1. Global Illumination: Radiosity, Photon Mapping & Path Tracing Rama Hoetzlein, 2009 Lecture Notes Cornell University

2. Rendering Equation Outgoing light Emitted light Bidirectional Reflectance Distribution Function (BRDF) Incoming light Incident attenuation X Surface point w Outgoing direction λ Wavelength t Current time Integral over all incoming light directions James Kajiya, 1982. The rendering equation. SIGGRAPH.

3. incoming outgoing x w w’ N Perfect Reflection: Light entering at one angle, leaves at same angle only.

4. incoming outgoing x w w’ N Phong Reflectance: Light entering at some angle, leaves in a uniform diffuse direction, and in a cone of around reflected angle.

5. incoming outgoing x w w’ N Diffuse Reflectance: Light entering at any angle, can leave at any angle, as a different color, or a different time.

6. incoming outgoing x w w’ N Diffuse Reflectance: Light entering at any angle, can leave at any angle, as a different color, or a different time.

7. Mapping from incoming angle and color to outgoing angle and color, is called the: Bidirectional Reflectance Distribution Function (BRDF) Phong is a simple example of a BRDF: incoming outgoing wavelength time position = cos ( θ ) n Bidirectional Reflectance Distribution Function

8. BRDF can be measured directly from materials.

9. BRDF How does a material respond at every incoming light angle?

12. Rendering Equation Outgoing light Emitted light Bidirectional Reflectance Distribution Function (BRDF) Incoming light Incident attenuation X Surface point w Outgoing direction λ Wavelength t Current time Integral over all incoming light directions James Kajiya, 1982. The rendering equation. SIGGRAPH.

13. Global Illumination Consider all energy moving in a space, not just the light that reaches the eye.

14. First used in the study of Heat Transfer (1950s), how does energy move around a room or object.

15. First radiosity experiment. 1984

16. Real box (color-sensitive photography)

17. Spherical Harmonic Radiosity. 1991

18. First used in Computer Graphics, 1984 Radiosity Modeling the interaction of light between diffuse surfaces, C. Goral, K. E. Torrance, D. P. Greenberg and B. Battaile. 1984 Computer Graphics, Vol. 18, No. 3.

19. Fij i j

20. Radiosity Solution One eqn. for each patch

23. Radiosity - Overview - Each patch contributes energy to other patches - Each patch i has a Radiosity equation: - Solve all equations simultaneously to get the energy at each patch - What is the hardest part of this eqn? Ei = Energy emitted Ri = Energy reflected Fij = Energy on patch I from j

24. Radiosity - Form Factors What things might contribute to the Form Factor? Remember: Form Factor is amount of energy hitting patch i from patch j

25. Radiosity - Form Factors What things might contribute to the Form Factor? Remember: Form Factor is amount of energy hitting patch i from patch j 1.Size of the patch Bigger = more energy 2.Angle between patches Direct = more energy 3.Dist. between patches Father = less energy 4.Objects between patches Occlusion = less energy

27. How much does patch j block patch i ?

28. Raytracing

29. Raytracing /w Caustics

30. Radiosity

33. Benefits 1. Very realistic (actually computes energy) 2. View independent.. Compute once, then view 3. Effects: Caustics, Color bleeding Drawbacks 1. Even more expensive than raytracing 2. Cannot simulate mirror reflections ! (energy travels diffusely, not coherently)

34. Combine Raytracing and Radiosity: - Radiosity to give energy transfer: Color bleeding Light diffusion Caustics Soft shadows -Raytracing to give view-dependent terms: Reflections Refractions Specular highlights Hybrid Rendering

35. Lady and Gentleman at the Virginals Johannes Vermeer (Dutch), 1662-65 Two Pass Rendering Wallace, Cohen, Greenberg, 1987

36. Photon Mapping Instead of computing all patches simultaneously, cast “photon rays” from light source. Uses points instead of patches. Photon Mapping - photons propogateRadiosity – patches don’t move

37. Photon Mapping - Much faster.. No form factors - Need lots of photons but easier to compute. - Realistic. Photons move the way light does. Two pass approach: 1. Shoot photons around scene 2. Collect photons to create image (nearby photons are smoothed)

40. Photon Mapping Made Easy, Yu, Lowther, Shene, SIGCSE 2005

42. Future Trends Recent Developments (past 5 yrs): - Ambient Occlusion – Approximation to Photon Mapping - Real-Time Raytracing using GPUs - Hybrid Rasterization and Raytracing - Volumetric Raytracing & Radiosity