microfacet models for reflection and refractionfor reflection and refraction steve marschner cornell...
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![Page 1: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/1.jpg)
Microfacet modelsfor reflection and refraction
Steve Marschner
Cornell University CS 6630 Spring 2012
(based on presentation forWalter, Marschner, Li, and Torrance EGSR ’07)
Tuesday, February 14, 2012
![Page 2: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/2.jpg)
air
dielectric
microsurface macrosurface
Microfacet scattering modelsRough dielectric surface• smooth at wavelength scale• rough at microscale• !at at macroscale
Tuesday, February 14, 2012
![Page 3: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/3.jpg)
Microfacet scattering models
Incident irradiance Ei illuminates macrosurface area dA from direction i. i
dA
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Microfacet scattering models
Incident irradiance Ei illuminates macrosurface area dA from direction i.
Scattered radiance Lr or Lt measured in direction o in solid angle dωo.
dωo
oi
Tuesday, February 14, 2012
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Microfacet scattering models
Incident irradiance Ei illuminates macrosurface area dA from direction i.
Scattered radiance Lr or Lt measured in direction o in solid angle dωo.
dωo
oi
fs(i,o) =Lr,t
Ei
Bidirectional Scattering Distribution Function
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io
o
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
Tuesday, February 14, 2012
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Gives the one microsurface normal m that will scatter light from i to o. i
o
o
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
m = h(i,o)
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Gives the one microsurface normal m that will scatter light from i to o. i
The size of the set of relevant normals dωm
relative to the receiving solid angle dωo is determined by h.
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dωo
dωo
dωm
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Measures density of microsurface area with respect to microsurface normal.
dA
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
mi
Tuesday, February 14, 2012
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Measures density of microsurface area with respect to microsurface normal.
dA
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
mi
Tuesday, February 14, 2012
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Measures density of microsurface area with respect to microsurface normal.
dAm = D(m) dωm dA
dAdAm
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dωm
mi
The ratio of relevant microsurface area dAm to macrosurface area dA is D(m)dωm.
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Measures the fraction of points with microsurface normal m that are visible in directions i and o.
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) dωm dA
io
o
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Measures the fraction of points with microsurface normal m that are visible in directions i and o.
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) dωm dA
io
o
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Measures the fraction of points with microsurface normal m that are visible in directions i and o.
dAm = D(m) G(i,o,m) dωm dA
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
io
o
Tuesday, February 14, 2012
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Measures the fraction of points with microsurface normal m that are visible in directions i and o.
dAm = D(m) G(i,o,m) dωm dA
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
io
oWe now know the size of the scattering area, which determines how much light re!ects.
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Gives the fraction of the power incident on the scattering area dAm that is scattered.
Φi
Φo
Φo
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) G(i,o,m) dωm dA
dΦmo =
|i · m||i · n| ρ(i,o) dAmdEi
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Gives the fraction of the power incident on the scattering area dAm that is scattered.
Φi
Φo
Φo
G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) G(i,o,m) dωm dA
This scattered power is related to the incident irradiance by the attenuation and the scattering area, projected in the incident direction.
dΦmo =
|i · m||i · n| ρ(i,o) dAmdEi
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) G(i,o,m) dωm dA
The BSDF is the ratio of scattered radiance to incident irradiance:
dΦmo =
|i · m||i · n| ρ(i,o) dAmdEi
fs(i,o) =dLo
dEi=
dΦmo /(dA |o · n| dωo)
dEi
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
dAm = D(m) G(i,o,m) dωm dA
The BSDF is the ratio of scattered radiance to incident irradiance:
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
dΦmo =
|i · m||i · n| ρ(i,o) dAmdEi
Tuesday, February 14, 2012
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
Tuesday, February 14, 2012
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
Fresnel re!ection
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
surface roughnessFresnel re!ection
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G(i,o,m)shadowing–masking
D(m)normal distribution
h(i,o)“half-vector” function
ρ(i,o)attenuation
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
determined by geometry
surface roughnessFresnel re!ection
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i o
m
i + o parallel to m
Construction of half-vectorre!ection refraction
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i o
m
i + o parallel to m
Construction of half-vectorre!ection refraction
