1. © 2003 University of Wisconsin
Last Time
Some advanced reflection models
Fresnel
Cook-Torrance
Ward
Schlick
02/24/03
© 2003 University of Wisconsin

2. © 2003 University of Wisconsin
Today
Some more reflection/illumination models
Managing dynamic range
02/24/03
© 2003 University of Wisconsin

3. © 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

4. © 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

5. © 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
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6. © 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
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7. © 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

8. 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

9. 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
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10. © 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
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11. © 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
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12. © 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
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13. © 2003 University of Wisconsin
Copper Strips
Urban
Rural
Marine
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14. © 2003 University of Wisconsin
Others
02/24/03
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15. 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
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16. © 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

17. © 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