A Practical Analytic Model for Daylight

1. A Practical Analytic Modelfor 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. 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