Rendering Outdoor Light Scattering in Real Time

Rendering Outdoor Light
Scattering in Real Time
Naty Hoffman
Westwood Studios
naty@westwood.com
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Arcot J Preetham
ATI Research
preetham@ati.com

Outline
– Basics
• Atmospheric Light Scattering
• Radiometric Quantities
• From Radiance to Pixels
– Scattering Theory
• Absorption, Out-Scattering, In-Scattering
• Rayleigh and Mie Scattering
– Implementation
• Aerial Perspective, Sunlight, Skylight
• Vertex Shader
– Future Work
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Atmospheric Light Scattering
• Is caused by a variety of particles
– Molecules, dust, water vapor, etc.
• These can cause light to be:
– Scattered into the line of sight (in-scattering)
– Scattered out of the line of sight (out-scattering)
– Absorbed altogether (absorption)
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Atmospheric Light Scattering
• Illuminates the sky

Atmospheric Light Scattering
• Attenuates and colors the Sun

Atmospheric Light Scattering
• Attenuates and colors distant objects

Atmospheric Light Scattering
• Varies by
– Time of Day
– Weather
– Pollution

Atmospheric Light Scattering
• Varies by
– Time of Day
– Weather
– Pollution

Atmospheric Light Scattering
• Varies by
– Time of Day
– Weather
– Pollution

Atmospheric Light Scattering
• Varies by
– Time of Day
– Weather
– Pollution

Atmospheric Light Scattering
• Varies between planets

Atmospheric Light Scattering
• Extinction (Absorption, Out-scattering)
– Phenomena which remove light
– Multiplicative:
• In-scattering:
– Phenomenon which adds light
– Additive:
• Combined:
Lin
L =
extinction
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F
ex
L =
F L +
scattering
ex
0
L
L
0
in

Radiometric Quantities
• Radiant Flux
• Radiance
• Irradiance
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Radiometric Quantities
• Radiant Flux Φ
– Quantity of light through a surface
– Radiant power (energy / time)
– Watt
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Radiometric Quantities
• Radiance L
– Quantity of light in a single ray
– Radiant flux / area / solid angle
– Watt / (meter 2 * steradian)
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Radiometric Quantities
• Irradiance E
– Quantity of light incident to a surface point
– Incident radiant flux / area (Watt / meter 2 )
– Radiance integrated over hemisphere
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From Radiance to Pixels
• Compute radiance incident to eye
through each screen pixel
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From Radiance to Pixels
• Pixel value based on radiance
• But radiance is distributed
continuously along the spectrum
– We need three numbers: R, G, B
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From Radiance to Pixels
• SPD (Spectral Power Distribution) to RGB
S
– Fast approach:
• Do all math at R, G, B sample wavelengths
– Correct approach:
• Use SPDs, convert final radiance to RGB
M L
400nm 500nm 600nm 700nm
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Absorption
• Absorption cross section ó ab
– Absorbed radiant flux per unit incident
irradiance Φ / E
– Units of area (meter 2 )
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ó ab

Absorption
• Absorption cross section ó ab
Φ = E * ó ab
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ó ab = Φ / E
ó ab

Absorption
• Absorption coefficient â ab
– Particle density ñ ab times
absorption cross section ó ab
– Units of inverse length (meter -1 )
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Absorption
• Total absorption cross section:
A ab = ó ab ñ ab A dx
• Probability of absorption:
P ab = A ab / A = ó ab ñ ab dx = â ab dx
A
dx
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Absorption
• Attenuation of radiance from travel
through a constant-density
absorptive medium:
L 0
L
( s)
s
=
L
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0
e
− β
ab
s
L(s)

Out-Scattering
• Exactly as in the absorption case
– Scattering cross section ó sc
– Scattering coefficient â ñ ó sc = sc sc
– Attenuation due to out-scattering in
a constant-density medium:
L(
s)
= L e
− β
0
ósc make
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sc
s

