Definition Platforms for this talk –Windows / DirectX11 –OpenGL 4 / OpenGL ES 3.0 –PlayStation 4 –Xbox One

Definition• Platforms for this talk

– Windows / DirectX11– OpenGL 4 / OpenGL ES 3.0– PlayStation 4– Xbox One

ALU Budgets• What do you use higher ALU performance for?

– Full HD resolution(1920x1080)• 2.25 times larger than half HD resolution(1280x720)

– Post-processing• High quality post-processing with existing algorithms

– High resolution post-processing– Glare, de-focus blur, motion blur– Screen-space anti-aliasing

• New post-processing– Screen-space lighting (reflections), ambient obscurance, sub-surface

scattering, volume rendering

Recent GPU Trend• ALU free

– Current GPU performance doesn’t depend on the number of ALU cycles

• B/W of cache / texture / render targets• Register / multi-threading• Limitations of render backend resources

– Increasing the number of ALU instructions doesn’t tend to decrease performance

• ALU is typically used to save B/W by encoding and decoding• It depends on the design of rendering passes

How About Shading?• Many texture samples

– For both forward and deferred techniques• The only difference is the rendering pass

– Albedo, Reflectance– Normal / Height, Roughness, AO– G-Buffer– Light source (IBL / SSL) / accumulation, GI info.

– Do we have a budget to use more ALU?

More ALU?• Can we use more ALU instructions for shading?

– Old normalized Blinn-Phong model uses 20 to 30 instructions

– 100 instructions / light are affordable for new generation consoles

– Using more instructions for shading is a good candidate to use ALU efficiently

),max(

))(()(1 0

210 enln

hn

n

specdFF

cncFR

The Current Popular Model• A physically based model for specular

– Microfacet model• GGX (Trowbridge-Reitz) (D)• Schlick approximation (F)• Smith (G)

))((4

),(),(),(),(

enln

elelelel

GFDfr

Better Model for Fresnel?• Spherical Gaussian Approximation

– This model approximates the Schlick approximation

– Should we approximate the Fresnel equation?– Should we use more a accurate

approximation?

hehehe 98316.6)(55473.500 2)1(),( ffF

Evaluation

Yellow : Fresnel equation (IOR = aluminum at 610nm)Green : Schlick approximation (IOR = aluminum at 610nm)Blue : Fresnel equation (IOR = 1.5)Purple : Schlick approximation (IOR = 1.5)

F( q)

q

Need Approximation?• Do we have to approximate Fresnel for

new generation consoles?– Fresnel equation w.r.t. reflectance ( f0 )

• It is easier to handle than refractive index

2

00

00

2

00

00

)1(cos)1(

)1(cos)1(

)1(cos)1(

)1(cos)1(5.0

ff

ff

ff

ffF

20

220

)1(

)cos1()1(1

f

f

(IOR = 1.3 + 7.48i)Blue : Fresnel equation with the refractive indexPurple : Fresnel equation with the real reflectance

Fresnel with Reflectance• This Fresnel equation is inaccurate for large f0

– A large real f0 is calculatedfrom a complex refractive index

– The Fresnel equation should take complex numbers

– The complex version is more complicated

F( q)

q

Improved Spherical Gaussian• Fresnel behavior is complicated

– Need a complex approximation to represent the behavior

– Try to improve accuracy with most useful value IOR = 1.5

cos58092.8cos60232.900

8

2)1()( ffF

Improved Spherical Gaussian

(IOR = 1.5)Blue : Schlick approximation Purple : Fresnel equationYellow : Improved Spherical Gaussian

Schlick

Improved SphericalGaussian

F( q)

q

Conclusion for F Term• Schlick is a good enough approximation

– It still has a problem with complex refractive indices with a large imaginary part

• It can be improved with Fresnel Term Approximations for Metals [WSCG 2005]

– It requires a complex refractive index as a parameter

– This difference is difficult to distinguish with punctual lights, but is more visible with image based lighting

• We use the Schlick approximation in this talk, though you can choose better approximations (including improved Spherical Gaussian) as you like

How about Diffuse?• Lambert?

– It is not realistic– We use microfacet models for specular, so

why not for diffuse?

Oren-Nayar?• Use Oren-Nayar [SIGGRAPH 1994]

– Diffuse model taking into account the microfacet model and roughness

• View dependent component• Matte-look depending on roughness• Retro-reflective effect

• NDF is not GGX– NDF of Oren-Nayar is

• G term is not Smith– Torrance-Sparrow V-cavity model

• Oren-Nayar doesn’t conserve energy with specular on each facet– Not a physically based model

2

2

2)( l

ecD

l

Problems with Oren-Nayar

Our Goal• Better diffuse model

– Using the same microfacet model as specular– Physically based diffuse model

Microfacet Model for Specular• A reflectance model for specular can be

simple– You only take reflection in view direction into

account

))((4

),(),(),(),(

enln

elelelel

GFDfr

Microfacet Model for Diffuse• Since diffuse reflects incident light in all

directions, a reflectance model is complex– If we assume all facets are Lambertian– All facets reflect toward view direction

mdiffr dGFDf

),,(),,()())(())((

1)( elmelmmemlm

enlnel,n,

W : Hemisphere around the geometry normal(n)m : Microfacet normal

Try to Improve Oren-Nayar• The first problem is that Oren-Nayar

doesn’t take Fresnel into account– See “Improved Diffuse Reflection Models for

Computer Vision” [WOLFF et al. 1998]

Starting Point

if0)))((( lnenle

otherwise

),1Min()))(()(09.0

45.0()65.0

5.00.1)((2

2

2

2

0 en

lnlnenleln

E

rL

)))()(()(

09.045.0()

