Last TimeTodayMetallic PatinasLayer ModelOperating on LayersThickness/Height MapsKubelka-Munk (KM) ModelHomogeneous MediumMultiple LayersBRDFCopper StripsOthersSubsurface ScatteringHemispherical-Directional ReflectanceComputing hd (PBR 15.5.5)PBRT BSDF Structures (PBR Sect 10.1)PBRT Materials (PBR Sect 10.2)Bump Mapping (PBR Sect 10.3)ExamplesTextures (PBR Chap 11)Texture CoordinatesMappingsTexture TypesTexture AntialiasingNext Time02/4/05 © 2005 University of WisconsinLast Time•Microfacet models–Diffuse•Oren-Nayar–Specular•Torrance-Sparrow–Blinn–Ashikhmin-Shirley–Ward–Schlick•Lafortune’s model•Glossy over Diffuse02/4/05 © 2005 University of WisconsinToday•Assignment 1, Part 2, h=4•More reflectance models•Materials•Textures02/4/05 © 2005 University of WisconsinMetallic Patinas•Dorsey and Hanrahan, SIGGRAPH 1996•Aim: capture the weathering of metallic surfaces–Actually, only did copper•Underlying ideas:–Layer model–Modulation by textures–Scripting for time control02/4/05 © 2005 University of WisconsinLayer Model•Surface consists of several layers•Each layer has constants:–Standard diffuse, specular, roughness parameters (roughness is Phong exponent)–Transmission and back-scatter parameters, K and S•Scripting controls the layers over time•Layers are not uniform–Consider a stack of layers at a single point02/4/05 © 2005 University of WisconsinOperating on Layers•coat material thickness thickness-map–Add a new layer of material•erode thickness thickness-map–Remove some material•fill height height-map–Fill in valleys to a certain minimum height•polish height height-map–Remove down to a given height•offset radius–Apply material in corners (places not reachable by a sphere of radius)02/4/05 © 2005 University of WisconsinThickness/Height Maps•Use texture maps or triangulations to define the thickness of each layer•Growth models change the maps over time•Various methods–Steady thickening – quite uniform texture–Random deposition – drop points onto the surface–Ballistic deposition – point sticks when it first contacts something (gives overhangs)–Directed percolation depinning – points on surface are blocked or unblocked (with moisture) and surface grows into unblocked regions over time02/4/05 © 2005 University of WisconsinKubelka-Munk (KM) Model•A model used in the paint, printing and textile industries to predict diffuse scattering in layers•Describes light distribution at a height in a medium with forward and backward flux density (energy per unit area)•K is absorption per unit length, S is backscattering per unit lengthB-B+ddz  BSKSBzBSBBSKzB02/4/05 © 2005 University of WisconsinHomogeneous Medium•R is total reflectance through a layer of thickness dd for use in diffuse BRDF•T is total transmissiond for diffuse emission on the back side of the layer•But, hard to estimate S and K (they are colors)–Get ratio K/S from infinite thickness equation–Guess S    bSdbbSdabBdBTbSdbbSdabSdBBRcoshsinh0coshsinhsinh00 12abSKSa02/4/05 © 2005 University of WisconsinMultiple Layers•Model can be extended for multiple layers of varying thickness•For two layers:•Subsurface compositing operators–To get more layers, just apply the operator again–Order doesn’t matter•Bottom layer has R but T=0212121221111RRTTTRRRTRR02/4/05 © 2005 University of WisconsinBRDF•Diffuse term comes from previous equations: d=Rall•Gloss term is harder–Use physically viable Phong model at each interface, i, to compute a gloss color:–Scale by transmission of layers above:•Transmission composed for all layers above i –Sum terms from each layer:2ijTlNiisijsglossCTCR1,20,  eooglossisRC n,,02/4/05 © 2005 University of WisconsinCopper StripsMarineUrban Rural02/4/05 © 2005 University of WisconsinOthers02/4/05 © 2005 University of WisconsinSubsurface Scattering•Kubelka-Munk is a gross approximation to real scattering–Assumes isotropic light distribution and glossy transmittance is all wrong•Subsurface scattering is very important to capturing the appearance of organic materials–More later02/4/05 © 2005 University of WisconsinHemispherical-Directional Reflectance•Hemispheric-Directional Reflectance is the fraction of the incident irradiance in a given direction that is reflected by the surface•Useful for computation of some reflectance functions and for some algorithms•Note error in book on page 689 – see www.pbrt.org for errata nxx2cos),,(),(Hrhddf02/4/05 © 2005 University of WisconsinComputing hd (PBR 15.5.5)•For many reflectance functions, this value is not easy to compute, so use Monte Carlo integration to compute it•Evaluating this is easy in PBRT:–Samples are passed in (or you generate them somehow), as is –Iterate over each sample•Ask for a sampled direction Sample_f. It returns both fr and p–Add up all samples and divide by N•In fact, if you inherit from BxDF then you already get it   NjjjjrhdpfN1)(cos),,(1),(xx02/4/05 © 2005 University of WisconsinPBRT BSDF Structures (PBR Sect 10.1)•A BxDF is a component of a BSDF – one of the things we have been looking at so far•BSDF can be made up of multiple components•The PBRT BSDF structure has code for managing these components – read Chapter 10•When sampling, choose a BxDF–Uniform probability of choosing any one matching component–PDF of choosing some direction must account for all components•But it still assumes we’re talking about a single point02/4/05 © 2005 University of WisconsinPBRT Materials (PBR Sect 10.2)•A Material described how the BSDF varies over the entire surface of an object•All parameters to the components BxDFs are given in the form of textures–More on textures in a minute•The job of the Material is:–Manage local surface variations via textures and pass a single set of point properties (color, normal, etc) to BSDFs–Provide BSDFs with information about the neighborhood, particularly the geometric normal and the shading normal (bump mapped or otherwise modified)02/4/05 © 2005 University of WisconsinBump Mapping (PBR Sect 10.3)•Bump mapping modifies the