投稿一覧に戻る Ｋｕｄａｎ(株)【4425】の掲示板 2021/09/09〜2021/09/27 504 夢追人 強く買いたい 2021年12月9日 06:56 >>9059 ぎゃ！？！ メタバースの世界の数式ってこんなん？！ 理解不能（笑）SupplementaryMaterialof RecoveringReal-WorldReflectancePropertiesandShadingFromHDRImagery BjoernHaefner1,2SimonGreen2AlanOursland2DanielAndersen2 MichaelGoesele2DanielCremers1RichardNewcombe2ThomasWhelan2 1TechnicalUniversityofMunich2FacebookRealityLabsResearch {bjoern.haefner,cremers}@tum.de, {simongreen,ours,andersed,goesele,newcombe,twhelan}@fb.com A.Detailsonimportancesampling(Section 3.4.2) Thissectiondiscussesthetechnicalimplementationdetailsonanefficientsamplingstrategytoevaluate Ind(p;ϕ,ψ):= H2 fnd(x,ω,ωo;ϕ,ψ)L(x,ω)ω,ndω. (1) Importancesamplingisapowerfultooltoestimatetheintegralin(1)andwerefertheinterestedreaderto[9],Chapter 13forthemathematicalreasoningbehindit.TheMonteCarloestimatorusedforEqn.(1)usingthenon-diffusepart ofthesimplifiedDisneyBRDFisthefinitesumoftheform, Ind(p;ϕ,ψ)=1 N N j=1 fnd(x,Ωj,ωo;ϕ,ψ)L(x,Ωj)Ωj,n p(Ωj), (2) wheretherandomvariablesΩjaresamplesdrawnfromthe probabilitydensityfunctionp(ω).Weexpect,i.e.given enoughsamplesN, E[Ind(p;ϕ,ψ)]=Ind(p;ϕ,ψ),∀p,ϕ,ψ.(3) Theprobabilitydensityfunctionusedinourapproachis p(ω)=1 2 |ω,n| π+1 2 D(ϕ)|h,n| 4|ωo,h|.(4) Toevaluate(2),weneedtobeabletosamplerandomvariablesΩjfromp(ω)andwerealizethisthefollowingway: Giventhej-thobservationofrandomvariablesfollowinga uniformdistributionover[0,1),Xj 0,Xj 1,Xj 2∼U(0,1),we calculateasampleofincidentdirectionas Ωj=TsH2(Xj 1,Xj 2),Xj 0<1 2, R(ωo,Ths(Xj 1,Xj 2)),else,(5) whereR(ωo,h)=2ωo,hh−ωoresemblesthereflection ofωoonh,andT:=(t1,t2,t3)∈R3×3isanorthonormal basistransforminthenormal’scoordinatesystem,aligning thenorthpoleofH2withthenormaln, t1=t2×t3(6) t2= (−ny,nx,0) (−ny,nx,0),|nx|>|nz|, (0,−nz,ny) (0,−nz,ny),else, (7) t3=n.(8) TosamplethediffuselobeoftheBRDF(thecasewhen Xj 0<1 2in(5)),wegeneraterandomsamplesontheupperhemisphereH2usingsH2:[0,1)2→H2, sH2(x1,x2)= s1 s2 max(0,1−s2 1−s2 2) ,(9) withs1:=√x1cos(2πx2)ands2:=√x1sin(2πx2). Thenon-diffuselobeoftheBRDF(thecasewhenXj 0≥1 2in(5))issampledusinghs:[0,1)2→H2, hs(x1,x2)= そう思う9 そう思わない10 開く お気に入りユーザーに登録する 無視ユーザーに登録する 違反報告する 証券取引等監視委員会に情報提供する ツイート 投稿一覧に戻る
>>9059
ぎゃ！？！
メタバースの世界の数式ってこんなん？！
理解不能（笑）SupplementaryMaterialof RecoveringReal-WorldReflectancePropertiesandShadingFromHDRImagery BjoernHaefner1,2SimonGreen2AlanOursland2DanielAndersen2 MichaelGoesele2DanielCremers1RichardNewcombe2ThomasWhelan2 1TechnicalUniversityofMunich2FacebookRealityLabsResearch {bjoern.haefner,cremers}@tum.de, {simongreen,ours,andersed,goesele,newcombe,twhelan}@fb.com A.Detailsonimportancesampling(Section 3.4.2) Thissectiondiscussesthetechnicalimplementationdetailsonanefficientsamplingstrategytoevaluate Ind(p;ϕ,ψ):= H2 fnd(x,ω,ωo;ϕ,ψ)L(x,ω)ω,ndω. (1) Importancesamplingisapowerfultooltoestimatetheintegralin(1)andwerefertheinterestedreaderto[9],Chapter 13forthemathematicalreasoningbehindit.TheMonteCarloestimatorusedforEqn.(1)usingthenon-diffusepart ofthesimplifiedDisneyBRDFisthefinitesumoftheform, Ind(p;ϕ,ψ)=1 N N j=1 fnd(x,Ωj,ωo;ϕ,ψ)L(x,Ωj)Ωj,n p(Ωj), (2) wheretherandomvariablesΩjaresamplesdrawnfromthe probabilitydensityfunctionp(ω).Weexpect,i.e.given enoughsamplesN, E[Ind(p;ϕ,ψ)]=Ind(p;ϕ,ψ),∀p,ϕ,ψ.(3) Theprobabilitydensityfunctionusedinourapproachis p(ω)=1 2 |ω,n| π+1 2 D(ϕ)|h,n| 4|ωo,h|.(4) Toevaluate(2),weneedtobeabletosamplerandomvariablesΩjfromp(ω)andwerealizethisthefollowingway: Giventhej-thobservationofrandomvariablesfollowinga uniformdistributionover[0,1),Xj 0,Xj 1,Xj 2∼U(0,1),we calculateasampleofincidentdirectionas Ωj=TsH2(Xj 1,Xj 2),Xj 0<1 2, R(ωo,Ths(Xj 1,Xj 2)),else,(5) whereR(ωo,h)=2ωo,hh−ωoresemblesthereflection ofωoonh,andT:=(t1,t2,t3)∈R3×3isanorthonormal basistransforminthenormal’scoordinatesystem,aligning thenorthpoleofH2withthenormaln, t1=t2×t3(6) t2= (−ny,nx,0) (−ny,nx,0),|nx|>|nz|, (0,−nz,ny) (0,−nz,ny),else, (7) t3=n.(8) TosamplethediffuselobeoftheBRDF(thecasewhen Xj 0<1 2in(5)),wegeneraterandomsamplesontheupperhemisphereH2usingsH2:[0,1)2→H2, sH2(x1,x2)= s1 s2 max(0,1−s2 1−s2 2) ,(9) withs1:=√x1cos(2πx2)ands2:=√x1sin(2πx2). Thenon-diffuselobeoftheBRDF(thecasewhenXj 0≥1 2in(5))issampledusinghs:[0,1)2→H2, hs(x1,x2)=