H' Quynh Dinh

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Cook Torrance Model of Reflectance
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Motivations

• Want to simulate metal better
• Better prediction of specular highlight spread
• Want a physical rather than empirical model
  (i.e., Phong illumination model)

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Basic Concept

• Model surface roughness as microfacets in the
  form of are v-shaped grooves

Increasing roughness
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Equations
R ks Rs kd Rd
Coefficients are weights, ks kd 1
Diffuse component Rd is dependent on wavelength
only that is Rd(?) Specular component is now
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Microfacet Distribution Term

• D is distribution of microfacet orientation
• D is equal to the proportionate area of
  microfacets oriented at angle a to the average
  normal of the surface at the point of interest
  (for which we are computing intensity)
• Different distributions can be used. Cook and
  Torrance use

m root mean square (RMS) slope
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Microfacet Shadowing Term

• G is attenuation due to shadowing and masking of
  incoming and reflected light by microfacets

No shadowing G min(1, Gs, Gm)
Shadowing - shadowed incident light Gs
Masking shadowed reflected light Gm H
(LV)/2
2(NH)(NV) (VH)
2(NH)(NL) (VL)
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Intensity Term

• Intensity term, ?(?,?i), depends on the
  wavelength and direction of incoming light
• Also called Fresnel term
• With this term, specular highlight can now take
  on surface or light color depending on angle of
  incidence
• No longer dependent on interaction between kd and
  ks
• Especially good for modeling metallic surfaces
  with near zero diffuse contribution

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Where Does N V Come From?

• Related to the visible surface area of
  microfacets
• If surface is viewed at a low angle, then a large
  area of the microfacets will be seen
• N V approaches 0 as V approaches N, so
  (N V)-1 increases

view
view
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Summary

• Why is this model able to simulate specular
  highlights of metallic surfaces better than the
  Phong model of illumination?
• Intensity term, ?, depends on wavelength and
  incoming light direction, so specular highlight
  can take on surface color or light color
  depending on the angle of incidence
• Specular is no longer just dependent on
  interaction between the specular and diffuse
  coefficients
• Other illumination effects that can be modeled
  using the Cook and Torrance model of illumination
  (but not using the Phong model)
• Multi-spectral
• Light sources with wavelengths that are not
  dominated just by R,G, B, such as fluorescent
  light