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A Practical Analytic Model for Daylight

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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

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