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Local Reflection Model

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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 ... – PowerPoint PPT presentation

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Title: Local Reflection Model


1
Local Reflection Model
  • Jian Huang, CS 594, Fall 2002

2
Phong Reflection
Phong specular highlight is a simplification
3
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

4
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

5
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
6
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

7
Orientation of Facets
  • Only a certain proportion (D) of facets will in a
    particular direction, e.g. viewing direction

light
H
eye
8
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

9
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
10
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

11
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

12
Recap Snells Law
13
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!
14
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

15
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

16
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

17
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

18
Aluminium
19
Bronze
20
Chrome
21
Stainless Steel
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