• No results found

Appearance of Interfaced Lambertian Microfacets, using STD Distribution

N/A
N/A
Protected

Academic year: 2022

Share "Appearance of Interfaced Lambertian Microfacets, using STD Distribution"

Copied!
56
0
0

Laster.... (Se fulltekst nå)

Fulltekst

(1)

BRDF Interfaced Lambertian Microfacets

Appearance of Interfaced Lambertian Microfacets

using STD Distribution

M. Ribardi`ere, D. Meneveaux, B. Bringier, L. Simonot

University of Poitiers, XLIM (CNRS UMR7252) and PPRIME (UPR3346)

M. Ribardi`ere (Poitiers) IL microfacets and STD 1 / 25

(2)

BRDF Interfaced Lambertian Microfacets

Contents

1 BRDFs and Microfacet Theory

Microfacet BRDFs Issues and Needs

2 Interfaced Lambertian Materials

Model definition

Appearance and discussion 3 Student’s T-Distribution

Definition Discussion

4 Combination of IL with STD

Influence on appearance 5 Conclusion and Future Work

M. Ribardi`ere (Poitiers) IL microfacets and STD 2 / 25

(3)

BRDFs and Microfacet Theory Microfacet BRDFs

BRDF Models

n o i

dS θo

θi

o i

ϕo ϕi

L(i,o,n) = d2φo(i,o) dScosθoo

f(i,o,n) =dL(o,n) dE(i,n)

Many existing models [Phong,Ward,CT82,ON94,Ash00,Jak14,Wu15,Bel17,etc.]

Only few parameters, more or less intuitive and easy to control Some are designed specifically for fitting parameters

Some of them aim designed for physically-based applications (Energy conservation and reciprocity)

⇒Microfacet-based models often employed

M. Ribardi`ere (Poitiers) IL microfacets and STD 3 / 25

(4)

BRDFs and Microfacet Theory Issues and Needs

Microfacet Representation

General Equation [ON94,Walt07]:

f(i,o,n) = Z

+

|im|

|in|fµ(i,o,m)|om|

|on|D(m)G(i,o,m)dωm. (1)

⇒All microfacets may contribute

⇒Rough surfaces imply multiple light reflections

Simplifies with specular microfacetsfµ [TS67,CT82,Walt07]:

f(i,o,n) =F(i,h)D(h)G(i,o,h)

4|in||on| , (2)

⇒Only one microfacet orientation can contribute

⇒Multiple light reflections are ignored Many authors have discussed:

Relationships between D and GAF [TS67,Ash00,SB,Heitz,etc.]

Energy conservation with specular microfacets [Kel01,TVCG17]

Multiple scattering [Heitz,TVCG17]

M. Ribardi`ere (Poitiers) IL microfacets and STD 4 / 25

(5)

BRDFs and Microfacet Theory Issues and Needs

Microfacet Representation

Playing withfµoffers a large panel of different materials.

Geometrical Attenuation Factor (GAF). Normal Distribution Functions.

Multiple scattering between microfacets.

Torrance-Sparrow (V-cavity profile) Smith-Bourlier (Uncorrelated microfacets)

Beckmann distribution GGX or Trowbridge-Reitz

(image from [Heitz16])

M. Ribardi`ere (Poitiers) IL microfacets and STD 5 / 25

(6)

BRDFs and Microfacet Theory Issues and Needs

Microfacet Representation

Playing withfµoffers a large panel of different materials.

Geometrical Attenuation Factor (GAF).

Normal Distribution Functions.

Multiple scattering between microfacets.

Torrance-Sparrow (V-cavity profile) Smith-Bourlier (Uncorrelated microfacets)

Beckmann distribution GGX or Trowbridge-Reitz

(image from [Heitz16])

M. Ribardi`ere (Poitiers) IL microfacets and STD 5 / 25

(7)

BRDFs and Microfacet Theory Issues and Needs

Microfacet Representation

Playing withfµoffers a large panel of different materials.

Geometrical Attenuation Factor (GAF).

Normal Distribution Functions.

Multiple scattering between microfacets.

