Reflectance Models

1
Reflectance Models

• CS 319
• Advanced Topics in Computer Graphics
• John C. Hart

2
Reflectance Models

• Phong/Blinn
• Diffuse using Lambertian model
• Specular using a hack
• Cook-Torrance
• Specular
• Useful for metals, sheens

• Seeliger
• Diffuse
• Skin, softer than Lambertian
• Hair
• Anisotropic
• Uses grain direction

3
Vectors
N
H
(R)
N Normal L Source V View R Reflection H
Halfway R 2(N?L)N L H (VL)/VL
(L)
L
R
V
x
4
Phong and Blinn

• Phong
• L(V) ka La kd Li (N?L) ks Li (V?R)n
• Blinn
• L(V) ka La kd Li (N?L) ks Li (N?H)n
• In general ignore ambient term and assume a
  diffuse/specular decomposition

5
Cook-Torrance

• Models specular BRDF component
• F Fresnel term
• D Roughness term
• G Geometry term

6
Fresnel Term

• Derived fromMaxwells equations
• Coefficients
• qr angle of reflection w.r.t. H
• qt angle of transmission w.r.t. H
• c cos qr L?H V?H
• g2 ??2 c2 1
• Index of refraction actually complex!

7
Fresnel Effect

• Normal incident light reflects color of surface
• Tangential incident light reflects color of light
• Reflectivity increases as incidence becomes more
  tangential

8
Roughness Term
m

• Statistical model of light reflectance
• Centered around reflection direction R
• Blinn model
• Beckman function
• (a N?H)

9
Geometry Term

• Shadowing
• Incident light does not reach material
• Gs 2(N?H)(N?V)/(V?H)
• Masking
• Reflected light does not reach viewer
• Gm 2(N?H)(N?L)/(V?H)
• Use minimum
• Gm min Gs, Gm

10
Seeliger

• fr N?L/(N?L N?V)
• Model for diffuse reflectance from skin
• Softer appearance than Lambertian
• Derived from first principles
• Used as a basis for multilayer shading
• See Hanrahan Krueger SIGGRAPH 93

11
Hair
L
L
T

• Anisotropic
• Uses tangent vector T
• Diffuse anisotropic
• fd sin(T,L)
• Specular anisotropic
• fs (T?L) (T?V) sin(T,L) sin(T,V)