A Survey of Modelling and Rendering of the Earth s Atmosphere

Transcription

1 Spring Conference on Computer Graphics 00 A Survey of Modelling and Rendering of the Earth s Atmosphere Jaroslav Sloup Department of Computer Science and Engineering Czech Technical University in Prague 0

2 Talk Outline Introduction. Models of the atmosphere. Atmosphere composition. Light transfer through the atmosphere. Rendering of the atmosphere. 0

3 Motivation Photo-realistic image synthesis of outdoor scenes most of scene objects illumination comes directly from the sun and sky sky forms the background of the scene atmosphere causes change of colors of distant objects Instance of participating media simulation problem long distances make the effects of atmosphere visible 0

4 Models of the Atmosphere Plane-parallel model Klassen [] approximates the atmosphere as a set of plane-parallel layers neglects the sphericity of Earth introduces large errors near the horizon Spherical model Nishita et al.[0,], Irwin [], Jackel et al. [0] for each atmospheric component one submodel submodel = a set of non-interleaving spherical layers 0 H + H = ground ground ground submodel i th spherical layer submodel combination of submodel and

5 Composition of the Atmosphere Major atmospheric constituents clean dry air aerosols ozone water vapour, rain drops and ice crystals Constituents characteristics at point P extinction coefficient σ eλ (P ) (losses by absorption and scattering) scattering function p λ (P, θ) (angular distribution of scattered light) 0 single scattering albedo ϖ λ (P ) (relation between absorption and scattering ϖ λ (P ) = Ω p λ(p,θ) dθ σ e )

6 Composition of the Atmosphere cont. Constituents properties depend on particle size wavelength of incident light λ refractive index of the particle number of particles in unit volume Sources of constituents properties Mie scattering theory Rayleigh scattering theory geometric optics measured data 0

7 Composition of the Atmosphere cont. Mie Scattering Theory developed by G.Mie(0) general theory - valid for all particle sizes strong forward scattering absorption of energy occurs scattering function depends on particle size and wavelength rays of scattered light 0 incident light θ scattering function

8 Composition of the Atmosphere cont. Rayleigh Scattering Theory established by Lord Rayleigh () approximation for particles smaller than wavelength of light no absorption of light simple scattering function radiance of scattered light is proportional to the ratio λ blue color of the sky color of the sun (yellow orange red) extinction [m^-] e-0 e-0 e-0 e-0 e-0 e-0 extinction coefficient wavelength [nm] 0

9 Light Transfer Equation L λ (P (s 0 ), s) = phase function L (P, s) λ 0 scattering volumes L λ (P 0, s) τ(s 0, s E ) + θ P 0 τ( s,s ) s 0 E skylight L (P, s ) λ J (P, s) λ s P incident skylight radiance skylight scattered along direction s towards the observer s E beams of sunlight penetrating the atmosphere s τ( s 0,s) L (P(s ), s) λ 0 atmosphere s 0 J λ (P (s), s) τ(s 0, s) σ eλ (P (s))ds initial ray radiance atte- integral of skylight radiance scattered tonuated along the viewing wards the observer by volume elements ray by transmittance τ along the viewing ray attenuated by τ 0

10 Light Transfer Equation cont. Source function J λ (P, s) = π Ω [ n i= ϖ i λ (P ) pi λ (P, θ) ] L λ (P, s ) dω 0

11 Light Transfer Equation cont. Boundary condition at the top of the atmosphere ] f L λ (P 0, s) = { λ [ u( d rs) ray hits the solar disc 0.0 outside the solar disc irradiance decrease factor irradiance decrease factor limb darkening distance from the center of solar disc [km] atmosphere distance from the center of solar disc s 0 P 0 L (P, s) λ solar irradiance f λ solar irradiance black body at K

12 Light Transfer Equation cont. Boundary condition for ground reflection L λ (P 0, s) = ρ λ ( s, s π ) L λ (P 0, s ) cos ϑ dω, s L (P, s) λ 0 Ω N ϑ d ω s L (P 0, s ) λ 0 brfd ρ λ P 0 Earth s surface y x

13 Rendering of the Atmosphere For rendering we need function F (P, dir, date, atm cond) spectral radiance to simulate the color of the sky and sun function G(P, dir, date, atm cond, L r (P r )) spectral radiance to simulate the change of color of distant objects observed through the atmosphere 0 atm_cond F(...) P G(...) dir L r (P r) Pr F and G are based on the light transfer equation

14 Rendering of the Atmosphere cont. Rendering of the sky color For every pixel covered by the sky do evaluate LTE to determine amount of spectral radiance convert spectral radiance CIE XYZ color space apply tone mapping techniques convert CIE XYZ color RGB color to be displayed Simulation of the aerial perspective For all pixels not covered by the sky find intersection with the scene object calculate amount of light reflected towards the observer evaluate LTE to calculate gains and losses of reflected light tone mapping and conversion to the RGB color 0

15 Rendering of the Atmosphere cont. Methods to solve the light transfer equation analytic methods + fast and easy to use hardly extendable numerical methods still very difficult to solve require a lot of computational time + work with arbitrarily complex atmospheric conditions Simplifying assumptions Nishita et al.[,0,], Jackel et al.[,0] uniform medium, simple geometry or very small albedo restriction of order of scattering single scattering methods 0

16 Rendering of the Atmosphere cont. Hybrid methods Dobashi et al.[,], Preetham et al.[] numerical solution analytical approximation sky approximated by hemisphere with a large radius numerical solution sky spectral radiance distribution for several sun altitudes approximation by a series of basis functions / simple parametrically fitted formulas weights / parameters values are stored in tables 0

17 Rendered Images 0 Preetham et al.[] Walter and Jackel [,0]

18 Summary We discussed two models of the atmosphere atmosphere composition and properties of the major atmospheric constituents light transfer equation overview of methods used for rendering of the atmosphere 0

19 Spring Conference on Computer Graphics 00 QUESTIONS? 0

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23 H + H = ground ground ground submodel i th spherical layer submodel combination of submodel and

24 rays of scattered light incident light θ scattering function

25 e-0 extinction coefficient e-0 extinction [m^-] e-0 e-0 e-0 e wavelength [nm]

26 L (P, s) λ 0 P 0 τ( s,s ) 0 E scattering volumes beams of sunlight penetrating the atmosphere P τ( s 0,s) s skylight incident skylight radiance L (P, s ) λ s L (P(s ), s) λ 0 phase function θ skylight scattered along direction s towards the observer J (P, s) λ s atmosphere

27 limb darkening irradiance decrease factor irradiance decrease factor distance from the center of solar disc distance from the center of solar disc [km] solar irradiance f λ atmosphere s 0 P 0 L (P, s) λ

28 . solar irradiance black body at K

29 N s d ω s L (P, s) λ 0 ϑ L (P, s ) λ 0 brfd ρ λ P 0 Earth s surface y x

30 atm_cond F(...) P G(...) dir L r (P r) Pr

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