1. 02/28/05© 2005 University of Wisconsin Last Time Scattering theory Integrating tranfer equations

2. 02/28/05© 2005 University of Wisconsin Today Sub-surface scattering Sky models

3. 02/28/05© 2005 University of Wisconsin Subsurface Scattering Kubelka-Munk is a gross approximation to real scattering Subsurface scattering is very important to capturing the appearance of organic materials

4. 02/28/05© 2005 University of Wisconsin BSSRDF Bidirectional surface scattering reflectance distribution function, S Relates the outgoing radiance at one point to the incident flux at another BRDF makes the assumption that x i = x o To get the total radiance leaving a point, integrate over the surface and the incoming directions S depends on the sub-surface scattering of the material

5. 02/28/05© 2005 University of Wisconsin Practical Model Wann Jensen, Marschner, Levoy and Hanrahan, 2001 Handles non-isotropic media Does not require extensive Monte-Carlo raytracing –Just a modified version of distribution ray-tracing Approximation based on: –Multiple bounce scattering – diffuse component –Single bounce scattering – directional component

6. 02/28/05© 2005 University of Wisconsin Single Scattering Term Assume one scattering event on the path from incoming to outgoing ray To get outgoing radiance, integrate along refracted ray ii oo xixi xoxo s

7. 02/28/05© 2005 University of Wisconsin Single Scattering Term S (1) is defined by this formula

8. 02/28/05© 2005 University of Wisconsin Multiple Scattering Observation: multiple scattering tends to look diffuse –Each scattering event tends to blur the distribution of radiance, until it looks uniform For flat, semi-infinite surfaces, the effect of multiple scattering can be approximated with two virtual light sources –One inside the medium –One “negative” light outside the medium –The diffusion approximation

9. 02/28/05© 2005 University of Wisconsin Diffuse Scattering Term (the flavor) This equation uses the Fresnel, coefficients to scale the incoming radiance, coefficients for transmission and adsorption, and variables for the location of the virtual light sources

10. 02/28/05© 2005 University of Wisconsin Fitting Parameters There are 4 material dependent parameters:  ’ s,  a, ,  –Each parameter, except , depends on wavelength Measure by taking a high dynamic range image of a sample piece illuminated by a focused light –High dynamic range imagery will be covered later

11. 02/28/05© 2005 University of Wisconsin Rendering with the BSSRDF Rendering has to take into account: –Efficient integration of the BSSRDF including importance sampling –Single scattering for arbitrary geometry –Diffuse scattering for arbitrary geometry –Texture on the surface Use a distribution ray-tracer Each time you hit a surface point, x o, have to sample incoming points, x i to estimate integral

12. 02/28/05© 2005 University of Wisconsin Sampling Approaches For single scattering terms, sample points along the refracted outgoing ray –Cast shadow ray to light to find out incoming radiance –Push this through single scattering equation to get outgoing –Make distant light approximation to ease computations For diffuse scattering term, sample points around the outgoing point –Then place the virtual lights and evaluate the equation –Must be careful to put virtual lights in appropriate places For texture, use parameters from x i for diffuse, and combination of x i and x o for single scattering

13. 02/28/05© 2005 University of Wisconsin Results

14. 02/28/05© 2005 University of Wisconsin More Results

15. 02/28/05© 2005 University of Wisconsin Can’t Escape the Bunny

16. 02/28/05© 2005 University of Wisconsin Sky Illumination The sky is obviously an important source of illumination The atmosphere is an important participating medium over large distances (hundreds of meters) –People use atmospheric effects to judge distances (stereo and disparity effects are useless at large distances) Three models: –CIE model –Perez model –Preetham, Shirley and Smits model

17. 02/28/05© 2005 University of Wisconsin Atmospheric Phenomena Due to solar illumination and scattering in the atmosphere Air molecules are modeled by Rayleigh scattering –Optical extinction coefficient varies with -4 –What phenomena does this explain? Scattering due to larger particles is modeled with Mie scattering –Scattering depends less on wavelength, so what color is haze? Turbidity is a useful measurement: T=(t m +t h )/t m –t m is vertical optical thickness of molecular atmosphere –t h is vertical optical thickness of haze atmosphere

18. 02/28/05© 2005 University of Wisconsin Simulation Models These attempt to simulate the scattering in the atmosphere to produce images –Very expensive for practical use –But work with any atmospheric conditions

19. 02/28/05© 2005 University of Wisconsin Coordinate System

20. 02/28/05© 2005 University of Wisconsin CIE Model Predicts luminance of a point in the sky for a particular sun position on a clear day –What color space do we do sky computations in? Y z is the luminance of the zenith, which can be found in tables or formulas that incorporate sun position This formula is used in Radiance, among other systems

21. 02/28/05© 2005 University of Wisconsin CIE Cloud Model For completely overcast skies (thick clouds)

22. 02/28/05© 2005 University of Wisconsin Perez Model Five parameters: –A: darkening or brightening of the horizon –B: luminance gradient near the horizon –C: relative intensity of the circum-solar region –D: width of the circum-solar region –E: relative backscattered light

23. 02/28/05© 2005 University of Wisconsin Aerial Perspective The change in color due to passage of light through the atmosphere Has been modeling in various ways: –Fog models –Full scattering simulations –Fake ambient illumination –Single scattering integrated along a line from source to viewer

24. 02/28/05© 2005 University of Wisconsin Preetham, Shirley and Smits Practical model (or so they claim) Model sun with NASA data and attenuation along path to viewer Model skylight with Perez model –Run lots of simulation of particle scattering –Fit parameters for Perez model –Also fit chromaticity values Model aerial perspective with simplifications to scattering integrals

25. 02/28/05© 2005 University of Wisconsin Results

26. 02/28/05© 2005 University of Wisconsin Turbidity

27. 02/28/05© 2005 University of Wisconsin Ward’s Model vs Preetham

28. 02/28/05© 2005 University of Wisconsin Next Time High Dynamic Range