1. CS348B Lecture 16Pat Hanrahan, Spring 2005 Participating Media & Vol. Scattering Applications Clouds, smoke, water, … Subsurface scattering: paint, skin, … Scientific/medical visualization: CT, MRI, … Topics Absorption and emission Scattering and phase functions Volume rendering equation Homogeneous media Ray tracing volumes

2. CS348B Lecture 16Pat Hanrahan, Spring 2005 Absorption Absorption cross-section: Probability of being absorbed per unit length

3. CS348B Lecture 16Pat Hanrahan, Spring 2005 Transmittance Optical distance or depth Homogenous media: constant

4. CS348B Lecture 16Pat Hanrahan, Spring 2005 Transmittance and Opacity Transmittance Opacity

5. CS348B Lecture 16Pat Hanrahan, Spring 2005 Out-Scatter Scattering cross-section: Probability of being scattered per unit length

6. CS348B Lecture 16Pat Hanrahan, Spring 2005 Extinction Total cross-section Attenuation due to both absorption and scattering Albedo

7. CS348B Lecture 16Pat Hanrahan, Spring 2005 Black Clouds From Greenler, Rainbows, halos and glories

8. CS348B Lecture 16Pat Hanrahan, Spring 2005 In-Scatter Reciprocity Energy conserving Phase function

9. CS348B Lecture 16Pat Hanrahan, Spring 2005 Phase Functions Phase angle Phase functions (from the phase of the moon) 1.Isotropic -simple 2.Rayleigh -molecules 3. Mie scattering - small spheres... Huge literature...

10. CS348B Lecture 16Pat Hanrahan, Spring 2005 Blue Sky = Red Sunset From Greenler, Rainbows, halos and glories

11. CS348B Lecture 16Pat Hanrahan, Spring 2005 Coronas and Halos Moon CoronaSun Halos From Greenler, Rainbows, halos and glories

12. CS348B Lecture 16Pat Hanrahan, Spring 2005 Henyey-Greenstein Phase Function Empirical phase function g : average phase angle g = -0.3 g = 0.6

13. CS348B Lecture 16Pat Hanrahan, Spring 2005 The Volume Rendering Equation Integro-differential equation Integro-integral equation Attenuation: Absorption and scattering Source: Scatter (+ emission)

14. CS348B Lecture 16Pat Hanrahan, Spring 2005 Simple Atmosphere Model Assumptions Homogenous media Constant source term (airlight) Fog Haze

15. CS348B Lecture 16Pat Hanrahan, Spring 2005 The Sky From Greenler, Rainbows, halos and glories

16. CS348B Lecture 16Pat Hanrahan, Spring 2005 Atmospheric Perspective From Greenler, Rainbows, halos and glories

17. CS348B Lecture 16Pat Hanrahan, Spring 2005 Atmospheric Perspective Aerial Perspective: loss of contrast and change in color From Musgrave

18. CS348B Lecture 16Pat Hanrahan, Spring 2005 Semi-Infinite Homogenous Media Reduced Intensity Effective source term Volume rendering equation Integrating over depths

19. CS348B Lecture 16Pat Hanrahan, Spring 2005 Semi-Infinite Homogenous Media Integrating over depths

20. CS348B Lecture 16Pat Hanrahan, Spring 2005 Semi-Infinite Homogenous Media BRDF Seeliger’s Law or The Law of Diffuse Reflection

21. CS348B Lecture 16Pat Hanrahan, Spring 2005 Subsurface Scattering Skin

22. CS348B Lecture 16Pat Hanrahan, Spring 2005 Volume Representations 3D arrays (uniform rectangular) CT data 3D meshes CFD, mechanical simulation Simple shapes with solid texture Ellipsoidal clouds with sum-of-sines densities Hypertexture

23. CS348B Lecture 16Pat Hanrahan, Spring 2005 Scalar Volumes Interpolation Map scalars to optical properties Voxel

24. CS348B Lecture 16Pat Hanrahan, Spring 2005 Scalar Volumes Scatter Voxel

25. CS348B Lecture 16Pat Hanrahan, Spring 2005 Ray Marching Primary ray Direct Lighting

26. CS348B Lecture 16Pat Hanrahan, Spring 2005 Ray Marching Shadow ray Direct Lighting

27. CS348B Lecture 16Pat Hanrahan, Spring 2005 Beams of Light From Greenler, Rainbows, halos and glories From Minneart, Color and light in the open air

28. CS348B Lecture 16Pat Hanrahan, Spring 2005 Color and Opacity Volumes M. Levoy, Ray tracing volume densities Voxel

29. CS348B Lecture 16Pat Hanrahan, Spring 2005 Ray Marching Primary ray Direct Lighting

30. CS348B Lecture 16Pat Hanrahan, Spring 2005 Volume Rendering Examples From Marc Levoy From Karl Heinz Hoehne