65.05.00.1)((

2

2

2

2

0 lnlnenleln

E

Blue : Original Oren-NayarPurple : Improved one (SIGGRAPH 2012)

Lr

qe

Intuition• When surface gets rougher

– Microfacet model behaves like a blur filter– When roughness = 0

• Fresnel effect with Lambertian

– When roughness increases• Fresnel effect gets blurrier

Oren-Nayar analysis

),1Min()))(()(09.0

45.0()65.0

5.00.1)((2

2

2

2

0 en

lnlnenleln

E

Lambertian View-dependent factor(microfacet effect)

Blending factor(with roughness)

Diffuse Fresnel Term• Using “A Practitioners’ Assesment of Light

Reflection Models” [PG 1997]

550 )1(1)1(1)1(

20

21)( enlnel, fFdiff

Add Fresnel Term

),1Min()))(()(09.0

45.0()65.0

5.00.1)()(,()1(2

2

2

2

00 en

lnlnenlelnel

diffFfE

55 )1(1)1(120

21)( enlnel, diffF

550 )1(1)1(1

20

21)1()( enlnel, fFdiff

Result

Lambert Improved Oren-Nayar[SIGGRAPH 2012]

Oren-Nayar with Fresnel

roughness = 0.7

AnalysisBlue : Oren-Nayar, roughness = 0.0Purple: Oren-Nayar w/ Fresnel, roughness = 0.0Yellow: Oren-Nayar, roughness = 1.0Green : Oren-Nayar w/ Fresnel, roughness = 1.0

ql

n·e 1 (0)

cos 1 (0)

f0 0.04

Lr


ql

n·e 0.707 (45)

cos 1 (0)

f0 0.04

Lr


ql

n·e 0.174(80)

cos 1 (0)

f0 0.04

Lr

Is This Physically Based Diffuse?

• This is still a compromise– F term

• In reality, each facet must follow Fresnel• Integrate Fresnel (with other terms) over facets

– D and G terms• Still not GGX and Smith

Try to Derive a New Diffuse Model

• Simply, integrating the diffuse microfacet model with given D, F and G functions– Not modifying Oren-Nayar

mdiffr dGFDf

),,()),,()(())(())((

1)( elmelmmemlm

enlnel,n,

Deriving a New Model• The model doesn’t have a closed form

– It is numerically integrated

AnalysisBlue : Oren-NayarPurple: Oren-Nayar w/ FresnelGreen : New model

n·e 1.0 (0)

cos 1.0 (0)roughness 0.0

f0 0.04

ql

Lr


n·e 1.0 (0)


f0 0.04

ql

Lr


n·e 1.0 (0)


f0 0.04

ql

Lr


n·e 0.5 (60)


f0 0.04

ql

Lr


n·e 0.342 (70)


f0 0.04

ql

Lr

AnalysisBlue : Oren-NayarPuprle: Oren-Nayar w/ FresnelGreen : New model

n·l 0.866 (30)


f0 0.04

qe

Lr


n·l 0.866 (30)


f0 0.04

qe

Lr


n·l 0.866 (30)


f0 0.04

qe

Lr


n·l 0.259 (75)


f0 0.04

qe

Lr

Implementation of the New Model

• Baking the model to a texture is the simplest way– 3 vectors and 2 scalars

• f0 can be factored out of texture

– It is difficult to bake the model directly

mdiffr drGfFrDrff

),,,(),,,(),())(())((

1),,( 00 elmelmmemlm

enlnel,n,

ALU implementation• When your shader is texture-bound

– Typically, it is texture-bound– Complex fitted model is better than texture

reads

Fitted Shading Model

1116402.150912.1733996.036053.1

)1(1

36053.1

303573.0542026.01),,( 1

139

123

2

45

2

24

2

enen

lerF

0)))((( if lnenle

25 )(5.05.011,2Min110,21Max),( lnlnlnl mL

en

en

lnen

le,388410.0188566.0

2)(3726732.01

11))(995584.031072.1)(09.0(

),(2

2

dV

)(),(),(),(120

21),,( 00 le,le,lle,le, pdmrr BVLFffL

))((

))(())((4.1)(

lnenle

lnenlelnenle,pB

otherwise

Complexity• The model is very complicated

– Only a slight performance difference between our new model and Oren-Nayar in typical scenes

– ALU is free!

Fitted Model Analysisn·e 1.0 (0)


f0 0.04

Blue : Fitted modelOrange Dash : Numerically integrated

ql

Lr



f0 0.04


ql

Lr



f0 0.04


ql

Lr



f0 0.04


n·l

Lr



f0 0.04


ql

Lr

Fitted Model Analysisn·l 0.866 (30)


f0 0.04


qe

Lr



f0 0.04


qe

Lr



f0 0.04


qe

Lr

Fitted Model Analysisn·l 0.259(75)


f0 0.04


qe

Lr

Limitation• Accuracy at grazing angles for both view and

light vectors is not enough with this model– It may be noticeable on the edges

• Roughness is assumed to be from 0 to 1• The fitting model shouldn’t be used to

compute AmbientBRDF texture

Results

Lambert Oren-Nayar w/Fresnel New model

Roughness 0.0

Results


Roughness 0.05

Results


Roughness 0.1

Results


Roughness 0.3

Results


Roughness 1.0

Results


Roughness 1.0 (diffuse only)




Conclusion• From a physically based perspective, the

same microfacet model should be used for both diffuse and specular– It makes more persuasive visuals– New consoles have enough computational

power to implement such complex models

Acknowledgements• Tatsuya Shoji• Stephen McAuley• Stephen Hill

Questions?

http://research.tri-ace.com/

You can find these slides, including past presentations, at

Documents

Definition Platforms for this talk –Windows / DirectX11 –OpenGL 4 / OpenGL ES 3.0 –PlayStation 4 –Xbox One