Bruce Walter, Sebastian Fernandez, Adam Arbree, Mike Donikian,

Kavita Bala, Donald Greenberg Copyright of figures and other materials in the paper belong to original authors.

Presenter: 이성호

Korea University Computer Graphics Lab.

이성호| 26 July 2011 | # 2 KUCG |

Rendering equation

Korea University Computer Graphics Lab.

이성호| 26 July 2011 | # 3 KUCG |

BRDF (Bidirectional reflectance distribution function)

Korea University Computer Graphics Lab.

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Quiz (yes or no)

• (매질이 빛을 흡수하거나 산란하지 않는 경우) 관찰자가 광원에 가까워질수록 측정되는 빛의 세기가 세짂다?

아 눈부셔

이카루스의 추락

Korea University Computer Graphics Lab.

이성호| 26 July 2011 | # 5 KUCG |

Illumination Equation (Simplified)

result = Mi Gi Vi Ii S lights

Korea University Computer Graphics Lab.

이성호| 26 July 2011 | # 6 KUCG |

Illumination Equation

result = Mi Gi Vi Ii S lights

(BRDF)

Korea University Computer Graphics Lab.

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Illumination Equation

result = Mi Gi Vi Ii S lights

cos 𝜃

𝑑

𝑑 𝜃

for oriented light

Korea University Computer Graphics Lab.

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Types of Point Lights

• Omni

Spherical lights

• Oriented

Area lights, indirect lights

• Directional

HDR env maps, sun&sky

X=측정지점 𝑦𝑖=i번째 광원의 위치 𝜙𝑖=i번째 광원의 방향과 측정지점과의 각도

X

𝜙𝑖

Korea University Computer Graphics Lab.

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Quiz

result = Mi Gi Vi Ii S lights

𝑑 𝜃

• 빛의 세기는 광원과의 거리와 상관 없다며?

Korea University Computer Graphics Lab.

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Quiz

L = Mi Gi Vi Ii S lights

어느 텀을 연산하는 것이 가장 오래 걸리는가?

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Lightcuts Problem

Visible surface

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Lightcuts Problem

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Lightcuts Problem

Camera

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Key Concepts

• Light Cluster

Approximate many lights by a single brighter light (the representative light)

Korea University Computer Graphics Lab.

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Illumination Equation revisited

L = Mi Gi Vi Ii S lights

Korea University Computer Graphics Lab.

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Cluster Approximation

Cluster

𝐿 ≈ 𝐿 = Mj Gj Vj Ii 𝑖

j is the representative light

Korea University Computer Graphics Lab.

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Key Concepts

• Light Cluster

• Light Tree

Binary tree of lights and clusters

Clusters

Individual Lights

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Constructing lightcut

is the total intensity of the cluster

(oriented light only)

Create the smallest cluster according to this metric:

Korea University Computer Graphics Lab.

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Key Concepts

• Light Cluster

• Light Tree

• A Cut

A set of nodes that partitions the lights into clusters

Simple Example

#1 #2 #3 #4

1 2 3 4

1 4

Light Tree

Clusters

Individual Lights

Representative Light

4

Three Example Cuts

1 2 3 4

1 4

4

1 2 3 4

1 4

4

1 2 3 4

1 4

4

Three Cuts

#1 #2 #4 #1 #3 #4 #1 #4

회색 영역: 에러가 있는 부분

Three Example Cuts

1 2 3 4

1 4

4

1 2 3 4

1 4

4

1 2 3 4

1 4

4

Three Cuts

#1 #2 #4 #1 #3 #4 #1 #4

Good Bad Bad

Three Example Cuts

1 2 3 4

1 4

4

1 2 3 4

1 4

4

1 2 3 4

1 4

4

Three Cuts

#1 #2 #4 #1 #3 #4 #1 #4

Bad Good Bad

Three Example Cuts

1 2 3 4

1 4

4

1 2 3 4

1 4

4

1 2 3 4

1 4

4

Three Cuts

#1 #2 #4 #1 #3 #4 #1 #4

Good Good Good

Korea University Computer Graphics Lab.

