1. A Practical Analytic Model for Daylight
A. J. Preetham, Peter Shirley, Brian Smits
SIGGRAPH ’99
Presentation by Jesse Hall

2. Introduction Outdoor scenes are becoming more feasible and common
Most light comes from sun and sky
Distances make atmosphere visible

3. Important in photographs, paintings
Example
Important in photographs, paintings

4. Goals
Accurate formulas for sun and sky color, aerial perspective effects
Simple, intuitive parameters
Location, direction, date, time of day, conditions…
Computationally efficient

5. Background
Sky color and aerial perspective are caused by atmospheric scattering of light (Minneart 1954)
Primary and secondary scattering most important

6. 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

7. 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

8. 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

9. 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)

10. 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

11. Sunlight Look up spectral radiance outside atmosphere in table
Calculate attenuation from different particles using constants given in Iqbal 1983
Multiply extra-terrestrial spectral radiance by all attenuation coefficients to get direct spectral radiance

12. Skylight: Geometry

13. Skylight: Model Use Perez et al. model (1993)
A) darkening/brightening of horizon
B) luminance gradient near horizon
C) relative intensity of circumsolar region
D) width of circumsolar region
E) relative backscattered light

14. Skylight: Simulation
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

15. 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

16. CIE Chromaticity

17. 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

18. Aerial Perspective: Geometry

19. 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

20. Aerial Perspective: Inscattering
S(,,x): Light scattered into viewing direction at point x
If |s cos |«1, Ii reduces to simple closed-form equation

21. 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

22. Conclusions Reasonably accurate model
Efficient enough for practical use
Great pictures!
Doesn’t model cloudy sky, fog, or localized pollution sources