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～Reservoir Spatio-Temporal Importance Resampling～
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https://www.youtube.com/watch?v=AQXRiP6XQdo
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https://www.youtube.com/watch?v=Tk7Zbzd-6fs
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https://dl.acm.org/doi/10.1145/3478512.3488613
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Big Wave
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• 𝐼 𝐼 𝜀
• 𝜖
𝔼 𝐼 − 𝐼 = 𝜀
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𝐿𝑜
𝑥, 𝜔 = 𝐿𝑒
𝑥, 𝜔 + න
Ω
𝑓𝑟
𝑥, 𝜔′, 𝜔 𝐿𝑖
𝑥, 𝜔 cos 𝜃 𝑑𝜔
Emissive BSDF
=BRDF+BTDF
Light
解析解が無い（答えが一意に定まらない）。
再帰的に書きなおすことが出来る。
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𝐼 =
1
𝑁
𝑖=1
𝑁
𝑓 𝑥𝑖
𝜌 𝑥𝑖
𝑓 𝑥𝑖
：被積分関数
𝜌 𝑥𝑖
：確率密度関数
𝑁：サンプル数
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• Importance Sampling
• Stratified Sampling ( )
• Multiple Importance Sampling
• Quasi Monte Carlo Method ( )
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𝑓 𝑥 𝜌 𝑥
𝑃 𝑋 ≤ 𝑥
𝑃 𝑥 𝑃−1 𝑢
𝑓 𝑥
※レンダリングにおける具体的な例は[Pocol 2021]を参照。
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𝑥
𝑓 𝑥
𝑎 𝑏
strata
0
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𝑤𝐵𝑆𝐷𝐹
𝑥 =
𝑝𝐵𝑆𝐷𝐹
𝑥
𝑝𝐵𝑆𝐷𝐹
𝑥 + 𝑝𝑙𝑖𝑔ℎ𝑡
𝑥
𝑤𝑙𝑖𝑔ℎ𝑡
𝑥 =
𝑝𝑙𝑖𝑔ℎ𝑡
𝑥
𝑝𝐵𝑆𝐷𝐹
𝑥 + 𝑝𝑙𝑖𝑔ℎ𝑡
𝑥
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•
•
𝑝 𝑀 𝑀 ≥ 1 𝐗 = 𝑋1
, ⋯ , 𝑋𝑀
𝑤𝑗
3. 𝐗 𝑤1
, ⋯ , 𝑤𝑀
𝑌
𝑤𝑗
= ො
𝑝 𝑋𝑗
𝑝 𝑋𝑗
を 𝑌 Ƹ
𝑝
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𝐼 =
1
𝑁
𝑖=1
𝑁
𝑓 𝑌𝑖
Ƹ
𝑝 𝑌𝑖
∙
1
𝑀
𝑗=1
𝑀
Ƹ
𝑝 𝑋𝑖𝑗
𝑝 𝑋𝑖𝑗
• 𝑓が Ƹ
𝑝 𝑝
• 𝑀 𝑁
補正項がくっついている
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𝑀
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𝑓 = 𝐹𝑟
𝐺 𝑉 𝐿𝑒
Ƹ
𝑝 = 𝐹𝑟
𝐺 𝐿𝑒
𝐹𝑟
𝐺
𝑉
𝐿𝑒
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比較的軽量な候補サンプルが生成できる!!
