incoming radiance

# render

samples

Sampling probability ofoutin j

Estimated outgoing radiance

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M

j j

jjj BRDFLM

L1 ,pdf

cos,,~1,~

outin

inoutinininoutout p

p

ResultsSHRC vs. SDRC

◦SHRC = Spherical harmonics caching◦SDRC = new Spatial-Directional caching

MC vs. SHRC vs. SDRC vs. REF◦MC = Monte Carlo importance sampling◦REF = reference solution

SDRC scalabilityAnimation

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SHRC vs. SDRC

SDRC adapts to the BRDF lobe exponent automatically

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MC vs. SHRC vs. SDRC vs. REF

SDRC produce less noise than MC SDRC produce no ringing artifacts as SHRC.

MC SDRC (new)

SHRC REF

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SDRC scalabilityN=64 / t≈6.2s

N=128 / t≈13.0s N=256 / t≈23.6s

SDRC

MC

Rendering time is O(N).

indirect lighting compu-tation time of

the detail

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AnimationWithout reusing cache

record

With reusing cache record- Flickering reduced

Side-by-side comparison

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DiscussionInterpolation

◦MC performs better than SDRC for highly glossy materials

Supported materials◦Spatially varying ones without sudden

changes◦Availability of sampling procedure

Memory consumption◦≈ higher memory requirements than

SHRC (N = 512 and SH order of 10)

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ConclusionIndirect lighting computation on glossy

surfacesPROS:

+Exploits spatial / directional coherence+No blurry / banding artifacts+Adapts automatically to the glossiness+Less noisy than MC

CONS−Higher memory requirements−Potentially difficult parallelization

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Future WorkPrecise formalization of illumination

coherenceDecrease flickering in animation

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AcknowledgementsChess pieces courtesy of T.

HachisukaRay tracing system - PBRT

Thank you for your attention

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Cache Record Density Control