BSSRDF 理論と実装 / BSSRDF Theory and Implementation

レイトレ合宿4!?のセミナーで使用した資料 + 会場で口頭で話したことをまとめた資料です。
スライドの趣旨：BSSRDFの基礎理論と実装面の話、コードレベルの話は無し。
主な対象者：パストレーシングなどのオフラインレンダリングアルゴリズムの実装経験があり、ある程度慣れている方。

2017/12/8: BSSRDFの基礎的な理論を紹介する記事を書きました。
https://rayspace.xyz/CG/contents/BSSRDF/

https://twitter.com/Shocker_0x15

Transcript

1. ཧ࿦ͱ࣮૷
   ౉෦৺
   !4IPDLFS@Y
   ϨΠτϨ߹॓
   https://sites.google.com/site/raytracingcamp4/
   BSSRDF
   

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2. #443%'
   #JEJSFDUJPOBM4DBUUFSJOH4VSGBDF3FGMFDUBODF%JTUSJCVUJPO'VODUJPO
   ೔ຊޠͩͱ
   ૒ํ޲ ਂ૚
   ࢄཚ໘൓ࣹ཰෼෍ؔ਺
   ͱ͔
   S(xi, i, xo, o
   )
   ෺ମද໘ʹ͓͚Δޫͷ
   ೖࣹҐஔɺೖࣹํ޲ɺग़ࣹҐஔɺग़ࣹํ޲
   ࣍ݩؔ਺
   ද໘Լࢄཚ 4VC4VSGBDF4DBUUFSJOH
   ͷϨϯμϦϯάʹ༻͍Δ
   

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3. #443%'ʹΑΔ൓ࣹޫ
   ൺֱɿ#3%'ʹΑΔ൓ࣹޫ
   #3%'͸
   ʮ͋Δํ޲͔Βͷඍখ์ࣹর౓ʯΛ์ًࣹ౓ʹม׵͢Δ
   #443%'͸
   ʮ͋Δ఺ɾ͋Δํ޲͔Βͷඍখ์ࣹଋʯΛ์ًࣹ౓ʹม׵͢Δ
   

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4. Circle Tracing for Subsurface Scattering A Practical Model for Subsurface Light Transport
   ද໘Լࢄཚࡐ࣭
   

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5. ͦΕͬΆͨ͘͠#3%' #443%'
   #443%'͸ޫ͕௚઀౰ͨΒͳ͍എ໘ʹ΋ಁա
   ΍ΘΒ͔ͳӄӨɺ࣭ײΛ࠶ݱͰ͖Δ
   

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6. ϘϦϡʔϜϨϯμϦϯάํఔࣜ
   Li
   (x, ) = T(xS, x)Lo
   (xS, )+
   xS x
   0
   T(x , x) LV
   e
   (x , ) +
   s
   (x )
   S2
   fp
   (x , , )L(x , )d ds
   ʮ෺ମද໘Λग़ͨޫ͕ݮਰͨ͠෼ʯ
   
   ʮ్தͰൃޫͱJOTDBUUFSJOHͰ૿͑ͨޫ͕ݮਰͨ͠෼ʯ
   

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7. ؔ༩ഔ࣭ͷύϥϝλʔ
   ٵऩ܎਺ ࢄཚ܎਺ ফࢄ܎਺
   ෺ମද໘ʹ͓͚Δ#3%'ʹ͍ۙ ͕ɺਖ਼نԽ͞Ε͍ͯΔ
   
   ࢄཚΞϧϕυ
   Ґ૬ؔ਺
   ޫ͕ؔ༩ഔ࣭ͱ൓Ԡͨ͠ͱ͖ʹࢄཚ͕ى͖Δ֬཰
   

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8. ද໘Լࢄཚ͸ϘϦϡʔϜϨϯμϦϯάํఔࣜ 7-5&
   Λ
   ਅ໘໨ʹϞϯςΧϧϩ๏Ͱղ͘͜ͱͰ΋ϨϯμϦϯάͰ͖Δ
   ͕ɺଟ͘ͷද໘Լࢄཚࡐ࣭͸
   ࢄཚɺٵऩͱ΋ʹඇৗʹى͖΍͔ͭ͘͢ඇৗʹΞϧϕυ΋ߴ͍ɿ
   ճ͘Β͍ࢄཚͯ͠΋·ͩ·ͩΤωϧΪʔΛ͍࣋ͬͯΔͨΊ
   ܭࢉ΋ଧͪ੾Γʹ͍͘
   ෺ମද໘ԼͰඇৗʹଟ͘ͷϨΠΛτϨʔε͢Δඞཁ͕͋Γ௒ߴෛՙ
   

