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**A Practical Analytic Model for Daylight**

A. J. Preetham, Peter Shirley, Brian Smits SIGGRAPH ’99 Presentation by Jesse Hall

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**Introduction Outdoor scenes are becoming more feasible and common**

Most light comes from sun and sky Distances make atmosphere visible

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**Important in photographs, paintings**

Example Important in photographs, paintings

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

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

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**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

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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

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**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

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**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)

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**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

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**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

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Skylight: Geometry

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**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

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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

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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

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CIE Chromaticity

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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

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**Aerial Perspective: Geometry**

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**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

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**Aerial Perspective: Inscattering**

S(,,x): Light scattered into viewing direction at point x If |s cos |«1, Ii reduces to simple closed-form equation

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**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

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**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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