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• 𝑀
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• 𝑀
• 𝑥1
, 𝑥2
, ⋯ , 𝑥𝑀
•
𝑀
• 𝑥1
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• 𝑥1
𝑚 𝑥𝑚
• 𝑥𝑖
• 𝑥𝑖
𝑥𝑚+1
𝑤 𝑥𝑖
σ
𝑗=1
𝑚 𝑤 𝑥𝑗
𝑤 𝑥𝑚+1
σ
𝑗=1
𝑚+1 𝑤 𝑥𝑗
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• 𝑥𝑚+1
𝑥𝑖
𝑤 𝑥𝑖
σ
𝑗=1
𝑚 𝑤 𝑥𝑗
1 −
𝑤 𝑥𝑚+1
σ
𝑗=1
𝑚+1 𝑤 𝑥𝑗
=
𝑤 𝑥𝑖
σ
𝑗=1
𝑚+1 𝑤 𝑥𝑗
𝒎 𝒎 + 𝟏
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𝑝 𝑥𝑖
𝑤𝑖
𝑀 = 32
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• 𝑀 Ƹ
𝑝
• 𝑓
𝑀
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𝐿
𝑟𝑖𝑠
1,𝑀 =
𝑓(𝑦)
Ƹ
𝑝(𝑦)
∙
1
𝑀
𝑗=1
𝑀
𝑤 𝑥𝑗
= 𝑓 𝑦 ∙
1
Ƹ
𝑝 𝑦
1
𝑀
𝑗=1
𝑀
𝑤 𝑥𝑗
= 𝑓 𝑦 𝑊 𝐱, 𝑧 𝑊 𝐱, 𝑧 =
1
Ƹ
𝑝 𝑥𝑧
1
𝑀
𝑖=1
𝑀
𝑤𝑖
𝑥𝑖
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𝑊 𝐱, 𝑧 Τ
1 𝑝 𝑦
• 𝑊 𝐱, 𝑧
𝔼 𝑊 𝐱, 𝑧 =
1
𝑝 𝑦
𝑍 𝑦
𝑀
𝑍 𝑦 = 𝑖 | 1 ≤ 𝑖 ≤ 𝑀 and 𝑝𝑖
𝑦 > 0
𝑝𝑖
𝑦 > 0
𝑦
𝑖 𝑝𝑖
𝑦 = 0の 𝑦
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𝔼
𝑀
𝑍 𝑦
𝑊 𝐱, 𝑧 =
1
𝑝 𝑦
𝐼 =
1
𝑁
𝑖=1
𝑁
𝑓 𝑌𝑖
Ƹ
𝑝 𝑌𝑖
∙
1
𝑍 𝑌𝑖
𝑗=1
𝑀
Ƹ
𝑝 𝑋𝑖𝑗
𝑝 𝑋𝑖𝑗
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𝑍
• 𝑍
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if 𝑝 𝜔 > 0 when 𝑓 𝜔 > 0
if Ƹ
𝑝 𝜔 > 0 and 𝑞𝑗
𝜔 > 0 when 𝑓 𝜔 > 0
if Ƹ
𝑝𝑖
𝜔 > 0 and 𝑞𝑗
𝜔 > 0 when 𝑓 𝜔 > 0
𝑍 𝜔 𝑀
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Ƹ
𝑝
Ƹ
𝑝
Ƹ
𝑝𝐴
𝑎 > 0 but Ƹ
𝑝𝐵
𝑎 = 0
Ƹ
𝑝𝐴
𝑑 = 0 Ƹ
𝑝𝐵
𝑎 = 0
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𝑋𝑖
𝑓 Ω
𝑝
𝑝𝑖
𝑋
𝑚𝑖
𝑋𝑖
𝑊𝑖
Τ
1 𝑝𝑖
𝑋𝑖
Ω𝑖
𝑋𝑖
𝑝𝑖
𝑓
𝑓 𝑌 𝑊𝑌
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• 𝑋𝑖
Ω𝑖
𝑊𝑖
∈ ℝ
Τ
1 𝑝𝑖
𝑋𝑖
• 𝑓 Ω 𝑇𝑠
: Ω𝑠
→ Ω
𝑋𝑠
∈ Ω𝑠
Ω
•
Τ
𝜕𝑇𝑖
𝜕𝑥
• 𝑇𝑖
𝑤𝑖
= 𝑚𝑖
𝑇𝑖
𝑋𝑖
Ƹ
𝑝 𝑇𝑖
𝑋𝑖
𝑊𝑖
∙ 𝜕𝑇𝑖
𝜕𝑋𝑖
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• 𝐱𝑖
, 𝐱𝑖+1
𝐲𝑖
𝐲𝑖+1
= 𝐱𝑖+1
•
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•
𝐲𝑖+1
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• 𝐲𝑖+1
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𝑦𝑖+1
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𝐱3
𝐱4
𝐱4
𝐱1
𝐱2
𝐲1
𝐲2
𝐲3
𝐱4
𝐲1
𝐱2
𝐲1
↔ 𝐱2
↔ 𝐱3
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𝐱𝑖+1
− 𝐱𝑖
≥ 𝑑𝑚𝑎𝑥
𝐱𝑖
, 𝐱𝑖+1
, 𝐲𝑖
𝑦𝑖+1
𝑥𝑖+1
𝑥𝑖+1
− 𝑦𝑖
≥ 𝑑𝑚𝑎𝑥
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𝑖 𝑋𝑖
𝑡 𝑊
𝑋𝑖
𝑡
𝑌𝑖
𝑡−1 𝑋𝑖
𝑡
𝑍𝑖
𝑗 𝑍𝑖
𝑍𝑗
𝑌𝑖
𝑡 𝑍𝑖
≔ 𝑌𝑖
𝑡
𝐼𝑖
𝑡 ≈ 𝑓𝑖
𝑌𝑖
𝑡 𝑊
𝑌𝑖
𝑡
※𝑌𝑖
𝑡−1を 𝑡 − 1 𝑖
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• 𝑀𝑟
𝑀𝑐
•
• 𝑀𝑟
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• LightingPasses::RenderDirectLighting()
• ExecuteRayTracingPass(…, …, “GenerateInitialSamples”, …, …);
• ExecuteRayTracingPass(…, …, “TemporalResampling”, …, …);
• ExecuteRayTracingPass(…, …, “SpatialResampling”, …, …);
• ExecuteRayTracingPass(…, …, “ShadeSamples”, …, …);