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9. #443%'ͷཧ࿦
   

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10. ࢄཚ͕ඇৗʹڧ͍ഔ࣭ͷ৔߹ɺ
    ࢄཚ͍ͯ͠Δ͏ͪʹޫͷํ޲ੑ͕ࣦΘΕΔ
    àٿ໘ௐ࿨ؔ਺ల։ͷ ࣍ͷ߲Ͱۙࣅ
    લํࢄཚ͸ࢄཚ͍ͯ͠ͳ͍͜ͱʹ͍ۙ
    à౳ํࢄཚͱमਖ਼͞ΕͨࢄཚύϥϝλʔɹɹɹɹͰߟ͑௚͢
    

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11. ඇৗʹ໘౗ͳಋग़աఔΛܦͯ
    ޙ೔8ϖʔδܝࡌ༧ఆ
    
    àIUUQTSBZTQBDFYZ[$(DPOUFOUT444@EJGGVTJPO@BQQSPYJNBUJPO
    

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12. Α͘஌ΒΕ֦ͨࢄํఔࣜͷܗࣜʹؼண
    ղ͘ʂ ৄࡉল͘ʂʂ
    
    ڥք৚݅΋ٿ໘ௐ࿨ؔ਺࣍ۙࣅʂ
    ղ͘ʂʂ ৄࡉল͘ʂʂʂʂʂ
    
    

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13. ֦ࢄϓϩϑΝΠϧ %JGGVTJPO%JQPMFϞσϧ<+FOTFO>
    
    ΛಘΔ
    ֦ࢄϓϩϑΝΠϧ͸ɹ͔Β಺෦ʹಁաͨ͠์ࣹଋʹΑͬͯ
    ɹͷ֎ଆʹͲΕ͚ͩͷ์ࣹൃࢄ౓͕ੜ͡Δ͔Λࣔ͢
    Ծ૝తͳ఺ޫݯΛͭߟ͑Δ
    à%JQPMFϞσϧ
    

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14. ෺ମද໘ͷ#4%' ׬શڸ໘ಁա
    ͱ౷߹
    Ұճࢄཚ ਅ໘໨ʹ7-5&Λղ͘
    ͱ΋߹ΘͤΔඞཁ͕͋Δ
    ͭͷϑϨωϧ߲ɿ
    ෺ମ಺෦΁ͷޫͷಁա཰ɺग़͍ͯ࣌͘ͷಁա཰
    ֦ࢄϓϩϑΝΠϧʹΑͬͯهड़͞ΕΔ
    ์ࣹൃࢄ౓Λ์ًࣹ౓ʹม׵
    

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15. ೚ҙͷ෺ମද໘ͷ#4%'ʹҰൠԽ<%POOFS>
    
    ͋ʹ͋ํ޲͔Βഔ࣭಺ʹೖࣹ͢Δ์ࣹଋΛهड़
    ͋ͷ֎ଆ͔Βग़Δ์ࣹൃࢄ౓Λܭࢉɺ
    ͞ΒʹҰ༷ͳ์ًࣹ౓ʹม׵
    ͋ʹ͓͍ͯɹํ޲ʹग़ࣹ͢Δ์ًࣹ౓ͷ෼෍Λ
    #4%'ʹैͬͯܭࢉ
    

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16. #443%'ͷ࣮૷
    

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17. ࣮૷ʹ͓͚ΔΞϓϩʔν
    Α͘஌ΒΕ͍ͯΔ΋ͷʹஈ֊ख๏ 1#35W౳ʹ࣮૷ྫ
    ͕͋Δ
    •  ࣄલܭࢉ఺ͷ෼෍Λ͏·͘ௐ੔͢Δඞཁ͕͋Δ
    •  #443%'ʹΑΔؒ઀ޫΛߟྀͰ͖ͳ͍˞
    •  ϓϩάϨογϒ͞ʹ͚ܽɺ
    طଘͷޫ༌ૹΞϧΰϦζϜͱ౷߹͕໘౗
    ࣄલʹද໘Լࢄཚ෺ମͷද໘ʹ఺܈Λੜ੒
    લॲཧͱ֤ͯ͠఺Ͱ์ࣹর౓ܭࢉ<+FOTFO>
    ϝΠϯύε
    γΣʔσΟϯά఺ͷपลͷ఺Λݕࡧɺද໘Լࢄཚͷد༩ΛٻΊΔ
    ൺֱత҆ఆͨ݁͠Ռ͕ಘΒΕΔ͕ɺܽ఺΋͋Δ
    

