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
Clear Day Foggy Day
Light Transport in Scattering Media
Clear Day Foggy Day
Point Source
Surface PointViewer
Direct Transmission
Scattered (glows)
Our Technical Contributions
Explicit compact Airlight formula Explicit Surface Radiance formula
- Accurate
- Simple fragment shader
- Fully interactiveAssumptions: Isotropic point light sources Homogenous media Single scattering No volumetric shadows
20)(deIk
d
xd
edeIk
20)(
d
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
x vpD
vpD
: scattering coefficient of the medium
The Airlight Integral: 20
deI d
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
: scattering coefficient of the medium
The Airlight Integral: xd
edeIk
20)(
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
: scattering coefficient of the medium
The Airlight Integral: xd
edeIk
20)(
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
: scattering coefficient of the medium
The Airlight Integral: xd
edeIk
20)(
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
: scattering coefficient of the medium
The Airlight Integral: xd
edeIk
20)(
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
vpD
: scattering coefficient of the medium
The Airlight Integral:
vpD
xd
dxedeIk
02
0)(
The Airlight IntegralPoint Source, s
Surface Point, pViewer, v
svD
The Airlight Integral:
vpD
: scattering coefficient of the medium
vpD
xd
dxedeIk
02
0)(
),,,( vpsvairlight DDL
The Airlight Model
airlightL
Originally 4D: , , , svD vpD
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Point Source, s
Surface Point, pViewer, v
svD
vpD
airlightL
Originally 4D: , , , svD vpD
The Airlight Model
sin2
cos0
2
sv
T
TeI sv
sinsvT
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Point Source, s
Surface Point, pViewer, v
svD
vpD
The Airlight Model
airlightL
Originally 4D: , , , svD vpD
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Point Source, s
Surface Point, pViewer, v
svD
vpD
Special Function F
v
duvuF0
]tanexp[),(
Well behaved and purely numerical 2D function. Pre-computed once for all and stored as a 2D texture.
Shader Code for Airlight Modelfloat 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);
}
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Shader Code for Airlight Modelfloat 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);
}
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Shader Code for Airlight Modelfloat 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);
}
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Shader Code for Airlight Modelfloat 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);
}
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Shader Code for Airlight Modelfloat 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);
}
0A [ 1A , 2 )]1A )
sincos
arctan21
4 sv
svvp
TTT
,(F (F
Implementation Choices for Airlight
1. 64x64 floating point texture for F table
2. Add a skybox to invoke vertex/pixel shader to compute Airlight.
Nearest Neighbor
Bilinear Interpolation
Airlight Demo
Demo
The Surface Radiance ModelPoint Source, s
Surface Point, p
Viewer, v n̂BRDF
2D:F
The Surface Radiance ModelPoint Source, s
Surface Point, p
Viewer, v n̂BRDF
1D function on i2D : Lambertian, Phong
nG0G: ,
iiairlightsurface dBRDFLL cos
Special Function G
Shader Code for Surface Radiance
float SurfaceRadiance( )
{
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G;
}
)',(2
20
sspnsp
ssurface TG
TkIL
Shader Code for Surface Radiance
)',(2
20
sspnsp
ssurface TG
TkIL
float SurfaceRadiance( )
{
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G;
}
Shader Code for Surface Radiance
)',(2
20
sspnsp
ssurface TG
TkIL
float SurfaceRadiance( )
{
float4 G = texRECT(G_20, Tsp, thetas);
return Ks*Io*beta/(2*Dsp*PI)*G;
}
Implementation Choices for Surface Radiance
1. Need to add radiance contribution from attenuated direct lighting.
2. Attenuate the final radiance according to distance to the camera.
Point Source, s
Surface Point, p
Viewer, v n̂BRDF
Implementation Choices for Surface Radiance
1. Need to add radiance contribution from attenuated direct lighting.
2. Attenuate the final radiance according to distance to the camera.
Point Source, s
Surface Point, p
Viewer, v n̂BRDF
Lambertian and Phong Spheres
Lambertian Phong=10 Phong=20
Clear
Day
Foggy Day
The Complete Model
airlightsurfaceT LLeL vp
Airlight Model
Surface Radiance Model 2 LookupsF2 Lookups andnG0G
The Complete Model
Texture lookups Analytic expression
Maya Plug-in available from our website.NIS 4 IS8
Image size
Lights
Terms to approximate the phase function
airlightsurfaceT LLeL vp
Airlight Model
Surface Radiance Model 2 LookupsF2 Lookups andnG0G
Demo: Complex Geometry
Demo
Complex Lighting and Material
Rendering time is linear in the number of lights.
Surface Point, p
Viewer, vsvD
vpD
n̂
BRDF
Point Spread Function Assume equidistant point sources Scattering is essentially Point Spread Function (PSF).
PSFAngles
Intensity
Input Output
Angles
Intensity
Intensity
Angular Component Amplitude Component
Point Spread Function Assume equidistant point sources Scattering is essentially Point Spread Function (PSF).
PSFAngles
Intensity
Input Output
Angles
Intensity
Intensity
Angular Component Amplitude ComponentTsv*exp[-Tsv] * Pre-convolved Environment Map
Convolution with PSFBRDF Environment Map
Clear Day
Foggy Day
Demo: PSF for Complex Lighting
Demo
50fps 40fps
Summary
Analytic Airlight Model
An OpenGL-Like Practical Real-Time Rendering Technique:
Summary
Analytic Airlight Model Analytic Surface Radiance Model
An OpenGL-Like Practical Real-Time Rendering Technique:
50fps 60fps
Summary
Analytic Airlight Model Analytic Surface Radiance Model PSF for Complex Lighting and Natural Material
An OpenGL-Like Practical Real-Time Rendering Technique:
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
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