A Practical Analytic Single Scattering Model for Real Time Rendering

A Practical Analytic Single Scattering Model for Real Time Rendering

Bo Sun Columbia University Ravi Ramamoorthi Columbia UniversitySrinivasa Narasimhan Carnegie Mellon University Shree Nayar Columbia University

Sponsors: ONR, NSF

Scattering in Participating Media


Loss of contrast


Loss of contrast

Dimming and blur


GlowsLost of contrast Dimming and blur

Light Transport in Clear Day

Point Source

Surface PointViewer

Direct T

ransmiss

ion

Clear Day Foggy Day

Light Transport in Scattering Media

Clear Day Foggy Day

Point Source

Surface PointViewer

Direct T

ransmiss

ion

Scattered (glows)

Complexity of Rendering Scattering Media

Virtual Viewpoint

Virtual Screen

Objects

Complexity of Rendering Scattering Media

640 x 480 (image) x 4 (lights) x [ 50 (steps) + 100 ( directions ) x 50 (steps)] x 30 (intersect) = ?

1.9 Trillion Calculations

3.0 GHz CPU?

3 1000

Virtual Viewpoint

Virtual Screen

Objects

Previous Work

Monte Carlo Ray Tracing Methods

[Kajiya and Herzen 1984], [Max et al. 1994]…

- Impressive effects, but slow

Sp

eed

Accu

racy

Previous Work




Hardware-accelerated Numerical Methods

[ Dobashi et al. 2002 ], [ Riley et al. 2004 ] ….

- Specialized for skies or clouds and Expensive precomputation

- No effects of scattering on surface radiance

Sp

eed

Accu

racy

Previous Work




Hardware-accelerated Numerical Methods

[ Dobashi et al. 2002 ], [ Riley et al. 2004 ] ….

- Specialized for skies or clouds and Expensive precomputation

- No effects of scattering on surface radiance

Glows around point sources

[ Max et al. 1986 ], [ Biri et al. 2004 ]…

- Approximations which are not feasible in many cases

- Not extendable to surface radiance and complex lighting

Sp

eed

Accu

racy

Our Technical Contributions

Explicit compact Airlight formula

Explicit Surface Radiance formula

- Accurate

- Simple fragment shader

- Fully interactive

Assumptions:

Isotropic point light sources

Homogenous media

Single scattering

No volumetric shadows

20)(d

eIk

d

xd

ed

eIk

2

0)(

d

The Airlight IntegralPoint Source, s

Surface Point, pViewer, v

svD

x vpD

vpD

: scattering coefficient of the medium

20

d

eI d



svD


xd

ed

eIk

2

0)(



svD

vpD


vpD

xd

dxed

eIk

02

0)(



svD

vpD


vpD

xd

dxed

eIk

02

0)(

),,,( vpsvairlight DDL

The Airlight Integral

vp svsvD

x

svsv

xDxD

svsv

sv dxexDxD

e

xDDx

Dxk

I

022

cos2

22

0

cos2)

cos2

cosarccos(

4

22

),,,( vpsvairlight DDL 4D: svD vpD

We want:

- Low dimensional tabulation and cheap evaluation

- Interactively change physical parameters

vpD

xd

dxed

eIk

02

0)(

- combine and *D

- combine and svT

The Airlight Model-Solution

4D: svD vpD),,,( vpsvairlight DDL

vpD

xd

dxed

eIk

02

0)(

sin

cosarctan

2

1

4 sv

svvp

T

TT

2

sin2

cos0

2

sv

T

T

eI svsinsvT


1

2

lim

lim

exp[ d]tan),,(0 svTA ),(1 svTA

4D: svD vpD),,,( vpsvairlight DDL

vpD

xd

dxed

eIk

02

0)(

- combine and *D

- combine and svT

v

duvuF0

]tanexp[),(

1

2

lim

lim

exp[ d]tan),,(0 svTA ),(1 svTA

4D:

2D


svD vpD),,,( vpsvairlight DDL

vpD

xd

dxed

eIk

02

0)(

- combine and *D

- combine and svT

Special Function F

v

duvuF0

]tanexp[),(

Well behaved and purely numerical 2D function.