hr = normalize(i + o)
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i o
m
i
o
m
i + o parallel to m
Construction of half-vectorre!ection refraction
hr = normalize(i + o)
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i o
m
i
m
i + o parallel to m
Construction of half-vector
no
parallel to mi + no
re!ection refraction
hr = normalize(i + o)
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i o
m
i
m
i + o parallel to m
Construction of half-vector
no
parallel to mi + no
re!ection refraction
hr = normalize(i + o) ht = −normalize(i + no)
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i o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
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i o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
o
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i o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
dωo
o
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i o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
dωo
o
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i o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
dωm =|o · hr|�i + o�2
dωo
dωm
dωo
o
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i o
i
o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
dωm =|o · hr|�i + o�2
dωo
dωm
dωo
dωo
o
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i o
i
o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
dωm =|o · hr|�i + o�2
dωo
dωm
no
dωo
dωo
o
Tuesday, February 14, 2012
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i o
i
o
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
n2dωo
dωm =|o · hr|�i + o�2
dωo
dωm
no
dωo
dωo
o
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i o
i
o
ht
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
n2dωo
dωm =|o · hr|�i + o�2
dωo
dωm
no
dωo
dωo
o
Tuesday, February 14, 2012
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i o
i
o
ht
dωo
re!ection refraction
Construction of half-vector solid angle
hr = normalize(i + o) ht = −normalize(i + no)
hr
n2dωo
dωm =|o · hr|�i + o�2
dωo
dωm
no
dωm
dωo
dωo
o
dωm =|o · ht|
�i + no�2n2dωo
Tuesday, February 14, 2012
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Result: scattering functions
re!ection
transmission
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
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Result: scattering functions
fr(i,o) =|i·m|
|i·n| |o·n| F (i,m)D(m) G(i,o,m)|o·m|
�i + o�2
re!ection
transmission
fs(i,o) =|i · m|
|i · n| |o · n| ρ(i,o) D(m)G(i,o,m)dωm
dωo
Tuesday, February 14, 2012
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Result: scattering functions
ft(i,o) =|i·m|
|i·n| |o·n| (1− F (i,m))D(m) G(i,o,m)n2|o·m|�i + no�2
fr(i,o) =|i·m|
|i·n| |o·n| F (i,m)D(m) G(i,o,m)|o·m|
�i + o�2
re!ection
transmission
Tuesday, February 14, 2012
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Result: scattering functions
ft(i,o) =|i·m|
|i·n| |o·n| (1− F (i,m))D(m) G(i,o,m)n2|o·m|�i + no�2
fr(i,o) =|i·m| |o·m||i·n| |o·n|
F (i,m)D(m) G(i,o,m)�i + o�2
re!ection
transmission
Tuesday, February 14, 2012
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Result: scattering functions
ft(i,o) =|i·m| |o·m||i·n| |o·n|
n2(1− F (i,m))D(m) G(i,o,m)�i + no�2
fr(i,o) =|i·m| |o·m||i·n| |o·n|
F (i,m)D(m) G(i,o,m)�i + o�2
re!ection
transmission
Tuesday, February 14, 2012
![Page 44: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/44.jpg)
Result: scattering functions
ft(i,o) =|i·m| |o·m||i·n| |o·n|
n2(1− F (i,m))D(m) G(i,o,m)�i + no�2
re!ection
transmission
fr(i,o) =1
|i·n| |o·n|F (i,m) D(m)G(i,o,m)
4
Tuesday, February 14, 2012
![Page 45: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/45.jpg)
Result: scattering functions
fr(i,o) =F (i,m) D(m) G(i,o,m)
4|i·n| |o·n|
ft(i,o) =|i·m| |o·m||i·n| |o·n|
n2(1− F (i,m))D(m) G(i,o,m)�i + no�2
re!ection
transmission
Tuesday, February 14, 2012
![Page 46: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/46.jpg)
Fresnel re!ectance
Glas
sner,
Princ
iples
of Dig
ital Im
age S
ynth
esis
Tuesday, February 14, 2012
![Page 47: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/47.jpg)
Fresnel re!ectance
Glas
sner,
Princ
iples
of Dig
ital Im
age S
ynth
esis
Tuesday, February 14, 2012
![Page 48: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/48.jpg)
8
20–20 40–40
Normal distributions
Phong
Choice of distribution is determined by surface• Phong, Beckman are popular choices• “GGX” distribution is another option• [Smith 67] gives a way to produce smooth Gs
D(θm)Tuesday, February 14, 2012
![Page 49: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/49.jpg)
8
20–20 40–40
Normal distributions
PhongBeckman
Choice of distribution is determined by surface• Phong, Beckman are popular choices• “GGX” distribution is another option• [Smith 67] gives a way to produce smooth Gs
D(θm)Tuesday, February 14, 2012
![Page 50: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/50.jpg)
8
20–20 40–40
Normal distributions
PhongBeckmanGGX (new)
Choice of distribution is determined by surface• Phong, Beckman are popular choices• “GGX” distribution is another option• [Smith 67] gives a way to produce smooth Gs
D(θm)Tuesday, February 14, 2012
![Page 51: Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell University CS 6630 Spring 2012 (based on presentation for Walter, Marschner, Li,](https://reader034.vdocuments.us/reader034/viewer/2022051909/5ffd6c490f2c692bf636d455/html5/thumbnails/51.jpg)
8
20–20 40–40
Normal distributions
PhongBeckmanGGX (new)
Choice of distribution is determined by surface• Phong, Beckman are popular choices• “GGX” distribution is another option• [Smith 67] gives a way to produce smooth Gs
1
90–90
D(θm) G1(θi,o)Tuesday, February 14, 2012