1GR2-00 GR2 Advanced Computer Graphics AGR Lecture 2 Basic Modelling.
SI31 Advanced Computer Graphics AGR
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Transcript of SI31 Advanced Computer Graphics AGR
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SI31Advanced Computer
GraphicsAGR
SI31Advanced Computer
GraphicsAGR
Lecture 6Physically Based Reflection Model
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Phong ReflectionPhong Reflection
Objects tend to have plastic appearance
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Phong Model - LimitationsWhat’s Wrong with PhongPhong Model - LimitationsWhat’s Wrong with Phong
The Phong model is based more on common sense than physics
However 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 ModelPhysically Based Model
Cook and Torrance have proposed an alternative model which has a basis in physics and which more accurately represents specular highlights
Diffuse reflection handled as in Phong model
Start by assuming perfectly smooth surface, ie mirror type surface
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Fresnel EquationFresnel Equation
In general, light is partlyreflected, partly refracted
Reflectance = fraction reflected
reflected
refracted
Refractive Index: = sin / sin [Note that varies with the wavelength of light]
The Fresnel equation gives the reflectance, F, of aperfectly smooth surface in terms of refractiveindex of material and angle of incidence
N
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Fresnel EquationFresnel Equation Reflectance, F, is a minimum for incident
light normal to the surface, ie = 0 :F0 = ( - 1 )2 / ( + 1 )2
So different F0 for different materials Because the refractive index of a
material depends on the wavelength of light, , so we also have different F0 for different wavelengths– burnished copper has roughly:
F0,blue = 0.1, F0,green = 0.2, F0,red = 0.5 Thus colour of specular reflection does
depend on material
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Aluminium and BronzeAluminium and Bronze
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Fresnel EquationFresnel Equation
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
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In Reality...In Reality...
In reality, surfaces are not perfect mirrors
A physically based approach models the surface as microfacets
Each microfacet is a perfect reflecting surface, ie a mirror, but oriented at an angle to the average surface normal
cross-sectionthrough themicrofacetedsurface
averagesurfacenormal (N)
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Specular Reflection from Microfaceted Surface
Specular Reflection from Microfaceted Surface
The specular reflectance 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
– Fresnel’s reflectance equations predict colour change depending on angle of incidence
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Orientation of FacetsOrientation of Facets
Only a certain proportion (D) of facets will be correctly aligned with the viewer
Cook and Torrancegive formula for Din terms of:- angle of viewer- average roughness
Heye
light
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Orientation of FacetsOrientation of Facets
The distribution of facets is modelled as:D() = (1/4m2cos4())
exp(-(tan()/m)2)
where is angle between facet and average normal n.
m gives a measure of roughness of surface
D has maximum - where?
N
H
N
microfacet
Overall effectfrom many microfacets
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Shadowing and MaskingShadowing and Masking
Light can be fully reflected
Some reflected light may hit other facets (masking)
Some incident light may never reach a facet (shadowing)
Cook and Torrance give formula for G, fraction of reflected light,depending on angle of incidence and angle of view
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Shadowing and Masking Formulae
Shadowing and Masking Formulae
Masking:– Gm = 2(N.H)(N.L) /
(H.L)
Shadowing:– Gs = 2(N.H)(N.V) /
(H.L)
Then, overall, we define G = min {1, Gm, Gs}
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Specular TermSpecular Term
This leads to:
Rs( ) = F( ) D G / (N.V)
where:D = proportion of microfacets correctly alignedG = fraction of light shadowed or maskedF = Fresnel factorN.V adjusts for facets visible to viewer
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
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 Further reading: Watt (3rd ed) Chap 7;
Foley et al, Ch 16
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AluminiumAluminium
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BronzeBronze
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ChromeChrome
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Stainless SteelStainless Steel
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Phong MoviePhong Movie
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Physically Based MoviePhysically Based Movie