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

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

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

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

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

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

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

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

#443%'ͷཧ࿦

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

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

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

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

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

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

#443%'ͷ࣮૷

࣮૷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

#443%'ͷ࣮૷ ϓϩάϨογϒͳΞϓϩʔν 1#35W౳

ύετϨʔγϯάʹ͓͚Δ#3%' ೖࣹํ޲Λαϯϓϧ

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

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

࣮૷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

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

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

#443%'ͷϓϩάϨογϒͳ࣮૷ ೖࣹҐஔͷαϯϓϦϯά

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

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

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

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

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

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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