Independent of the scene.

Evaluate once for all and stored as a 2D texture.

Our Compact Airlight Formula

Compact 2D representation.

Real time cheap evaluation.

Arbitrarily change physical parameters.

Fully interactive

),(),( 22110 vuFvuFA 2D:

Comparison with Monte Carlo simulation

Low RMS error shows our model is physically accurate

Video: Glows

Video clip 1

Light Transport Revisited

Point Source, s

Surface Point, p

Viewer, vn̂

BRDF

Lambertian and Phong Spheres

Lambertian Phong=10 Phong=20

Clear

Day

Foggy Day

2D:F

The Surface Radiance Model

Point Source, s

Surface Point, p

Viewer, vn̂

BRDF

1D function on i2D : Lambertian, Phong

nG0G: ,

iiairlightsurface dBRDFLL cos

Video: Diffuse and Glossy Shading

Video clip 2

The Complete Model

airlightsurfaceT LLeL vp

Airlight Model

Surface Radiance Model

2 LookupsF2 Lookups andnG0G

The Complete Model

Texture lookups

Analytic expression

NIS 4

IS8

Image size

Lights

Terms to approximate the phase function

= 5 Million

= 10 Million

15 Million VS 1.9 Trillion

airlightsurfaceT LLeL vp

Airlight Model

Surface Radiance Model

2 LookupsF2 Lookups andnG0G

float AirLight( )

{

float u = A1(beta, Dsv, gammasv);

float v1 = 0.25*PI+0.5*atan((DvpDsv*cos(gammasv))/(Dsv*sin(gammasv)));

float v2 = 0.5*gammasv;

float4 f_1=texRECT(F, v1, u);

float4 f_2=texRECT(F, v2, u);

return A0(lightIntensity, beta, Dsv, gammasv)*(f_1.x-f_2.x);

}

float SurfaceRadiance( )

{

float4 G = texRECT(G_20, Tsp, thetas);

return Ks*Io*beta/(2*Dsp*PI)*G;

}

Snap Shot of Shader Code

Video: Complex Geometry

Video clip 3

For Live Demo, please visit sketch at 10:30am, Patree Hall A.

Complex Lighting and Materials

Rendering time is linear in the number of lights.

Surface Point, p

Viewer, v

svD

vpD

n̂

BRDF

Point Spread Function

Equidistant point sources

Scattering is essentially Point Spread Function (PSF).

[Narasimhan and Nayar 2003], [Premoze et al. 2004]…

PSF

Angles

Inte

nsi

ty

Input Output

Complex Materials

Clear Day Foggy Day

PSF

Angles

Inte

nsi

ty

BRDF

Effective BRDF

with Scattering

Environment Maps

Clear Day Foggy Day

PSF

Angles

Inte

nsi

ty

Lighting

Foggy Lighting

PSF for Complex Lighting and Material

Video clip 4 and 5

Visual Effects and Performance Comparisons

Methods Shadows GlowsSurface shading

Complex

lighting&

materials

Real Time

OpenGL Like

Monte Carlo

Numerical Simulation

Other Analytic Methods

Our Model

50fps 40fps

Summary

Analytic Airlight Model

An OpenGL-Like Practical Real-Time Rendering Technique:

Summary


Analytic Surface Radiance Model


40fps 50fps

Summary


Analytic Surface Radiance Model

PSF for Complex Lighting and Natural Materials


100fps 20fps

Acknowledgement

R. Wang, J. Tran and D. Luebke for the PRT code.

S. Premoze for the Monte Carlo simulation code.

P. Debevec for the light probes.

W. Matusik for the tabulated BRDF.

Supported by a Columbia University Presidential Fellowship, an ONR Grant, an NSF Grant, an NSF CAREER award, and equipment donations from Intel and NVIDIA.

Thanks for Listening!Maya Plug-in, 2D tables, and Shader code:

http://www.cs.columbia.edu/~bosun/research.htm

The End

A Practical Analytic Single Scattering Model for Real Time Rendering

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