1. A Practical Analytic Single Scattering Model for Real Time Rendering
Bo Sun Columbia University
Ravi Ramamoorthi Columbia University
Srinivasa Narasimhan Carnegie Mellon University
Shree Nayar Columbia University
Sponsors: ONR, NSF

2. Light Transport in Scattering Media
Scattered (glows)
Point Source
Direct Transmission
Viewer
Surface Point
Clear Day Foggy Day
Clear Day Foggy Day

3. 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

4. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

5. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

6. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

7. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

8. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

9. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

10. The Airlight Integral : scattering coefficient of the medium
Point Source, s
Viewer, v
Surface Point, p
The Airlight Integral:

11. The Airlight Model Originally 4D: , , , Point Source, s
Surface Point, p
Viewer, v
Originally 4D: , , ,

12. The Airlight Model Originally 4D: , , , Point Source, s
Surface Point, p
Viewer, v
Originally 4D: , , ,

13. The Airlight Model Originally 4D: , , , Point Source, s
Surface Point, p
Viewer, v
Originally 4D: , , ,

14. Special Function F Well behaved and purely numerical 2D function.
Pre-computed once for all and stored as a 2D texture.

15. Shader Code for Airlight Model
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); }

16. Shader Code for Airlight Model
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); }

17. Shader Code for Airlight Model
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); }

18. Shader Code for Airlight Model
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); }

19. Shader Code for Airlight Model
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); }

20. Implementation Choices for Airlight
64x64 floating point texture for F table
Add a skybox to invoke vertex/pixel shader to compute Airlight.
Nearest Neighbor
Bilinear Interpolation

21. Airlight Demo
Demo

22. The Surface Radiance Model
Point Source, s
BRDF
Viewer, v
Surface Point, p

23. The Surface Radiance Model
Point Source, s
BRDF
Viewer, v
Surface Point, p
: Lambertian, Phong
: ,
1D function on 2D
2D:

24. Special Function G

25. Shader Code for Surface Radiance
float SurfaceRadiance( ) {
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G; }

26. Shader Code for Surface Radiance
float SurfaceRadiance( ) {
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G; }

27. Shader Code for Surface Radiance
float SurfaceRadiance( ) {
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G; }

28. Implementation Choices for Surface Radiance
Need to add radiance contribution from attenuated direct lighting.
Attenuate the final radiance according to distance to the camera.
Point Source, s
BRDF
Viewer, v
Surface Point, p

29. Implementation Choices for Surface Radiance
Need to add radiance contribution from attenuated direct lighting.
Attenuate the final radiance according to distance to the camera.
Point Source, s
BRDF
Viewer, v
Surface Point, p

30. Lambertian and Phong Spheres
Clear Day
Lambertian Phong= Phong=20
Foggy Day

31. The Complete Model Surface Radiance Model Airlight Model 2 Lookups
2 Lookups and

32. The Complete Model Surface Radiance Model Airlight Model 2 Lookups
2 Lookups and
Image size
Lights
Terms to approximate the phase function
Texture lookups Analytic expression
Maya Plug-in available from our website.

33. Demo: Complex Geometry

34. Complex Lighting and Material
Rendering time is linear in the number of lights.
Viewer, v
BRDF
Surface Point, p

35. Point Spread Function Assume equidistant point sources
Scattering is essentially Point Spread Function (PSF).
Angles
Intensity
Input
Output
Angles
Intensity
Angular Component Amplitude Component
PSF

36. Point Spread Function Assume equidistant point sources
Scattering is essentially Point Spread Function (PSF).
Angles
Intensity
Input
Output
Angles
Intensity
Angular Component Amplitude Component
PSF
Tsv*exp[-Tsv] * Pre-convolved Environment Map

37. Convolution with PSF
BRDF Environment Map
Clear Day
Foggy Day

38. Demo: PSF for Complex Lighting

39. Summary
An OpenGL-Like Practical Real-Time Rendering Technique:
Analytic Airlight Model
50fps fps

40. Summary
An OpenGL-Like Practical Real-Time Rendering Technique:
Analytic Airlight Model
Analytic Surface Radiance Model
50fps fps

41. Summary
An OpenGL-Like Practical Real-Time Rendering Technique:
Analytic Airlight Model
Analytic Surface Radiance Model
PSF for Complex Lighting and Natural Material
100fps fps

42. 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.

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

44. The End

45. The End