Previous lectureMicrofacet Reflectance ModelsOutlineMicrofacet Models (Text ch. 9.4)Basic microfacet modelingMicroscopic geometryOren-Nayar model (Text ch. 9.4.1)Oren-Nayar effectsTorrance-Sparrow (Text ch. 9.4.2)Torrance-Sparrow BRDFGeometry termBlinn’s microfacet distributionSampling Blinn’s model (Text ch. 15.5.1)Blinn sampling continuedArbitrary reflectionAnisotropic microfacet distributionsSampling anisotropic distributionWard’s isotropic modelWard’s anisotropic modelSampling Ward’s modelSchlick’s model (Schlick 94)Schlick’s modelPutting it togetherMore to it than thatPhong reloadedOriented PhongLafortune’s model (Text ch. 9.5)Lafortune’s claySampling LafortuneTwo-layer models (Text chs. 9.6 and 15.5.3))Fresnel blend modelUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellPrevious lectureReflectance IBRDF, BTDF, BSDFIdeal specular modelIdeal diffuse (Lambertian) modelPhongUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellMicrofacet Reflectance ModelsUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellOutlineMicrofacet modelsDiffuseOren-NayarSpecularTorrance-SparrowBlinnAshikhmin-Shirley (anisotropic)WardSchlickLafortune’s modelTwo layer modelsUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellMicrofacet Models (Text ch. 9.4)Model surface as set of polygonal facetsCapture surface roughness effectsMicrofacets can be diffuse or specularUse facet distribution to model roughnessStatistical model of microscopic effects gives macroscopic appearanceMore realistic, particularly at high incidence anglesUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellBasic microfacet modelingSurface normal distributionHow the surface normals of the facets are distributed about the macroscopic normalFacet BRDFAre the facets diffuse or specular?University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellMicroscopic geometryMasking – viewer can’t see a microfacetShadowing – light can’t see a microfacetInterreflection – light off one facet hits anotherAim is to capture these effects as efficiently as possibleUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellOren-Nayar model (Text ch. 9.4.1)Model facet distribution as Gaussian with s.d. (radians)Facet BRDF is LambertianResulting model has no closed form solution, but a good approximationSample using cosine-weighted sampling in hemisphere( ) ( )( )( )βαφφπρωω tansincos,0max,oiiorBAf −+=( )( )( )oioiBAθθβθθασσσσ,min,max09.045.033.0212222==+=+−=University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellOren-Nayar effectsLambertian Oren-NayarUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellTorrance-Sparrow (Text ch. 9.4.2)Specular BRDF for facetsArbitrary (in theory) distribution of facet normalsAdditional term for masking and shadowingExplicit Fresnel terminhoHalf vector – facet orientation to produce specular transferUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellTorrance-Sparrow BRDFG(o , i) handles microfacet geometryD(h) is the microfacet orientation distribution evaluated for the half angleChanging this changes the surface appearance Fr(o) is the Fresnel reflection coefficient( )( ) ( )ioorhioiorFDGfθθωωωωωωcoscos4),(, =University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellGeometry termMasking:Shadowing:Together:( )( )( )ohohiomaskGωωωωωω•••=nn2,( ) ( ) ( ){ }ioshadowiomaskioGGG ωωωωωω ,,,,1min, =( )( )( )ohihioshadowGωωωωωω•••=nn2,( )( ) ( ) ( )ioorhioiorFDGfθθωωωωωωcoscos4,, =University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellBlinn’s microfacet distributionParameter e controls “roughness”( ) ( )ehheD n•+= ωπω22University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellSampling Blinn’s model (Text ch. 15.5.1)Sampling from a microfacet BRDF tries to account for all the terms: G, D, F, cos But D provides most variation, so sample according to DThe sampled direction is completely determined by halfway vector, h, so sample thatThen construct reflection ray based upon itSo how do we sample such a direction …University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellBlinn sampling continuedNeed to sample spherical coords: , Book has details, and probably an error on page 684Complication: We need to return the probability of choosing i, but we have the probability of choosing hSimple conversion termWe need to construct the reflection direction about an arbitrary vector …University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellArbitrary reflectionCoordinate system is not nicely aligned, so use construction( )hhooiωωωωω ⋅+−= 2University of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellAnisotropic microfacet distributionsParameters for x and y direction roughness, where x and y are the local BRDF coordinate system on the surfaceGives the reference frame for ( )( )( )( )( )( )φφωπω22sincos21221121yxeehyxyxheeeeD+•⎟⎟⎠⎞⎜⎜⎝⎛++++= nUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellSampling anisotropic distributionSampling is discussed in section 15.5.2 of the text Similar to Blinn but with different distributionNote that there are 4 symmetric quadrants in the tangent planeSample in a single quadrant, then map to one of 4 quadrantsTake care to maintain stratification0 11st 2nd 3rd 4thUniversity of Texas at Austin CS395T - Advanced Image Synthesis Fall 2007 Don FussellWard’s isotropic model“the simplest empirical formula that will do the job”Leaves out the geometry and Fresnel termsMakes integration and sampling easier3 terms, plus some angular values:d is the diffuse reflectances is the specular reflectance is the standard deviation of the micro-surface slope( )( )[ ]2222tanexpcoscos1,πσσθθθρπρωωhoisdiorf−+=University of Texas at Austin CS395T -
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