© 2003 University of Wisconsin Last Time Some advanced reflection models Fresnel Cook-Torrance Ward Schlick 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Today Some more reflection/illumination models Managing dynamic range 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Assignment 2 Easy: Minimum: receive at triangles, form factors by single ray test center-to-center and disk approximation Receive at vertices variant Harder: Use multiple rays to estimate form factor – subdivide shooter, or use random points on receiver Very hard: Subdivide receiver – tough to keep accurate track of radiosity estimates and corrections Don’t try this – make your ray-tracer faster instead 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Upcoming Events Assignment 2 grading March 6-7 Next assignment: Select a non-photorealistic rendering paper Read it and understand it in detail Present it in class with a 15 min presentation Details week after next 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Metallic Patinas Dorsey and Hanrahan, 1996 Aim: capture the weathering of metallic surfaces Actually, only did copper Underlying ideas: Layer model Modulation by textures Scripting for time control 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Layer Model Surface consists of several layers Each layer has: 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 point 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Operating 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) 02/24/03 © 2003 University of Wisconsin

Thickness/Height Maps Want a method for generating variation over surfaces that looks like corrosion Use regular texture maps or triangulations 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 time 02/24/03 © 2003 University of Wisconsin

Kubelka-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 length B- dz B+ d 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Homogeneous Medium R is total reflectance through a layer of thickness d T is total transmission But, hard to estimate S and K Get ratio K/S from infinite thickness equation Guess S 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Multiple 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 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin BRDF Diffuse term comes from previous equations Gloss term is harder Sum terms from each layer Incoming light is scaled by T2 for layers above Then use Phong model at each interface 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Copper Strips Urban Rural Marine 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Others 02/24/03 © 2003 University of Wisconsin

Subsurface Scattering Kubelka-Munk is a gross approximation to real scattering Assumes isotropic light distribution Subsurface scattering is very important to capturing the appearance of organic materials 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin BSSRDF Bidirectional surface scattering distribution function, S Relates the outgoing radiance at one point to the incident flux at another BRDF makes the assumption that xi = xo To get the total radiance leaving a point, integrate over the surface and the incoming directions S depends on the sub-surface scattering of the material 02/24/03 © 2003 University of Wisconsin

© 2003 University of Wisconsin Practical Model Wann Jensen, Marschner, Levoy and Hanrahan, 2001 Handles non-isotropic media Does not require extensive Monte-Carlo raytracing Just a modified version of distribution ray-tracing Approximation based on: Single bounce scattering – can be done directly Multiple bounce scattering – can be done with averaging arguments 02/24/03 © 2003 University of Wisconsin