an analytic model for full spectral skydome radiance
DESCRIPTION
An Analytic Model for Full Spectral Skydome Radiance. Alexander Wilkie Charles University. Lukáš Hošek Charles University. Motivation: Skydome models. outdoor scenes prediction of material appearance architecture, outdoor scenes alternative: skyboxes. The Preetham Model. - PowerPoint PPT PresentationTRANSCRIPT
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An Analytic Model for Full Spectral Skydome Radiance
Lukáš HošekCharles University
Alexander WilkieCharles University
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Motivation: Skydome models•outdoor scenes•prediction of material appearance •architecture, outdoor scenes
•alternative: skyboxes
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The Preetham Model• De facto standard analytic skydome model• Simple closed form formulas• Outputs tristimulus data, convertible to spectral• Perez formula, fitted to the outputs of Nishita model• Fitting results publicly available
B/cos θ D 2θ, γ 1+Ae 1+ Ce γ+ EcF( ) os= γ
solar anglezenith angle
luma distribution parameters
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The Preetham Model
A,B,C,D,Ez
A,B,C,D,E s
F (θ,γ)x = x ·
F (0,γ )
output zenith angles
A 0.1787 -1.4630B -0.3554 0.4275
T=C -0.0227 5.3251
1D 0.1206 -2.5771E -0.0670 0.3703
2z
3S2S
S
0.00166 -0.00375 0.00209 0x = T T 1 -0.02903 0.06377 -0.03202 0.00394
0.11693 -0.21196 0.06052 0.25886
θθθ1
zenith luminance luma distribution parameters
for each sample
turbidity
solar-zenith angle
once per scene
inputs
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Issues With the Preetham Model
•Simple functions for calculating zenith luminance and luma distribution parameters•Only a small subset of possible atmospheric
conditions can be captured•Lack of localised aureole at higher turbidities•Spectral data are obtained by conversion from
trisitmulus data
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Issues with the Preetham Model
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•spectral (including UV)•larger range of turbidities•eliminate artifacts•ground albedo (came later & almost for free)
Goals for the New Model
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•Brute force Monte Carlo path tracer that incorporates•Mie scattering•Rayleigh scattering•Albedo & colour of Earth surface
•Delta scattering•Approaches the simulation as a transport problem, the same way physicists simulate e.g. gamma rays passing through containment shells of nuclear reactors
Obtaining Reference Data
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Obtaining Reference Data
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Result: Raw Data
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Result: Comparison
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Modified formulas for a better fit
2
32 2
1+cosαχ(g,α) =(1+g ·cos- α)2g
Eγ 2θ+0.B 1
c 201osF(θ, γ) = 1+Ae · C+De γ +G χ(H,γ) +I cos+ F cos θ
B/cos θ D 2θ, γ 1+ Ae 1+Ce γ+ EcF( ) os= γ
fudge factor to preventdivergence to infinityat zenith
anisotropic termfor luminance peaksaround sun
supresses luminance peakexending too far up
original Perez formula
modified formula
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Model flowchart
output
mean radiance radiance distribution parameters
for each sample
solar elevationalbedo
turbidity
once per scene
inputs
dM
AB
= B (η,α, T)
I
M
rz Mx = B (η,α, T)
z A, B, ,Ix = x ·F )(θ,γ
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How the Fitting was Done•Levenberg-Marquardt nonlinear optimization•Yields a mean radiance and radiance distribution
array•These are then used as control points for Bezier interpolation
•Albedo 0-1Turbidity 1-10Solar elevation 0-90°320nm – 720nm bands, 40nm increment
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Results
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Sky Colour Patterns (sunset)
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UV & Fluorescence
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Ground Albedoblack white
water blue forest green
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Conclusion
•Reference implementation and data available for download
•Version 1.1 out!•http://cgg.mff.cuni.cz/projects/SkylightModelling/