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18. #443%'ͷ࣮૷
    ϓϩάϨογϒͳΞϓϩʔν
    1#35W౳
    

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19. ύετϨʔγϯάʹ͓͚Δ#3%'
    ೖࣹํ޲Λαϯϓϧ
    

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20. ύετϨʔγϯάʹ͓͚Δ#443%'
    ೖࣹҐஔͱೖࣹํ޲Λαϯϓϧ
    ग़ࣹҐஔΛத৺ͱͯ͠
    ֦ࢄϓϩϑΝΠϧʹൺྫͨ͠ೖࣹҐஔͷαϯϓϦϯά͕๬·͍͠
    

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21. ͞Βʹ
    ೚ҙͷ෺ମද໘ʹҰൠԽ͞Εͨ#443%'ͷ৔߹
    #443%'ʹؚ·ΕΔͭͷ#4%'ͷੵ෼΋ධՁ͢Δඞཁ͕͋Δ
    

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22. ࣮૷Ҋ
    ᶃ ᶄ ᶅ ᶆ
      ग़ࣹҐஔͰ#4%'ΛαϯϓϦϯά
    /FYU&WFOU&TUJNBUJPO΋͓ͯ͘͠
      #5%'͔ͩͬͨͭ444෺࣭ͷ৔߹
    ೖࣹҐஔͷαϯϓϦϯά
      ద౰ͳ಺෦ೖࣹํ޲ͷαϯϓϦϯά
      ೖࣹҐஔͰ#4%'ͷαϯϓϦϯά
    /FYU&WFOU&TUJNBUJPO΋͓ͯ͘͠
    اΈɿ Λந৅Խ͢Ε͹΄΅طଘͷύετϨʔγϯάͷίʔυͷ··
    ͖ͬ͢Γ࣮ͨ͠૷ʹͳΔͷͰ͸ʁ
    

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23. ݱ࣮
    ద౰ʹબΜͩ಺෦ೖࣹํ޲Ͱ͸
    /FYU&WFOU&TUJNBUJPO͕ۃΊͯ௿ޮ཰ʹͳΔ
    
    ֎෦ೖࣹํ޲ͷαϯϓϦϯά͕શ൓ࣹͱͳͬͨ৔߹͸ϦδΣΫτ
    #443%'ͷڥք৚͕݅શ൓ࣹߟྀࡁΈ
    
    ௿͍د༩
    ϦδΣΫτ
    

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24. ղܾҊ
    ߴ͍د༩
    ಺෦ೖࣹํ޲͕
    શ൓ࣹํ޲͸ى͜Γ͑ͳ͍
    #443%'ʹ͓͚Δ಺෦ɾ֎෦ೖࣹํ޲ͷαϯϓϦϯάʹ͸
    ͍ͣΕ͔ʹࣗ༝౓͕͋Δ
    à֎ଆ͔ΒαϯϓϦϯάͨ͠΄͏͕෼ࢄΛݮΒͤΔ
    4VCEJWJTJPO/&&<%BWJE>
    #443%'Ͱ͸ͳ͘7-5&Λਅ໘໨ʹղ͘λΠϓ͕ͩɺࣅͨΑ͏ͳߟ͑ʁ
    

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25. #443%'ͷϓϩάϨογϒͳ࣮૷
    ೖࣹҐஔͷαϯϓϦϯά
    

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26. ৭ʑํ๏͸͋Δ͕
    ग़ࣹ఺Λத৺ͱͯ͠#443%'ͷݶքൣғɹɹͷٿΛద౰ʹઃ͚ͯ
    ͦͷ಺෦๏ઢํ޲ͰϓϩʔϒϨΠΛඈ͹͢
    ܏͖͕ٸͳՕॴͷαϯϓϦϯάີ౓͕Լ͕ͬͯ͠·͏໰୊
    à෼ࢄ͕૿͑Δ
    ٸͳՕॴ͸໘ੵ͋ͨΓͰ
    ϨΠ͕ώοτ͠ʹ͍͘
    

