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1、ParticipatingMediaValerieSzudziejkaOutlineLightscatteringThevolumerenderingequationPhasefunctionsRaymarchingRenderingspecificsLightscatteringPhotoncancontinuethroughmediumunaffectedOrcanbeout-scattered(outofpathoflightray)orabsorbed-reducedradianceOrcanbein-s
2、cattered(intopathoflightray)ormediumcanemitmorelight-increasedradianceLightscatteringReducedradianceduetoout-scattering:(ω!·∇)L(x,ω!)=−σs(x)L(x,ω!)Reducedradianceduetoabsorption:(ω!·∇)L(x,ω!)=−σa(x)L(x,ω!)LightscatteringIncreasedradianceduetoin-scattering:!(
3、ω!·∇)L(x,ω!)=σs(x)Ω4πp(x,ω!",ω!)Li(x,ω!")dω!"integrateoveralldirectionsonasphere(surfacearea)Increasedradianceduetoemission:(ω!·∇)L(x,ω!)=σa(x)Le(x,ω!)LightscatteringChangeinradiance:emission-out-scattering-absorption+in-scattering!(ω!·∇)L(x,ω!)=σa(x)L!e(x,ω
4、!)−σt(x)L(x,ω!)+σs(x)Ω4πp(x,(ω!·∇)L(x,ω!)=σa(x)Le(x,ω!)−σt(x)L(x,ω!)+σs(x)Ω4πp(x,ω!#,ω!)Li(x,ω!#)dω!#whereσt=σs+σaistheextinctioncoefficient.Volumerenderingequation!sL(x,ω!)=e−τ(x,x")σ(x!)L(x!)dx!+0ae!s!e(−τ(x,x")σ(x!)p(x!,ω"!,ω")L(x!,ω"!)dω"!dx!+0sΩ4πie−τ(x,
5、x+sω")L(x+sω!,ω!)!x!whereτ(x,x!)=σt(t)dtistheopticaldepth.xintegrateoverlengthofsegment(s)MustbenumericallyintegratedCostlierthanrenderingequationPhasefunctions!p(x,ω!!,ω!)dω!=1Ω4πsimilartoBRDF-butunitlessandnormalizedPhaseFunctionsanisotropicscattering:pref
6、erentialscatteringdirectionisotropic:nopreferenceanisotropicmedium:phasefunctiondependsonorientationofmediumisotropic:nodependenceIsotropicPhasefunctionscatteringcompletelyrandom1p(θ)=4πRaleighScatteringp(θ)=3(1+cos2θ)16πshorterwavelengthsscatteredmoreforpar
7、ticlessmallerthanawavelengthoflightwhytheskyisblueHenyey-Greenstein21−gp(θ)=4π(1+g2−2gcosθ)1.5gin(-1,1)g<0:backwardscatteringg>0:forwardscatteringg=0:isotropicscatteringHenyey-Greensteinellipsoid-shapedscatteringlargerg=morepreferentialscatteringcostly1.5exp
8、onentSchlickPhaseFunctionaccurateshapeofphasefunctionnotsoimportantuseequationofellipsetoapproximateHenyey-Greenstein21−kp(θ)=4π(1+kcosθ)2kissimilartoginHenyey-GreensteinRaymarchingSolvesvolumer
