![Page 1: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/1.jpg)
A Practical Analytic Modelfor Daylight
A. J. Preetham, Peter Shirley, Brian SmitsSIGGRAPH ’99
Presentation by Jesse Hall
![Page 2: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/2.jpg)
Introduction
• Outdoor scenes are becoming more feasible and common
• Most light comes from sun and sky
• Distances make atmosphere visible
![Page 4: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/4.jpg)
Goals
• Accurate formulas for sun and sky color, aerial perspective effects
• Simple, intuitive parameters
– Location, direction, date, time of day, conditions…
• Computationally efficient
![Page 5: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/5.jpg)
Background
• Sky color and aerial perspective are caused by atmospheric scattering of light (Minneart 1954)
• Primary and secondary scattering most important
![Page 6: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/6.jpg)
Scattering: Air Molecules
• Most important scattering due to air molecules
• Molecules smaller than wavelength: Rayleigh scattering
• Wavelength-dependent scattering gives sky overall blue color
• Also causes yellow/orange sun, sunsets
![Page 7: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/7.jpg)
Scattering: Haze
• Light also scattered by ‘haze’ particles (smoke, dust, smog)
• Haze particles larger than wavelength: Mie scattering, wavelength independent
• Usually approximated with turbidity parameter: T = (tm+th)/tm
![Page 8: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/8.jpg)
Previous Work: Sky Color
• Explicit modeling
• Measured data– CIE IDMP, Ineichen 1994
• Simulation– Klassen 1987, Kaneda 1992, Nishita 1996
• Analytic– CIE formula 1994, Perez 1993
![Page 9: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/9.jpg)
Previous Work:Aerial Perspective
• Explicit modeling
• Simulation– Ebert et al. 1998
• Analytic model for fog– Kaneda 1991
• Simple non-directional models– Ward-Larson 1998 (Radiance)
![Page 10: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/10.jpg)
Sunlight & Skylight
• Input: sun position, turbidity
• Output: spectral radiance
• Sun position calculated from latitude, longitude, time, date
• Haze density based on turbidity and measured data
![Page 11: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/11.jpg)
Sunlight
1. Look up spectral radiance outside atmosphere in table
2. Calculate attenuation from different particles using constants given in Iqbal 1983
3. Multiply extra-terrestrial spectral radiance by all attenuation coefficients to get direct spectral radiance
![Page 12: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/12.jpg)
Skylight: Geometry
![Page 13: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/13.jpg)
Skylight: Model
• Use Perez et al. model (1993)
A) darkening/brightening of horizonB) luminance gradient near horizonC) relative intensity of circumsolar regionD) width of circumsolar regionE) relative backscattered light
γ)ECe)(Ae(F DγθB/ 2cos11),( cos
),0(
),(
sz F
FYY
![Page 14: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/14.jpg)
Skylight: Simulation
1. Compute spectral radiance for various viewing directions, sun positions, and turbidities using Nishita (1996) model
• Multiple scattering, spherical or planar atmosphere
• 12 sun positions, 5 turbidities, 343 viewing directions
• 600 CPU hours• Requires careful implementation
![Page 15: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/15.jpg)
Skylight: Fitting
• Fit Perez coefficients to simulation using non-linear least-squares
• Luminance, chromaticity values require separate coefficients
• Result is three functions which combine to give spectral radiance
![Page 16: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/16.jpg)
CIE Chromaticity
![Page 17: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/17.jpg)
Aerial Perspective
• Can’t be precomputed since it depends on distance and elevations
• Simpler model required for feasibility
• Assume particle density decreases exponentially with elevation
• Assume earth is flat
inLLsL 0)(
![Page 18: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/18.jpg)
Aerial Perspective: Geometry
![Page 19: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/19.jpg)
Aerial Perspective: Extinction
• Molecules and haze vary separately
= exponential decay constant 0 = scattering coefficient at surface• u(x) = ratio of density at x to density at surface
0
cos00
222111
cos
1
)()(
h
ee
suHKsuHK
eH
eK
ees
h
![Page 20: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/20.jpg)
Aerial Perspective: Inscattering
• S(,,x): Light scattered into viewing direction at point x
• If |s cos |«1, Ii reduces to simple closed-form equation
dxxxuI
ISISLs
ii
in
),0()(
),(),(
0
2021
01
![Page 21: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/21.jpg)
Aerial Perspective: Solution
• Otherwise, computing Ii directly is too expensive to be practical
• Approximate some terms in expansion with Hermite cubic polynomial, which is easily integrable
• Result is an analytic equation
![Page 22: A Practical Analytic Model for Daylight A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649cd95503460f949a35a4/html5/thumbnails/22.jpg)
Conclusions
• Reasonably accurate model
• Efficient enough for practical use
• Great pictures!
• Doesn’t model cloudy sky, fog, or localized pollution sources