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• LightingPasses::RenderBrdfRays()
• ExecuteRayTracingPass(…, …, “BrdfRayTracingPass”, …, …);
• ExecuteRayTracingPass(…, …, “ShadeSecondarySurfaces”, …, …);
• ExecuteRayTracingPass(…, …, “GITemporalResampling”, …, …);
• ExecuteRayTracingPass(…, …, “GISpatialResampling”, …, …);
• ExecuteRayTracingPass(…, …, “GIFinalShading”, …, …);
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• ReSTIRPT/Source/RenderPasses/ReSTIRPTPass
• C++ ReSTIRPTPass.cpp
• Slang
• Shift.slang
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• [Talbot 2005] Justin F. Talbot, Davit Cline, Parris Egbert, “Importance Resampling fo Global Illumination”, ESGR’05, pp.139-146, 2005
• [Bitterli 2020] Benedikt Bitterli, Chris Wyman, Matt Pharr, Peter Shirley, Aaron Lefohon, Wojciech Jarosz, “Spatiotemporal reservoir
resampling for real-time ray tracing with dynamic direct lighting”, ACM Transactions on Graphics, Vol.39, No.4, 2020.
• [Wyman 2021] Chris Wyman, Alexey Panteleev, “Rearchitecting Spatiotemporal Resampling for Production”, High-Performance Graphics 2021.
• [Ouyang 2021] Y.Ouyang, S.Liu, M.Kettunen, M.Pharr, J.Pataleoni, “ReSTIR GI: Path Resampling for Real-Time Path Tracing”, High-
Performance Graphics 2021.
• [Lin 2022] Daqi Lin, Markus Kettunen, Benedikt Bitterli, Jacopo Pantaleoni, Cem Yukesel, Chris Wyman, “Generalized Resampled Importance
Sampling”, SIGGRAPH 2022.
• [Veach 1997] Eric Veach, “Robust Monte Carlo Methods for Light Transport Simulation”, Ph.D. dissertation, Standford University, 1997.
• [Shocker 2022] Shocker, “ (Path Tracing)”, memoRANDOM, https://rayspace.xyz/CG/contents/path_tracing/, 2022.
• [Pocol 2021] Pocol, “Direct3D 12 ”, , 2021.
• [KiNaNkomoti 2022] KiNaNkomoti, “Pathtracing Caustics ”, 8 , 2022.
• [Hirai 2022] , , “ 7 ”, CEDEC KUSYU 2022
• [NVIDIA 2023] NVIDIA, “ 2077 4 11 ”,
https://www.nvidia.com/ja-jp/geforce/news/cyberpunk-2077-ray-tracing-overdrive-update-launches-april-11/, 2023.
• [Capcom 2019] Capcom, “Devil May Cry5 Special Edition”, https://www.devilmaycry.com/5se/jp/, 2019.
• [EmbarkStudios 2023] EmbarkStudios, “kajiya”, https://github.com/EmbarkStudios/kajiya, 2023.
• [Halen 2021] Henrik Halen, Andres Brinck, Kyle Hayward, Xiangshun Bei, “Global Illumination Based on Surfels”, SIGGRAPH 2021 Advances in
Real-Time Rendering in Games course, 2021.
• [Boksansky 2021] Jakub Boksansky, Paula Jukarainen, Chris Wyman, “Rendering Many Lights With Grid-Based Reservoirs”, Ray Tracing Gems 2,
Chapter 23, pp.351-365, 2021.
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