[PPT] - Microfacet models for refraction through rough surfaces Bruce PowerPoint Presentation

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Microfacet models for refraction through rough surfaces

Bruce Walter Steve Marschner Hongsong Li Ken Torrance Cornell University Program of Computer Graphics

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Diffuse transmission

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10 5 1

measured transmission ground glass interface n = 1.51

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10 5 1

measured transmission ground glass interface n = 1.51

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10 5 1

measured transmission ground glass interface n = 1.51

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10 5 1

measured transmission ground glass interface n = 1.51

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10 5 1

measured transmission ground glass interface n = 1.51

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10 5 1

measured transmission ground glass interface n = 1.51 critical angle

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Prior work

Microfacet models in graphics

Blinn 1977 introduced Torrance-Sparrow model
Cook & Torrance 1982 Torrance-Sparrow specular
Ashikhmin et al. 2000 microfacet BRDF generator
Stam 2001 skin subsurface scattering model

Work outside graphics we build on

Smith 1967 shadowing–masking framework
Nee & Nee 2004 single-interface measurement idea

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Contributions

Microfacet transmission model

new geometric formulation
clean, simple generalization of reflection

Microfacet distribution functions

evaluate three choices against data
new GGX distribution fits some surfaces better

Importance sampling Measurement and validation

single interface transmission

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air dielectric microsurface macrosurface

Microfacet scattering models

Assumptions

rough dielectric surface
single scattering

m n

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Microfacet reflection models

Incident irradiance Ei illuminates macrosurface area dA from direction i.

i

dA Ei

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Microfacet reflection models

Incident irradiance Ei illuminates macrosurface area dA from direction i. Reflected radiance Lr measured at direction o in solid angle dωo.

dωo

i

Bidirectional Reflectance Distribution Function: fr(i, o) = Lr

Ei Ei Lr

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Microfacet reflection models

Incident irradiance Ei illuminates macrosurface area dA from direction i. Reflected radiance Lr measured at direction o in solid angle dωo.

i

Bidirectional Reflectance Distribution Function: fr(i, o) = Lr

Ei Ei

Bidirectional Transmittance Distribution Function: ft(i, o) = Lt

Ei

Lt dωo

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fr(i, o) = F(i, m) D(m) G(i, o, m) 4|i·n| |o·n|

Reflection to transmission

Traditional microfacet reflection model:

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geometric

fr(i, o) = F(i, m) D(m) G(i, o, m) 4|i·n| |o·n|

Reflection to transmission

We generalize the geometric analysis dealing with the surface area where scattering occurs. Traditional microfacet reflection model:

ptical

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G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

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G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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m

G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

m=h(i,o)

h gives the one microsurface normal m that will scatter light from i to o.

selects m

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dωm m G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

m=h(i,o)

h gives the one microsurface normal m that will scatter light from i to o.

dωo

selects m
determines size of dωm

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dωm m G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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D measures density of microsurface area with respect to microsurface normal m.

dωm m G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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D measures density of microsurface area with respect to microsurface normal m.

dA dAm dωm

m

dAm = ) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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D measures density of microsurface area with respect to microsurface normal m.

dA dAm dωm

m

G measures the fraction of points with microsurface normal m that are visible.

dAm = ) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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D measures density of microsurface area with respect to microsurface normal m.

dA dAm dωm

m

G measures the fraction of points with microsurface normal m that are visible.

dAm = ) D(m) dωm dA = G(i, o, m) G(i, o, m)

shadowing–masking

D(m)

normal distribution

h(i, o)

“half-vector” function

i

h gives the one microsurface normal m

that will scatter light from i to o.

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fs(i, o) = |i · m| |i · n| |o · n| ρ(i, o) dAm dA dωo

For reflection or transmission:

h(i, o)

“half-vector” function

dAm = G(i, o, m) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

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fs(i, o) = |i · m| |i · n| |o · n| ρ(i, o) D(m) G(i, o, m) dωm dωo

For reflection or transmission:

h(i, o)

“half-vector” function

dAm = G(i, o, m) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

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fs(i, o) = |i · m| |i · n| |o · n| ρ(i, o) D(m) G(i, o, m) dωm dωo

easy to generalize

For reflection or transmission:

h(i, o)

“half-vector” function

dAm = G(i, o, m) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

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fs(i, o) = |i · m| |i · n| |o · n| ρ(i, o) D(m) G(i, o, m) dωm dωo

key contribution easy to generalize

For reflection or transmission:

h(i, o)