Torrance-Sparrow (V-cavity profile) Smith-Bourlier (Uncorrelated microfacets)

Beckmann distribution GGX or Trowbridge-Reitz

(image from [Heitz16])

M. Ribardi`ere (Poitiers) IL microfacets and STD 5 / 25

(8)

BRDFs and Microfacet Theory Issues and Needs

Microfacet Representation

Playing withfµoffers a large panel of different materials.

Geometrical Attenuation Factor (GAF).

Normal Distribution Functions.

Multiple scattering between microfacets.

Torrance-Sparrow (V-cavity profile) Smith-Bourlier (Uncorrelated microfacets)

Beckmann distribution GGX or Trowbridge-Reitz

(image from [Heitz16])

M. Ribardi`ere (Poitiers) IL microfacets and STD 5 / 25

(9)

Interfaced Lambertian Materials Model definition

Interfaced Lambertian (IL) Model [TVCG17]

Several observations can be made:

The glossy term increases according to incidence angle

Thus, a constant Lambertian term is not adapted to energy conservation Solution: Rough Lambertian background covered with a flat Fresnel interface

Fresnel interface

microfacet distribution Lambertian substrate

single microfacet

Lambertian interfaced Lambertian interfaced

Light transmission at interface Multiple scattering under interface

1

πni2T(i,m)T(o,m)(1-KKddri), ri for multiple scattering

(analytical cf. [TVCG17]) Lambertian substrate Fresnel interface

incoming light first specular reflection

scattering after multiple reflections

substrate-interface multiple reflections

M. Ribardi`ere (Poitiers) IL microfacets and STD 6 / 25

(10)

Interfaced Lambertian Materials Model definition

Flat IL Material

Flat surface: Analytical representation, including multiple light scattering Body term decreases according to incidence angles, and specularity Decreases also at grazing observation angles

0 0.05 0.1 0.15 0.2 ni=1.0 ni=1.2 ni=1.33 ni=1.5

-90o 90o

-45o

0o θi=0o

0 0.05 0.1 0.15 0.2 ni=1.0 ni=1.2 ni=1.33 ni=1.5

-90o 90o

-45o

0o θi=80o

ni= 1 ni= 1.2 ni= 1.33 ni= 1.5

M. Ribardi`ere (Poitiers) IL microfacets and STD 7 / 25

(11)

Interfaced Lambertian Materials Model definition

Rough IL Material

The general BRDF equation should be integrated, with:

f(i,o,n) = Z

+

|im|

|in| [fsµ(i,o,m) +fbµ(i,o,m)]|om|

|on|D(m)G(i,o,m)dωm (3) The first integral corresponding tofs corresponds to the glossy term

fs(i,o,n) =F(i,m)D(m)G(i,o,m) 4|in||on| , The second termfb has no analytical solution

Monte Carlo for the rendering Equation:

Lo(x,o,n) =Le(x,o,n) + Z

+

Li(x,i,n)f(i,o,n)|in|dωi, (4) wheref is given by Equation 3, which includes

fbµ(i,o,n) = 1

πn2iT(i,m)T(o,m) Kd

(1 -Kdri) (5)

M. Ribardi`ere (Poitiers) IL microfacets and STD 8 / 25

(12)

Interfaced Lambertian Materials Appearance and discussion

Rough IL Material

Solution: use Monte Carlo process again.

Importance sampling of one microfacet for the body term Slightly increases noise (since increases integral dimension)

But allows to handle multiple scattering between microfacets [Heitz16,TVCG17]

isotropicni= 1.5,σ= 0.1 aniso.ni= 1.5,σx= 0.2,σy= 0.6 aniso.ni= 1.5,σx= 0.6,σy= 0.2

isotropicni= 1.0,σ= 0.1 aniso.ni= 1.0,σx= 0.2,σy= 0.6 aniso.ni= 1.0,σx= 0.6,σy= 0.2

⇒Inherently accounts for anisotropy, given anisotropic distributions

M. Ribardi`ere (Poitiers) IL microfacets and STD 9 / 25

(13)

