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

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

Important in photographs, paintings Example Important in photographs, paintings

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

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

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

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

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

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)

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

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

Skylight: Geometry

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

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

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

CIE Chromaticity

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

Aerial Perspective: Geometry

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

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

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

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