L
( s)
Extinction
• Both absorption and out-scattering
attenuate light
• They can be combined as extinction
• Extinction coefficient β ex = β ab + β sc
• Total attenuation from extinction
s
= L e ex F ( s)
=
e
−β
ex s
0
−β
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ex

In-Scattering
• Light is scattered into a view ray
from all directions
– From the sun
– From the sky
– From the ground
• We will only handle in-scattering
from the sun
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In-Scattering
• Where does a scattered photon go?
– Scattering phase function f(è, ö)
• If a photon is scattered, gives the
probability it goes in direction è, ö
• Most atmospheric particles are spherical
or very small: f(è, ö) = f(è)
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è

In-Scattering
• How do we use f(è) for in-scattering?
– In-scatter probability: f(è)ω sun
– In-scatter radiance : f(è)ω sun L sun =f(è)E sun
Sun
Eye ray
w sun
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è

In-Scattering
• In-scattering over a path
– Radiance from a single event: f(è)E sun
– Over a distance dx: f(è)E sun â sc dx
• Angular scattering coefficient
( θ ) =
β ( θ )
β f
sc
– In-scattering over dx: E sun â sc (è) dx
– Units of â sc (è) : meter -1 * steradian -1
sc
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L
In-Scattering
• Added radiance from solar inscattering
through a constantdensity
scattering medium:
in
1
( ) ( )( s )
s θ = E β θ 1−
e
−β
ex
, sun sc
βex
s
è
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( , θ ) in s L

Extinction and In-Scattering
( s θ ) L F ( s)
L ( s,
θ )
L = +
Fex
( s)
, 0 ex in
= e
−β
exs
( ) ( )( )
L s,
θ = E β θ 1−
e
−β
exs
in
sun sc
βex
L0
s
è
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1
L(
s,
θ )

Extinction and In-Scattering
( s θ ) L F ( s)
L ( s,
θ )
L = +
, 0 ex in
• Compare to hardware fog:
( s)
=
L ( )
( s ) + C ( s)
L - f f
0
1 fog
– Monochrome extinction
– Added color completely nondirectional
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Rayleigh Scattering
• Small particles (r < 0.05 ë)
• â sc is proportional to 1/λ 4
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Rayleigh Scattering
• Phase function:
f
R
( )
3 ( )
θ = 1+
cos
2
θ
16π
è
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Rayleigh Scattering

0.75
Mie Scattering
• Larger, spherical particles
• Phase function approximation:
– Henyey-Greenstein
0.5
0 -0.5
f
HG
( θ )
=
-0.75
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4π
( )
( ( ) ) 2 / 3
2
1−
g
2
1+
g − 2g
cos θ

Mie Scattering
• Wavelength dependence
– Complex and depends on exact size
of particle
– In practice, air usually contains a
mix of various sizes of Mie particles
• In the aggregate these tend to average
out any wavelength dependence
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Mie Scattering

Combined Scattering
• In practice, air contains both
Rayleigh and Mie scatterers
• Absorption is usually slight
• We will use:
ex
Rayleigh
sc
β = β +
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β
Mie
sc
( θ ) =
β
Rayleigh
f ( θ ) + β
Mie
f ( θ )
βsc sc R
sc HG

Parameters
• Atmospheric parameters:
β
Rayleigh
β
Mie g
sc
sc HG
Esun
– Affected by extinction
• Constant?
• Constant:
E
0
sun
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Without scattering
Implementation
How ?
With scattering

Implementation
• Aerial Perspective
– Extinction & Inscattering
– Rays low in atmosphere
– Constant density good approximation
θ
s

Implementation
• Sunlight
ground
sun
E =
E
0
– sun is white
– Density is not constant!
0
sun
– Use a more accurate model for Fex ?
E
0
sun
E
F
E
ground
sun
ex

Implementation
• Sunlight:
– Virtual sky dome, use simple model
density
s(θ)
θ
R(θ)
distance
θ R(θ)