Interfaced Lambertian Materials Appearance and discussion

Appearance

General model, accounts for:

Flat Lambertian (σ= 0.0,ni= 1.0)

Rough Lambertian (ni= 1.0), with backscattering Rough dielectric mirrors (Kd= 0.0)

Rough interfaced Lambertian (general case)

⇒Illustrated on next slide

An approximate model is proposed in [TVCG17], with:

Beckmann and Gauss distributions Torrance-Sparrow’s GAF

⇒Makes it possible to use with interactive applications and fitting

Note that:

Surface and substrate roughnesses are the same Light scattering between microfacets should be handled

M. Ribardi`ere (Poitiers) IL microfacets and STD 10 / 25

(14)

Interfaced Lambertian Materials Appearance and discussion

IL BRDF lobes

0 0.05 0.2 0.71 2.4 Gauss,TS Beckm,TS Beckm,SB GGX

-90o 90o

-45o

0o

θi=60o

(a)ni= 1.0, σ= 0.1

0 0.05 0.2 0.71 2.4 Gauss,TS Beckm,TS Beckm,SB GGX

-90o 90o

-45o

0o

θi=60o

(b)ni= 1.0, σ= 0.6

0 0.05 0.2 0.71 2.4 Gauss,TS Beckm,TS Beckm,SB GGX

-90o 90o

-45o

0o

θi=60o

(c)ni= 1.5, σ= 0.1

0 0.05 0.2 0.71 2.4 Gauss,TS Beckm,TS Beckm,SB GGX

-90o 90o

-45o

0o

θi=60o

(d)ni= 1.5, σ= 0.6

Distributions and GAFs for various values ofni andσ, illustrated atθi= 60o (log scale).

M. Ribardi`ere (Poitiers) IL microfacets and STD 11 / 25

(15)

Interfaced Lambertian Materials Appearance and discussion

With Beckmann Distribution and Smith GAF

ni=1.5ni=1.33ni=1.2ni=1.0

σ= 0.001 σ= 0.005 σ= 0.1 σ= 0.3

M. Ribardi`ere (Poitiers) IL microfacets and STD 12 / 25

(16)

Interfaced Lambertian Materials Appearance and discussion

IL BRDF lobes: approximate model

0 0.02 0.07 0.18 0.4 L G/TS exact L G/TS appr.

IL G/TS exact IL G/TS appr.

-90o 90o

-45o

0o θi=45o

0 0.02 0.07 0.18 0.4 L G/TS exact L G/TS appr.

IL G/TS exact IL G/TS appr.

-90o 90o

-45o

0o

θi=70o

(a)Gaussian distribution, withni= 1.5 andσ= 0.6

0 0.02 0.07 0.18 0.4 L B/TS exact L B/TS appr.

IL B/TS exact IL B/TS appr.

-90o 90o

-45o

0o θi=45o

0 0.02 0.07 0.18 0.4 L B/TS exact L B/TS appr.

IL B/TS exact IL B/TS appr.

-90o 90o

-45o

0o

θi=70o

(b)Beckmann distribution, withni= 1.5 andσ= 0.6

Comparison between Monte Carlo BRDF estimation of Lambertian (L) and interfaced Lambertian (IL) materials and our approximate model, with Gaussian (G) and Beckmann (B) distributions, and Torrance-Sparrow (TS) GAF (log scale).

M. Ribardi`ere (Poitiers) IL microfacets and STD 13 / 25

(17)

Interfaced Lambertian Materials Appearance and discussion

Discussion

Management of metals (conductors) ?

⇒Nothing new [CT82], since almost no transmission Generalization of approximate models ?

⇒much more complicated...

