This document presents a new analytic sky dome radiance model. It aims to improve upon previous models by allowing for a wider range of turbidity values and more accurate simulations across the full spectrum. The model extends the Perez luminance model and Preetham spectral radiance model by adding additional parameters to better fit real sky data. Ray tracing is used to generate reference sky radiance data for comparison. Results show the new model matches reference data more closely than the Perez model, especially under different turbidity and ground albedo conditions.

1. An Analytic Model for
Full Spectral Sky-Dome Radiance
SIGRAPH 2012
2012/12/05
ked

2. Authors
 Lukas Hosek, Alexander Wilkie

3. Outline
 Goal
 Why is the sky blue?
 Modeling
 Simulation
 Results

4. Outline
 Goal
 Why is the sky blue?
 Modeling
 Simulation
 Results

5. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
 Fix the flaws of old model

6. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
 Fix the flaws of old model

7. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
?
 Fix the flaws of old model

8. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
 Fix the flaws of old model
 Preetham model
 Limited turbidity range
 Fails at some spectrum

9. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
 Fix the flaws of old model
 Preetham model
 Limited turbidity range
 Fails at some spectrum

10. A new sky model is required
 Demo

11. A new sky model is required
 Accurate simulation is slow
 Environment maps are limited
how?
 Fix the flaws of old model
 Preetham model
 Limited turbidity range
 Fails at some spectrum

12. Outline
 Goal
 Why is the sky blue?
 Modeling
 Simulation
 Results

13. Scattering
http://www.sciencemadesimple.com/sky_blue.html

14. Scattering
http://www.sciencemadesimple.com/sky_blue.html
 Effected by
 Haze: dust particles, water droplets, …. (1859)
 Air molecules (1899)
 And finally settle by Einstein (1910)
“ 方勵之—天空為什麼是藍色
的”

15. Scattering – the sky near the horizen
http://www.sciencemadesimple.com/sky_blue.html
http://www.research-in-germany.de/25326/german-countryside-
bildergalerie,templateId=popup,currentContentId=25294.html

16. The red sunset
http://www.sciencemadesimple.com/sky_blue.html
http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.htm
l

17. Outline
 Goal
 Why is the sky blue?
 Modeling
 Simulation
 Results

18. Luminance model
 Perez (1993)

 The parameters A to E and Yz are used to tune
the luminance distribution.

19. Spectral radiance model
 Preetham (1999)


CIE xyY color space

20. Spectral radiance model
 Preetham (1999)
 The parameters of Perez model (A to E and
Yz) are linear functions of condition, turbidity.
 Turbidity,
 Ratio of the optical thickness to pure air
 T=2: very clear, Arctic-like sky
 T=3: clear sky in temperate climate
 T=6: warm, moist day

21. The new model
 Hosek (2012)
 Extend the Perez model

22. The new model
 Hosek (2012)
 Extend the Perez model

23. The new model
 Hosek (2012)
 Extend the Perez model

24. The new model
 Hosek (2012)
 Extend the Perez model

25. The parameters

 A, B, C, D, E, F, G, H, I, and
 10 parameters

26. The parameters

 A, B, C, D, E, F, G, H, I, and


 : control point

 : albedo
 : parameter

27. The parameters
 John von Neumann
 “With four parameters I can fit an elephant, and
with five I can make him wiggle his trunk”

28. Outline
 Goal
 Why is the sky blue?
 Modeling
 Simulation
 Results

29. Scattering models
 Molecules: Rayleigh scattering
 Haze: Mie scattering

30. Scattering models
 Molecules: Rayleigh scattering
 Cross section:
 Density:
 Phase function:
 Haze: Mie scattering
 Cross section:
 Density:
 Phase function:

31. Scattering models
 Molecules: Rayleigh scattering
 Cross section:
 Density:
 Phase function:
 Haze: Mie scattering
 Cross section:
 Density:
 Phase function:

32. Scattering models
 Molecules: Rayleigh scattering
 Cross section:
 Density: decays exponentially with altitude( )
 Phase function:
 Haze: Mie scattering
 Cross section
 Density
 Phase function:

33. Scattering models
 Molecules: Rayleigh scattering
 Cross section:
 Density: decays exponentially with altitude( )
 Phase function:
 Angle between outgoing and incoming light directions
 Haze: Mie scattering
 Cross section
 Density:
 Phase function:

34. Scattering models
 Molecules: Rayleigh scattering
 Cross section:
 Density: decays exponentially with altitude( )
 Phase function:
 : angle between outgoing and incoming light directions
 Haze: Mie scattering
 Cross section: pre-calculated tabulated values
 Density: decays exponentially with altitude( )
 Phase function:
 g: anisotropy factor

35. Scattering models
 Phase functions
http://home.comcast.net/~vinelandrobotics/

36. Ray tracer
100km cover 0.0005%
Lambertian
diffuse surface

37. Ray tracer
100km cover 0.0005%
path tracing
Lambertian
diffuse surface

38. Ray tracer
100km cover 0.0005%
path tracing
ignored
Lambertian
diffuse surface

39. Ray tracer
100km cover 0.0005%
path tracing
ignored
Lambertian
diffuse surface
10
720

40. Outline
 Goal
 Why is the sky blue?
 Modeling
 Reference data generation
 Results

41. Photos vs. simulation

42. Turbidity values
 Solar elevation = 4o

43. Ground albedo
 Solar elevation = 40o, T = 4
 In high turbidity settings, changing ground albedo
alters the brightness of the whole sky-dome

44. New model vs. Perez model
 SNR
 Reference: path tracing results

45. Photograph vs. new model

46. Feature work

47. Reference
 為什麼天空是藍的，方勵之
 www.sciencemadesimple.com/sky_blue.htm
 A Practical Analytic Model for Daylight, A.J.
Preetham, P. Shirley, and B. Smits.
 Unbiased Global Illumination with Participating
Media, M. Raab, D. Seibert, and A. Keller.

48. Thx.