Local Reflection Model

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Local Reflection Model

• Jian Huang, CS 594, Fall 2002

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Phong Reflection
Phong specular highlight is a simplification
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Phong Model - Limitations

• The Phong model is based more on common sense
  than physics
• Perfect specular reflection only occurs on a
  perfect mirror surface stroke by a thin light
  beam
• It fails to handle two aspects of specular
  reflection that are observed in real life
• intensity varies with angle of incidence of
  light, increasing particularly when light nearly
  parallel to surface
• colour of highlight DOES depend on material, and
  also varies with angle of incidence

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Physically Based Specular Reflection

• After Phongs work in 1975, Jim Blinn proposed
  physically simulated specular component
• In 1983, Cook and Torrance extended this model to
  account for the spectral composition of
  highlights, ie. dependencies on
• Material type
• Angle of incidence
• With physically based local reflection model, can
  computer pre-computer BRDF

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Modeling the Micro-geometry

• In reality, surfaces are not perfect mirrors
• A physically based approach models the surface as
  micro-facets
• Each micro-facet is a perfect reflecting surface,
  ie a mirror, but oriented at an angle to the
  average surface normal

cross-section through the microfaceted surface
average surface normal
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Specular Reflection

• The specular reflection from this surface depends
  on three factors
• the number of facets oriented correctly to the
  viewer (remember facets are mirrors)
• incident light may be shadowed, or reflected
  light may be masked
• Fresnels reflectance equations predict colour
  change depending on angle of incidence

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Orientation of Facets

• Only a certain proportion (D) of facets will in a
  particular direction, e.g. viewing direction

light
H
eye
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A Statistical Distribution

• Cook and Torrance give formula for D in terms of
• Gaussian distribution D k exp-(a/m)2
• a angle of viewer (angle between N and H)
• m standard deviation of the distribution
• Assumptions
• Small micro-facets is still larger than the
  wavelength of light in size
• Diameter of the light beam can intersect a large
  number of micro-facets to be statistically correct

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Shadowing and Masking

• Light can be fully reflected
• Some reflected light may hit other facets
• Some incident light may never reach a facet

Cook and Torrance give formula for G, fraction of
reflected light, depending on angle of incidence
and angle of view
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Degree of Masking and Shadowing

• Dependent on the ratio l1/l2
• G 1 - l1/l2
• L light vector, V view vector
• H (LV)/2
• For masking Gm 2(N.H)(N.V)/V.H
• For shadowing Gs 2(N.H)(N.L)/V.H

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The Glare Term

• Usually, as the angle between N and V approaches
  90, one sees more and more glare
• You are seeing more micro-facets
• Need a term to account for this effect
• 1/N.V

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Recap Snells Law
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Fresnel Term
N
reflected
In general, light is partly reflected, partly
refracted Reflectance fraction reflected
?
f
refracted
Refractive Index ? sin f / sin ? Note that ?
varies with the wavelength of light The
Fresnel term (the reflectance, F), of a perfectly
smooth surface is given in terms of
refractive index ? of material and angle of
incidence ? F is wavelength dependent!
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Fresnel Term

• Dont know how to calculate F for arbitrary ?
  directly, so usually started with a known or
  measured F0.
• F is a minimum for incident light normal to the
  surface, ie ? 0 F0 ( ? - 1 )2 / ( ? 1 )2
• So different F0 for different materials
• The refractive index ? of a material depends on
  the wavelength, ? , so have different F0 for
  different ?
• burnished copper has roughly
• F0,blue 0.1, F0,green 0.2,
  F0,red 0.5

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Fresnel Term

• As ? increases from 0 ...
• F? F0 ( 1 - cos ? )5 ( 1 - F0 )
• so, as ? increases, then F? increases until F90
  1 (independent of ? )
• This means that when light is tangential to the
  surface
• full reflectance, independent of ?
• reflected colour independent of the material
• Thus reflectance does depend on angle of
  incidence
• Thus colour of specular reflection does depend on
  material and incident light angle

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Specular Term

• This leads to
• Rs( ? ) F( ??) D G / (N.V)
• where
• D proportion of microfacets aligned to view
• G fraction of light shadowed or masked
• F Fresnel term
• N.V glare effect term
• In practice, Rs is calculated for red, green,
  blue
• Note it depends on angle of incidence and angle
  of view

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Cook and Torrance Reflection Model

• The specular term is calculated as described and
  combined with a uniform diffuse term
• Reflection (angle of incidence, viewing angle)
• s Rs d Rd
• 
  (where s d 1)
• Known as bi-directional reflectance
• For metals d 0, s 1
• For shiny plastics d 0.9, s 0.1
• Its BRDF does not depend on the incoming azimuth

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Aluminium
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Bronze
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Chrome
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Stainless Steel