“half-vector” function

dAm = G(i, o, m) D(m) dωm dA G(i, o, m)

shadowing–masking

D(m)

normal distribution

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i

m

i + o parallel to m

Construction of half-vector

reflection refraction

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i

m

i + o parallel to m

Construction of half-vector

reflection refraction

hr = normalize(i + o)

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i

m

i

m

i + o parallel to m

Construction of half-vector

reflection refraction

hr = normalize(i + o)

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i

m

i m

i + o parallel to m

Construction of half-vector

no

parallel to m

i + no

reflection refraction

hr = normalize(i + o)

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i

m

i m

i + o parallel to m

Construction of half-vector

no

parallel to m

i + no

reflection refraction

hr = normalize(i + o) ht = −normalize(i + no)

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i

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no)

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i

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no)

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i

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) dωo

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i

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr dωo

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i

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr dωm = |o · hr| i + o2 dωo dωm dωo

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i

i
dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr dωm = |o · hr| i + o2 dωo dωm dωo dωo

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i

i
dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr dωm = |o · hr| i + o2 dωo dωm no dωo dωo

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i

i
dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr n2dωo dωm = |o · hr| i + o2 dωo dωm no dωo dωo

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i

i
ht

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr n2dωo dωm = |o · hr| i + o2 dωo dωm no dωo dωo

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i

i
ht

dωo

reflection refraction

Construction of half-vector solid angle

hr = normalize(i + o) ht = −normalize(i + no) hr n2dωo dωm = |o · hr| i + o2 dωo dωm no dωm dωo dωo

dωm =

|o · ht| i + no2 n2dωo

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Result: scattering functions

reflection 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

reflection transmission

fs(i, o) = |i · m| |i · n| |o · n| ρ(i, o) D(m) G(i, o, m) dωm dωo fr(i, o) = |i·hr| |i·n| |o·n| F(i, hr) D(hr) G(i, o, hr) |o·hr| i + o2

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Result: scattering functions

reflection transmission

fr(i, o) = |i·hr| |i·n| |o·n| F(i, hr) D(hr) G(i, o, hr) |o·hr| i + o2 ft(i, o) = |i·ht| |i·n| |o·n| (1 − F(i, ht)) D(ht) G(i, o, ht) n2|o·ht| i + no2

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Result: scattering functions

reflection transmission

fr(i, o) = |i·hr| |o·hr| |i·n| |o·n| F(i, hr) D(hr) G(i, o, hr) i + o2 ft(i, o) = |i·ht| |i·n| |o·n| (1 − F(i, ht)) D(ht) G(i, o, ht) n2|o·ht| i + no2

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Result: scattering functions

reflection transmission

fr(i, o) = |i·hr| |o·hr| |i·n| |o·n| F(i, hr) D(hr) G(i, o, hr) i + o2 ft(i, o) = |i·ht| |o·ht| |i·n| |o·n| n2(1 − F(i, ht)) D(ht) G(i, o, ht) i + no2

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Result: scattering functions

reflection transmission

fr(i, o) = F(i, hr) D(hr) G(i, o, hr) 4|i·n| |o·n| ft(i, o) = |i·ht| |o·ht| |i·n| |o·n| n2(1 − F(i, ht)) D(ht) G(i, o, ht) i + no2

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8 20 –20 40 –40

Normal distributions

Phong

Choice of distribution is determined by surface

Phong describes same surfaces as Beckman
new GGX distribution fits some surfaces better
analytical Smith shadowing–masking

D(θm)

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8 20 –20 40 –40

Normal distributions

Phong Beckman

Choice of distribution is determined by surface

Phong describes same surfaces as Beckman
new GGX distribution fits some surfaces better
analytical Smith shadowing–masking

D(θm)

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8 20 –20 40 –40

Normal distributions

Phong Beckman GGX (new)

Choice of distribution is determined by surface

Phong describes same surfaces as Beckman
new GGX distribution fits some surfaces better
analytical Smith shadowing–masking

D(θm)

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8 20 –20 40 –40

Normal distributions

Phong Beckman GGX (new)

Choice of distribution is determined by surface

Phong describes same surfaces as Beckman
new GGX distribution fits some surfaces better
analytical Smith shadowing–masking

1 90 –90

D(θm) G1(θi,o)

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Importance sampling

Sampling procedure

choose normal according to D(m) |m • n|

explicit formulas in paper

compute o by reflection or refraction
compute pdf of o using dωm/dωo

leaves G and some cosines for the weight

can adjust sampling roughness to control weight

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measuring transmission

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Measurement setup

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