Cornell CS465 Fall 2004 Lecture 3© 2004 Steve Marschner 1 Ray Tracing CS 465 Lecture 3.
Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell...
Transcript of Microfacet models for reflection and refractionfor reflection and refraction Steve Marschner Cornell...
![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.fdocuments.in/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)
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air
dielectric
microsurface macrosurface
Microfacet scattering modelsRough dielectric surface• smooth at wavelength scale• rough at microscale• !at at macroscale
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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.fdocuments.in/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