Implementation
L sky , =
Fin
– Density is not constant!
• Sky color:
– More accurate model too expensive
• Many computations needed per frame
• Sky geometry
– Virtual sky dome
( θ ϕ ) ( θ , ϕ )

Implementation
• Compute:
– Can be done with textures
• 1D texture for
ex
– Texture coordinate is a function of s
• 2D texture for
– Texture coords are functions of s, θ
• Combine in pixel shader
( s θ ) L F ( s)
L ( s,
θ )
L = +
, 0 ex in
F
L
in
– We decided on a different approach
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Implementation
• Compute:
– Use vertex shader to compute
– Apply as vertex interpolated colors
• In pixel shader, or even fixed pipeline
– Pros:
• Doesn’t use valuable texture slots
• Can change atmosphere properties
– Cons:
( s θ ) L F ( s)
L ( s,
θ )
L =
+
, 0 ex in
• Somewhat dependent on tessellation
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F L
ex ,
in

Vertex Shader
Constants:
Transform Matrix
Sun Direction
Eye Position
â
â
R
M
gHG
Position
Esun Outputs:
Vertex
Shader
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oD0 =
Fext
oD1= Lin

Vertex Shader
L
in
( s θ ) L F ( s)
L ( s,
θ )
L = +
( )
, 0 ex in
Fex
( ) (
s = e
− β R + βM
)s
( θ ) + β ( θ ) −(
β + β )
βR
M
s,
θ =
Esun
βR
+ βM
3
( ) ( 2
β θ β θ )
R = R 1+
cos
16π
( ) 2
1
1−
g
β ( ) M θ =
β M
4π
2
1+
g − 2g
cos
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( s
e )
R M 1−
( ( ) ) 2 / 3
θ

Vertex Shader
• Current Implementation:
– 33 Instructions
• Not including macro expansion
• Could probably be optimized
– 8 registers
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Pixel Shader
Lo
F_ex
X
=
L = Lo * F_ex + L_in
Lo * F_ex

Pixel Shader
Lo * F_ex
L_in
+ =
L = Lo * F_ex + L_in
Lo * F_ex + L_in

Results

Rayleigh Scattering - high
Mie Scattering - low
Sun Altitude - high

Rayleigh Scattering - low
Mie Scattering - high
Sun Altitude - high

Rayleigh Scattering - medium
Mie Scattering - medium
Sun Altitude - low

Planet Mars like scattering

Demo

Conclusion
• Scattering is easy to implement.
• Easy to add to an existing
rendering framework
– compute F_ex & L_in
– apply these to existing color to get
final color
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Future Work
• In-scattering from sky
• Clouds (scattering and extinction)
• Volumetric cloud shadows
• Non-uniform density distributions
• Full-spectrum math?
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Acknowledgements
• We would like to thank
– Kenny Mitchell for the terrain
engine used in our demo
– Solomon Srinivasan for help with
the demo movie
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References
[Blinn1982] J. F. Blinn. Light Reflection Functions for Simulation of Clouds and
Dusty Surfaces.
[Dutré2001] P. Dutré. Global Illumination Compendium.
[Henyey1941] L. G. Henyey and J. L. Greenstein. Diffuse Reflection in the
Galaxy.
[Hoffman2001] N. Hoffman and K. J. Mitchell. Photorealistic Terrain Lighting in
Real Time.
[Klassen1987] R. V. Klassen. Modeling the Effect of the Atmosphere on Light.
[Mie1908] G. Mie. Bietage zur Optik truber Medien Speziell Kolloidaler
Metallosungen.
[Preetham1999] A. J. Preetham, P. Shirley, B. E. Smits. A Practical Analytic
Model for Daylight.
[Rayleigh1871] J. W. Strutt (Lord Rayleigh). On the light from the sky, its
polarization and colour.
[Yee2002] H. Yee, P. Dutré, S. Pattanaik. Fundamentals of Lighting and
Perception: The Rendering of Physically Accurate Images.
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THANK YOU
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