⇒Approximation relies on both D and G

⇒Our method extends [ON94], based on Gaussian/Beckman distributions Generalization of distribution and GAF

Many existing distributions

Without analytical GAF and/or analytical importance sampling

⇒This presentation provides some results with STD (next slides) Management of light scattering between microfacets

Two existing contributions: [Heitz16] with SB GAF; [TVCG17] with TS GAF Path tracing implementation

⇒Both applied to STD and IL in this presentation

M. Ribardi`ere (Poitiers) IL microfacets and STD 14 / 25

(18)

Student’s T-Distribution Definition

Student’s T-Distribution

Introduced at EG 2017 [EG17]:

DSTD(m) = (γ- 1)γσ-2

πcos4θm((γ- 1)σ2+ tan2θm)γ (6) Inspired from GTR (Generalized Towbridge Reitz) [TR75,Walter07]

Includes both GGX and Beckmann’s distributions

With analytical GAF formulation following the Smith’s formulation With analytical importance sampling

M. Ribardi`ere (Poitiers) IL microfacets and STD 15 / 25

(19)

Student’s T-Distribution Definition

Influence on appearance

⇒Anisotropy also handled (rough aluminium in this case)

M. Ribardi`ere (Poitiers) IL microfacets and STD 16 / 25

(20)

Student’s T-Distribution Definition

Influence on appearance

23

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(21)

Student’s T-Distribution Definition

Influence on appearance

24

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(22)

Student’s T-Distribution Definition

Influence on appearance

25

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(23)

Student’s T-Distribution Definition

Influence on appearance

26

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(24)

Student’s T-Distribution Definition

Influence on appearance

27

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(25)

Student’s T-Distribution Definition

Influence on appearance

28

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(26)

Student’s T-Distribution Definition

Influence on appearance

29

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(27)

Student’s T-Distribution Definition

Influence on appearance

30

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(28)

Student’s T-Distribution Definition

Influence on appearance

31

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(29)

Student’s T-Distribution Definition

Influence on appearance

32

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(30)

Student’s T-Distribution Definition

Influence on appearance

33

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(31)

Student’s T-Distribution Definition

Influence on appearance

34

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(32)

Student’s T-Distribution Definition

Influence on appearance

35

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(33)

Student’s T-Distribution Definition

Influence on appearance

36

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(34)

Student’s T-Distribution Definition

Influence on appearance

37

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(35)

Student’s T-Distribution Definition

Influence on appearance

38

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(36)

Student’s T-Distribution Definition

Influence on appearance

39

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(37)

Student’s T-Distribution Definition

Influence on appearance

40

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(38)

Student’s T-Distribution Definition

Influence on appearance

41

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(39)

Student’s T-Distribution Definition

Influence on appearance

42

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(40)

Student’s T-Distribution Definition

Influence on appearance

43

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(41)

Student’s T-Distribution Definition

Influence on appearance

44

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(42)

Student’s T-Distribution Definition

Influence on appearance

45

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(43)

Student’s T-Distribution Definition

Influence on appearance

46

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(44)

Student’s T-Distribution Definition

Influence on appearance

47

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(45)

Student’s T-Distribution Definition

Influence on appearance

48

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(46)

Student’s T-Distribution Definition

Influence on appearance

49

Visual impact of STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 17 / 25

(47)

Student’s T-Distribution Discussion

Discussion

Advantages of STD:

Accurate control of roughness

Interesting use for fitting (combines the advantages of GGX and Beckmann)

M. Ribardi`ere (Poitiers) IL microfacets and STD 18 / 25

(48)

Student’s T-Distribution Discussion

Fitting with STD

M. Ribardi`ere (Poitiers) IL microfacets and STD 19 / 25

(49)

Student’s T-Distribution Discussion

Discussion

Advantages of STD:

Accurate control of roughness

Interesting use for fitting (combines the advantages of GGX and Beckmann) Provides a general tool for choosing distribution

Advantages of combining IL with STD:

Accounts for a physical representation of body scattering Combines advantages of both

Further generalizes both Implementation issues:

Does not make any difference for IL

Possible to include the combination in any Monte Carlo rendering system Also possible to handle multiple scattering

M. Ribardi`ere (Poitiers) IL microfacets and STD 20 / 25

(50)

Student’s T-Distribution Discussion

Discussion

Advantages of STD:

Accurate control of roughness

Interesting use for fitting (combines the advantages of GGX and Beckmann) Provides a general tool for choosing distribution

Advantages of combining IL with STD:

Accounts for a physical representation of body scattering Combines advantages of both