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27. "YJT.*4<,JOH>
    ઀ઢํ޲͔Βͩͱ
    Α͘ώοτ͢Δ
    ઀ઢํ޲͔Β΋ϓϩʔϒϨΠΛඈ͹͢
    ϓϩʔϒϨΠ͕Ԋ͏ํ޲ɿ
    ๏ઢͱͭͷ઀ઢํ޲͸֬཰తʹબ୒
    د༩Λଟॏॏ఺తαϯϓϦϯάΛ࢖ͬͯܭࢉ
    

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28. ֦ࢄϓϩϑΝΠϧ
    ೖࣹҐஔ·Ͱͷڑ཭ͷαϯϓϦϯά͸
    ֦ࢄϓϩϑΝΠϧʹൺྫͨ͠1%'͔Βߦ͍͍ͨ
    à$%'ΛٻΊͯٯؔ਺๏Λ࢖͏
    ೖࣹ఺·Ͱͷڑ཭ͷαϯϓϦϯά
    

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29. $%'͸ҰԠܭࢉͰ͖Δ͕ [ͷ޲͖ͷఆٛͱ͔Ͱ৭ʑมΘΔ͕େମ͜Μͳײ͡
    ɺ
    ͱͯ΋ٯؔ਺͕ղੳతʹٻ·Βͳ͍
    $%'
    χϡʔτϯ๏Λ࢖ͬͯ਺஋తʹٯؔ਺αϯϓϦϯά
    àճ΄ͲͷΠςϨʔγϣϯͰे෼ͩͬͨ
    ॳظ஋࣍ୈͰ͸΋ͬͱॖΊΒΕΔ͔΋
    
    ΋͘͠͸ൺྫ౓߹͍͸௿Լ͢Δ͕ɺ
    ղੳతʹٯؔ਺͕ٻ·Δ1%'$%'Ͱଥڠ͢Δ
    

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30. #443%'ͷ੍ݶࣄ߲
    جຊతʹҰ༷ͳؔ༩ഔ࣭Λલఏͱ͍ͯ͠ΔͨΊ
    ඇҰ༷ؔ༩ഔ࣭͸ѻ͑ͳ͍
    ຊ౰͸෺ମද໘ͷςΫενϟʔ͢Βແ͍લఏ
    %JGGVTJPO%JQPMFϞσϧ͸൒ແݶͷฏ໘ΛԾఆ͍ͯ͠Δ
    àδΦϝτϦ͕͜ͷલఏ͔Β֎Ε͗͢ΔͱΞʔςΟϑΝΫτ
    ෳ਺૚ͷฏ໘Λѻ͏Ϟσϧ<%POOFS>΍
    ޫͷೖࣹํ޲Λߟྀ͢Δ΋ͷ<+FQQF>ͳͲ৭Μͳվળख๏΋͋Δ
    

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31. ࢀߟจݙ
    n  [David2016] KOERNER, D., NOVÁK, J. AND KUTZ, P. AND HABEL, R. AND Jarosz, W. 2016.
    Subdivision Next-Event Estimation for Path-Traced Subsurface Scattering. Eurographics Symposium on
    Rendering - Experimental Ideas & Implementations, June.
    n  [Donner2005] DONNER, C., AND JENSEN, H. W. 2005. Light diffusion in multi- layered translucent
    materials. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2005) 24, 3 (July), 1032–
    1039.
    n  [Donner2006] CRAIG, S. D. 2006. Towards Realistic Image Synthesis of Scattering Materials. PhD
    Thesis, University of California San Diego.
    n  [Jeppe2015] FRISVAD, J. R., HACHISUKA, T., and KJELDSEN, T. K. Directional dipole model for
    subsurface scattering. ACM Transactions on Graphics 34(1), pp. 5:1-5:12, November 2014. Presented at
    SIGGRAPH 2015.
    n  [Jensen2001] JENSEN, H. W., MARSCHNER, S. R., LEVOY, M., AND HANRAHAN, P. 2001. A practical
    model for subsurface light transport. In Proceedings of ACM SIGGRAPH 2001, 511–518.
    n  [Jensen2002] JENSEN, H. W., AND BUHLER, J. 2002. A rapid hierarchical rendering technique for
    translucent materials. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2002) 21, 3
    (July), 576–581.
    n  [King2013] KING, A., KULLA, C., CONTY, A., AND FAJARDO, M., 2013. BSSRDF importance sampling.
    ACM SIGGRAPH 2013 Talk, July.
    

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32. ͓͠·͍
    

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