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Cluster Approximation

Cluster

result ~ Mj Gj Vj Ii S lights

~

j is the representative light

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error≤ 𝐿 𝑗= Mub Gub Vub Ii

Cluster Error Bound

Cluster j

S lights

ub == upper bound

Korea University Computer Graphics Lab.

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Perceptual Metric

• Weber’s Law

Contrast visibility threshold is fixed percentage of signal

Used 2% in our results

• Ensure each cluster’s error < visibility threshold

Transitions will not be visible

Used to select cut

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Cut Selection Algorithm

Cut

• Start with coarse cut (eg, root node)

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Cut Selection Algorithm

Cut

• Select cluster with largest error bound

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Cut Selection Algorithm

Cut

• Refine if error bound 𝐿 𝑗> 2% of 𝐿 𝑗𝑗

𝐿 𝑗 = Mj Gj Vj Ii 𝑖

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Cut Selection Algorithm

Cut

Maximum 𝐿 𝑗

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Cut Selection Algorithm

Cut

Korea University Computer Graphics Lab.

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Cut Selection Algorithm

Cut

Maximum 𝐿 𝑗

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Cut Selection Algorithm

Cut

• Repeat until cut obeys 2% threshold

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Scalable

• Scalable solution for many point lights

0

100

200

300

400

500

600

0 1000 2000 3000 4000

Number of Point Lights

Tim

e (

secs)

Standard

Ward

Lightcut

Tableau Scene

Sub-linear cost

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Algorithm Overview

• Pre-process

Convert illumination to point lights

Build light tree

• For each eye ray

Choose a cut to approximate the illumination

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Convert Illumination

• HDR environment map

Apply captured light to scene

Convert to directional point lights using [Agarwal et al. 2003]

• Indirect Illumination

Convert indirect to direct illumination using Instant Radiosity [Keller 97] • Caveats: no caustics, clamping, etc.

More lights = more indirect detail

Korea University Computer Graphics Lab.

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Instant Radiosity

• Simulate indirect lighting

by placing a big number of point lights • where direct lighting hits the scene

• Research in this field tried hard

to keep the number of Virtual Point Lights low • while maintaining the indirect lighting effect

• Use a big number of VPLs without worrying

thanks to Lightcuts

Korea University Computer Graphics Lab.

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Lightcuts (128s) Reference (1096s)

Kitchen, 388K polygons, 4608 lights (72 area sources)

Lightcuts (128s) Reference (1096s)

Error Error x16

Kitchen, 388K polygons, 4608 lights (72 area sources)

Combined Illumination

Lightcuts 128s

4 608 Lights (Area lights only)

Lightcuts 290s

59 672 Lights (Area + Sun/sky + Indirect)

Combined Illumination

Lightcuts 128s

4 608 Lights (Area lights only)

Avg. 259 shadow rays / pixel

Lightcuts 290s

59 672 Lights (Area + Sun/sky + Indirect)

Avg. 478 shadow rays / pixel (only 54 to area lights)

Lightcuts Reference

Error x 16 Cut size

Kitchen, 388K polygons, 59,672 Lights

Kitchen, shadow ray false color

0 750 1500

Tableau, shadow ray false color

0 750 1500

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Talk Overview

• Lightcuts

Scalable accurate solution for complex illumination

• Reconstruction cuts

Builds on lightcuts

Use smart interpolation to further reduce cost

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Reconstruction Cuts

• Subdivide image into blocks

Generate samples at corners

• Within blocks

Interpolate smooth illumination

Use shadow rays when needed to preserve features • Shadow boundaries, glossy highlights, etc.