Further generalizes both

Implementation issues:

Does not make any difference for IL

Possible to include the combination in any Monte Carlo rendering system Also possible to handle multiple scattering

M. Ribardi`ere (Poitiers) IL microfacets and STD 20 / 25

(51)

Student’s T-Distribution Discussion

Discussion

Advantages of STD:

Accurate control of roughness

Interesting use for fitting (combines the advantages of GGX and Beckmann) Provides a general tool for choosing distribution

Advantages of combining IL with STD:

Accounts for a physical representation of body scattering Combines advantages of both

Further generalizes both Implementation issues:

Does not make any difference for IL

Possible to include the combination in any Monte Carlo rendering system Also possible to handle multiple scattering

M. Ribardi`ere (Poitiers) IL microfacets and STD 20 / 25

(52)

Combination of IL with STD Influence on appearance

Influence on appearance

According toγ, with two different roughnesses σ(Smith GAF withni= 1.5):

σ= 0.1, γ= 1.55 σ= 0.1, γ= 8

σ= 0.3, γ= 1.55 σ= 0.3, γ= 8

M. Ribardi`ere (Poitiers) IL microfacets and STD 21 / 25

(53)

Combination of IL with STD Influence on appearance

Influence on appearance

When changing GAF (γ= 1.75,ni= 1.5 andσ= 0.7):

Smith-Bourlier GAF Torrance-Sparrow GAF

For grazing observation angles:

Torrance-Sparrow’s GAF tends to overestimate gloss [Heitz14]

Glossy effects remain high despite increasing roughness

M. Ribardi`ere (Poitiers) IL microfacets and STD 22 / 25

(54)

Combination of IL with STD Influence on appearance

Influence on appearance

Comparisons with and without multiple scattering between microfacets:

Direct reflection only, SB GAF Multiple light bounces, SB GAF

Rough Lambertian (ni= 1.0) γ= 8, σ= 0.7

Smith-Bourlier GAF

M. Ribardi`ere (Poitiers) IL microfacets and STD 23 / 25

(55)

Combination of IL with STD Influence on appearance

Influence on appearance

Comparisons with and without multiple scattering between microfacets:

Direct reflection only, SB GAF Multiple light bounces, SB GAF

Interfacet Lambertian microfacets (ni= 1.5) γ= 1.75, σ= 0.5

Smith-Bourlier GAF

M. Ribardi`ere (Poitiers) IL microfacets and STD 24 / 25

(56)

Conclusion and Future Work

Conclusion and Future Work

STD with interfaced Lambertian microfacets:

Physically based model

Management of specular and body reflections Only few parameters

Extends the range of rendered materials

Future work:

Better STD importance sampling

⇒What about Visible Normals Importance Sampling?

In depth fitting analysis

Correlation between the interface and the substrate roughness in IL Any other idea ?

M. Ribardi`ere (Poitiers) IL microfacets and STD 25 / 25

Referanser

RELATERTE DOKUMENTER

The presented paper outlines possible ways to handle and analyze multiple response data. Several rather simple criteria for reducing the dimensionality of these

Dersom Trøndelag fylkeskommune er avsender og skal stå sammen med flere andre logoer skal fylkeskommunens logo plasseres til sist, og med større avstand en resten av

The developed Monte Carlo algorithm has been validated by employing 508 nm polystyrene beads and Arizona test dust as scattering agents, and has proven to be an accurate tool

Quasi-Monte Carlo rendering techniques (Keller) Interleaved sampling and parallelization, efficient volume rendering, strictly deterministic sampling in RenderMan,

Rendering the nucleus channel using a gray-scale map makes it possible to visualize a segmentation mask by rendering each region in a different color.. The combination of

The direct rendering of the time-varying interval volumes makes it possible to get the distribution and relationship of the interval volumes across time steps, and help us

With this system it is possible to observe the fish distribution around the surveying ship and trawl, and also to compare SA-values from the echosounder mounted on the

With this system it is possible to observe the fish distribution around the surveying ship and trawl, and also to compare SA-values from the echosounder mounted on the