Last TimeTodayMicrofacet Models (PBR 9.4)Describing Microfacet MaterialsMicroscopic EffectsOren-Nayar (PBR 9.4.1)Oren-Nayar EffectsTorrance-Sparrow (PBR Sect 9.4.2)Torrance-Sparrow BRDFGeometry TermBlinn’s Microfacet DistributionSampling Blinn’s Microfacet (PBR 15.5.1)More Blinn SamplingArbitrary ReflectionAnisotropic Microfacet DistributionSampling Anisotropic MicrofacetWard’s Isotropic ModelWard’s Anisotropic ModelSampling Ward’s ModelSchlick’s Model (Schlick94)Schlick’s ModelPutting it TogetherMore to it than thatPhong RevisitedOriented PhongLafortune’s Model (PBR 9.5)Lafortune’s ClaySampling From LafortuneTwo-Layer Models (PBR 9.6 and 15.5.3))Fresnel Blend ModelNext Time02/2/05 © 2005 University of WisconsinLast Time•Reflectance part 1–Radiometry–Lambertian–Specular02/2/05 © 2005 University of WisconsinToday•Microfacet models–Diffuse•Oren-Nayar–Specular•Torrance-Sparrow–Blinn–Ashikhmin-Shirley–Ward–Schlick•Lafortune’s model•Glossy over Diffuse02/2/05 © 2005 University of WisconsinMicrofacet Models (PBR 9.4)•Model fine detail as set of polygonal facets–Metals–Minerals–Things that solidified in crystal form, or were broken/cut by fracture/scraping•Aim to capture the macroscopic effects of the many microscopic facets02/2/05 © 2005 University of WisconsinDescribing Microfacet Materials•Surface normal distribution–How the surface normals of the facets are distributed about the macroscopic normal•Facet BRDF–Are the facets diffuse or specular?02/2/05 © 2005 University of WisconsinMicroscopic Effects•Masking – viewer can’t see a microfacet•Shadowing – light can’t see a microfacet•Interreflection – light off one facet hits another•Aim is to capture these effects as efficiently as possible02/2/05 © 2005 University of WisconsinOren-Nayar (PBR 9.4.1)•Model facet distribution as Gaussian with s.d.  (in radians)•Facet BRDF is Lambertian•Resulting model has no closed form solution, but a good approximation•Sample using cosine-weighted sampling in hemisphere     tansincos,0max,oiiorBAf    oioiBA,min,max09.045.033.021222202/2/05 © 2005 University of WisconsinOren-Nayar EffectsLambertian Oren-Nayar02/2/05 © 2005 University of WisconsinTorrance-Sparrow (PBR Sect 9.4.2)•Specular BRDF for facets•Arbitrary (in theory) distribution of facet normals•Additional term for masking and shadowinginhoHalf vector – facet orientation to get specular transfer02/2/05 © 2005 University of WisconsinTorrance-Sparrow BRDF•D(h) is the microfacet orientation distribution evaluated for the half angle–Changing this changes the surface appearance – but this equation doesn’t depend on the choice•Fr(o) is the Fresnel reflection coefficient    ioorhiorFDfcoscos4, 02/2/05 © 2005 University of WisconsinGeometry Term•Masking:•Shadowing:•Together:   ohohiomaskG---nn2,      ioshadowiomaskioGGG,,,,1min,    ohihioshadowG---nn2,      ioorhioiorFDGfcoscos4,, 02/2/05 © 2005 University of WisconsinBlinn’s Microfacet Distribution•Parameter e controls “roughness”   ehheD n-2202/2/05 © 2005 University of WisconsinSampling Blinn’s Microfacet (PBR 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 D•The sampled direction is completely determined by halfway vector, h, so sample that–Then construct reflection ray based upon it•So how do we sample such a direction …02/2/05 © 2005 University of WisconsinMore Blinn Sampling•Need to sample spherical coords: , •Book has details, and probably an error on page 684•Complication: We need to return the probability of choosing i, but we have the probability of choosing h–Simple conversion term•We need to construct the reflection direction about an arbitrary vector …02/2/05 © 2005 University of WisconsinArbitrary Reflection•Coordinate system is not nicely aligned, so use construction hhooi 202/2/05 © 2005 University of WisconsinAnisotropic Microfacet Distribution•Parameters for x and y direction roughness, where x and y are the local BRDF coordinate system on the surface–Gives the reference frame for       22sincos22211yxeehyxyxheeeeD- n02/2/05 © 2005 University of WisconsinSampling Anisotropic Microfacet•Sampling is discussed in PBR Sect 15.5.2 – similar to Blinn but with different distribution, and probably not quite right–Note that there are 4 symmetric quadrants in the tangent plane–Sample in a single quadrant, then map to one of 4 quadrants–Take care to maintain stratification0 11st 2nd 3rd 4th02/2/05 © 2005 University of WisconsinWard’s Isotropic Model•“the simplest empirical formula that will do the job”•Leaves out the geometry and Fresnel terms–Makes integration and sampling easier•3 terms, plus some angular values:d is the diffuse reflectances is the specular reflectance is the standard deviation of the micro-surface slope   2222tanexpcoscos1,hoisdiorf02/2/05 © 2005 University of WisconsinWard’s Anisotropic Model•For surfaces with oriented grooves•2 terms for anisotropy:x is the standard deviation of the surface slope in the x directiony is the standard deviation of the surface slope in the y direction   yxyhxhhoisdiorf4sincostanexpcoscos1,2222202/2/05 © 2005 University of WisconsinSampling Ward’s Model•Take 1 and 2 and transform to get h and h:•Only samples one quadrant, use same trick as before to get all quadrants•Not sure about correct normalization constant for solid angle measure   2222121sincoslog2tantanyxhxyh02/2/05 © 2005 University of WisconsinSchlick’s Model (Schlick94)•Empirical model well suited to