• Anti-aliasing

(5-50 samples per pixel)

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Image Subdivision

• Divide into max block size (4x4 blocks)

4x4 block

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Image Subdivision

• Divide into max block size (4x4 blocks)

• Trace multiple eye rays per pixel

• Subdivide blocks if needed

Based on material, surface normal, and local shadowing configuration

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Image Subdivision

• Divide into max block size (4x4 blocks)

• Trace multiple eye rays per pixel

• Subdivide blocks if needed

Based on material (same),

surface normal (30 degreees), and local shadowing configuration • (cone test)

• Compute samples at corners

Samples

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Cone test

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Image Subdivision

• Divide into max block size (4x4 blocks)

• Trace multiple eye rays per pixel

• Subdivide blocks if needed

Based on material, surface normal, and local shadowing configuration

• Compute samples at corners

• Shade eye rays using reconstruction cuts

Samples Reconstruction cut

Temple, 2.1M polygons, 505 064 lights, (Sun/sky+Indirect)

Temple, reconstruction cut block size

Kitchen with sample locations marked

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Sample Construction

• Compute a lightcut at each sample

• For each node on or above the cut

Create impostor light (directional light)

Reproduce cluster’s effect at sample

Cluster

Impostor Directional light

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Notation

For each sample k of the node of the cut n, store

Imposter’s intensity

Total radiance

Korea University Computer Graphics Lab.

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Computing reconstruction cut

Korea University Computer Graphics Lab.

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Reconstruction Cut

• Top-down traversal of light tree

Comparing impostors from nearby samples

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

• Recurse if samples differ significantly

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

• Discard if cluster occluded at all samples

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

• Interpolate if sample impostors are similar

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

• If cluster contribution small enough, shoot shadow ray to representative light

Lightcut-style evaluation

Not visited

Recurse

Occluded

Interpolate

Shadow ray

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Reconstruction Cut

Not visited

Recurse

Occluded

Interpolate

Shadow ray

Korea University Computer Graphics Lab.

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Result Statistics

• Temple model (2.1M polys, 505 064 lights)

Image algorithm Avg. eye rays

per pixel Image time

Lightcuts only 1 225s

Combined (anti-aliased) 5.5 189s

Cut type Avg. shadow rays per

cut

Lightcut 373

Reconstruction cut 9.4

Grand Central, 1.46M polygons, 143 464 lights, (Area+Sun/sky+Indirect)

Avg. shadow rays per eye ray 46 (0.03%)

Tableau, 630K polygons, 13 000 lights, (EnvMap+Indirect)

Avg. shadow rays per eye ray 17 (0.13%)

Bigscreen, 628K polygons, 639 528 lights, (Area+Indirect)

Avg. shadow rays per eye ray 17 (0.003%)

Korea University Computer Graphics Lab.

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Conclusions

• Lightcuts

Scalable, unified framework for complex illumination

Analytic cluster error bounds & perceptual visibility metric

• Reconstruction cuts

Exploits coherence

High-resolution, anti-aliased images

0

100

200

300

400

500

600

0 1000 2000 3000 4000

Number of Point Lights

Tim

e (

secs)

Standard

Ward

Lightcut

Korea University Computer Graphics Lab.

이성호| 26 July 2011 | # 74 KUCG |

Future Work

• Visibility bounds

• More light types

Spot lights etc.

• More BRDF types

Need cheap tight bounds

• Other illumination types

Eg, caustics

Korea University Computer Graphics Lab.

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• 아직 안 끝났다

Korea University Computer Graphics Lab.

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error≤ 𝐿 𝑗= Mub Gub Vub Ii

Cluster Error Bound

Cluster j

S lights

ub == upper bound

Korea University Computer Graphics Lab.

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Visibility term

Vub =1

Korea University Computer Graphics Lab.

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Geometric term

• Directional and omni

Trivial

• Oriented

Max(cos 𝜃)=1

However, tighter bound can be found

Korea University Computer Graphics Lab.

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Max(cos 𝜃)

Korea University Computer Graphics Lab.

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Max(cos 𝜃)

Korea University Computer Graphics Lab.

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Upper bound of oriented light

Korea University Computer Graphics Lab.

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Material term

• Diffuse

1

𝜋

• Phong Exploit max(cos 𝜃)

• Ward Refer [Walter 2005]

• Theoretically, any BRDF can be handled If it has cheap and tight bound