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Many-light methods – Clamping & compensation Jaroslav Křivánek Charles University, Prague

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1.Generate VPLs 2 Instant radiosity 2.Render with VPLs

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3 Clamping 1000 VPLs - no clamping missing energy 1000 VPLs - clampingreference (path tracing)

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Clamping Compensation Kollig & Keller, MCQMC 2004

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Clamping reduces variance but some energy is lost Find formula for the lost energy Compute the lost energy by selective path tracing 5 Idea path tracing compensation full solution clamping

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6 Clamping x p VPL power VPL emission distribution (BRDF lobe at p – for a diffuse VPL can be folded into ) Geometry term oo Visibility min{ c, }

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Clamping evaluates this equation Can be written as 7 Formal derivation

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Unbiased solution 8 What’s missing? Path tracing compensation of the clamped energy VPLs w/ clamping

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Compensation faster than path tracing everything (many path terminated early) 9 Result path tracing compensation full solution clamping

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10 Biased result with clamping

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11 Unbiased result with compensation

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Dealing with Glossy Transport

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13 Ground truth 1,000 VPLs100,000 VPLs Instant radiosity with glossy surfaces

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Effect of clamping 14

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Virtual Spherical Lights Hašan, Křivánek & Bala, SIGGRAPH Asia 2009

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Cosine-weighted BRDF lobe at the VPL location Emission distribution of a VPL 16 Glossy Diffuse

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Glossy VPL emission: illumination spikes Common solution: Only diffuse BRDF at light location 17

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Remaining spikes 18

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Common solution: Clamp VPL contributions 19 Remaining spikes xx VPL contribution = VPL power. BRDF( x ). cos( x ). 1 / || p – x || 2 spike! p As || p – x || → 0, VSL contribution → ∞

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Instant radiosity: The practical version 20 Clamping and diffuse-only VPLs: Illumination is lost!

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Comparison 21 Clamped VPLs: Illumination loss Path tracing: Slow

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Recall: Emission Distribution of a VPL 22 Spike!

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What happens as #lights ? 23 Spiky lights converge to a continuous function!

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Idea: We want a “virtual area light” 24 Aggregate incoming illumination Aggregate outgoing illumination “Virtual area light” Problem: What if surface is not flat?

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25 VPL to VSL x p l Non-zero radius (r) Ω Integration over non-zero solid angle

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26 Light Contribution x p l Non-zero radius (r) Ω Integration over non-zero solid angle y

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27 Light Contribution x p l Non-zero radius (r) Ω Integration over non-zero solid angle y Problem: Finding y requires ray-tracing

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28 Simplifying Assumptions x p l Non-zero radius (r) Ω Integration over non-zero solid angle y Constant in Ω: –Visibility –Surface normal –Light BRDF Taken from p, the light location

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29 Light Contribution Updated x p l Non-zero radius (r) Ω Integration over non-zero solid angle

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30 Virtual Spherical Light All inputs taken from x and p –Local computation Same interface as any other light –Can be implemented in a GPU shader Visibility factored from the integration –Can use shadow maps

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Matrix row-column sampling –Shadow mapping for visibility –VSL integral evaluated in a GPU shader Need more lights than in diffuse scenes 31 Implementation

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Results: Kitchen Most of the scene lit indirectly Many materials glossy and anisotropic Clamped VPLs 34 sec (GPU) – 2000 lights New VSLs: 4 min 4 sec (GPU) – 10000 lights Path tracing: 316 hours (8 cores) 32

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Results: Disney concert hall Curved walls with no diffuse component Standard VPLs cannot capture any reflection from walls Clamped VPLs: 22 sec (GPU) – 4000 lights New VSLs: 1 min 26 sec (GPU) – 15000 lights Path tracing: 30 hours (8 cores) 33

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Results: Anisotropic tableau Difficult case Standard VPLs capture almost no indirect illumination Clamped VPLs: 32 sec (GPU) – 1000 lights New VSLs: 1 min 44 sec (GPU) – 5000 lights Path tracing: 2.2 hours (8 cores) 34

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Limitations: Blurring VSLs can blur illumination Converges as number of lights increases 5,000 lights - blurred 35 1,000,000 lights - converged

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Many-light methods do not deal well with glossy scenes –Artifacts or energy loss –Energy loss -> change of material perception Handling glossy effects with many-lights –Virtual Spherical Lights –[Davidovič et al. 2010] 36 Conclusions

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