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Real-time Rendering of Heterogeneous Translucent Objects with Arbitrary Shapes

Yajun Wang, Jiaping Wang, Nicolas Holzschuch, Kartic Subr, Jun-Hai Yong, Baining Guo

Simulating translucency

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Subsurface scattering

Simulating translucency

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Subsurface scattering

Previous work

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Previous work

•Monte-Carlo methods [DEJ99, PH00, LPT05 ]

physically accurate slow (several hours)

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[DEJ99] [PH00]

Previous work

•Dipole diffusion approximation [JMLH01]

faster (minutes) homogenous, no complex shape

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[JMLH01]

Previous work

•Extension of Dipole model real-time [DS03] ,multi-layer [DJ05] ,

scalable [AWB08]

homogenous

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[DS03]

[AWB08] [DJ05]

Previous work

•Precomputed Radiance Transfer [XGL07]

[WCPW08]

real-time precomputation

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[XGL07][WCPW08]

Previous work

•Diffusion Equation [Ish78, Sta95]

Regular grid and multi-grid scheme [Sta95]

first step off-line

The polygrid method [WZT08]

real-time , heterogeneous simple shape

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Challenges

1. real-time rendering and editing

2. heterogeneous materials

3. complex shapes

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Our Method

1. in real-time

2. with heterogeneous materials

3. in arbitrary domain

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Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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Regular Grid

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Our Method

Incoming radiance L i

InitializationIteration

Outgoing radiance L o

Optical Properties ( )x ( )xRadiant Fluence ( )x

Regular grid introduces shape constraintsOur domain for diffusion: tetrahedralized geometryInput: radiance incident on surfaceInput: radiance incident on surfaceDiffusion: Flux within objectOutput: Exiting radiance on surfaceExtract exiting radiance from flux at boundary

Diffusion Equation +FEM (2D example)

Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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QuadGraph

1. Representation of the object volume

2. GPU-friendly

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QuadGraph

•Construction : TetrahedralizationGoal: Regular connection

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Output : 4 classes of tetrahedra

[ACSYD05]

QuadGraph

•Construction: SplittingGoal: Regular connection

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Only tetrahedra in C0 and C1 left

QuadGraph

•Construction: TransformationGoal: Regular connection

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C0

C1

inner node

inner node + boundary node

QuadGraph

•Result: Regular connection grid

•For inner nodes -> 4 neighbors•For surface nodes -> 1 neighbor

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Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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Discretized DE

•Using the same method in [Sta95] [WZT08]

•Based on Quadgraph

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For inner nodes

For surface nodes

4 2

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( ) ( ) /( )

( ) ( )

j t j ijjt i

i i

k n n dn

wk n n

1

4 ( )2 ( ) ( )

1( )

2 ( )

ss t k sk

drt s

s sk

q nA n n d

Fn

A n d

Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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Preprocess and Storage

• Per-node values stored using textures one part for interior nodes one part for surface nodes

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Iteration on GPU

1. Initialization according to the illumination

2. Iteration on GPU until convergence

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Initalization During iteration Convergence

Speeding up scheme

•GPU cache coherence (Speed + 30%)

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Packing the data of nodes by its spatial location

Speeding up scheme

•Multi-resolution (Speed + >100% )

Several Quadgraphs with different resolution

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Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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High genus

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Surface nodes: 121k Inner nodes: 260k Speed: 29.4 FPS

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High curvature

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Surface nodes: 82k Inner nodes: 226k Speed: 22.1FPS

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Real-time rendering

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Real-time editing of materials

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Real-time editing of geometry shape

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Speed

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Quality

Our Method

•Overview•Solving the Diffusion Equation

▫Quadgraph▫Discretized Diffusion Equation▫Implementation on GPU

•Results•Limitations and Conclusions

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Limitations

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1. Materials with high frequency

2. Deformation changing the topology

ConclusionsA new volumetric representation(Quadgraph) for

solving the diffusion equation.

Real-time rendering and editing Heterogeneous materials Complex shapes

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Questions ?

Thank you!

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