Understanding Light Transport Pathways in Radiosity: The Forward Problem

1. Interreflections and Radiosity : The Forward Problem Lecture #8 Thanks to Kavita Bala, Pat Hanrahan, Doug James, Ledah Casburn

2. Light Transport Pathways Light Source Scene Direct Component Viewer Slide adapted from Nayar et al

3. Light Transport Pathways Light Source Scene Direct Component Inter-reflections Viewer Slide adapted from Nayar et al

4. Light Transport Pathways Light Source Scene Direct Component Inter-reflections Sub-surface scattering Viewer Slide adapted from Nayar et al

5. Light Transport Pathways Volumetric Medium Light Source Scene Direct Component Inter-reflections Sub-surface scattering Viewer Volumetric Scattering Slide adapted from Nayar et al

6. Light Transport Pathways Volumetric Medium Light Source Scene Direct Component Inter-reflections Sub-surface scattering Viewer Volumetric Scattering Global Component Slide adapted from Nayar et al

7. Global illumination around us

8. Cost of Ignoring Global Illumination Photometric Stereo Shape from Focus Structured Light Measured Groundtruth

9. 3D scanning of metals for Industrial Inspection Strong inter-reflections Phase Shifting (162 images)

10. Specular Interreflections Mirror Reflection causes errors Regular Depth Map

12. Cornell Box

15. Cornell Box blue hue red hue

18. Phong Shading Plastic looking scene • no object interactions • no shadows

19. Ray Tracing Scene doesn’t look realistic enough. • where is the corner of room? • is window flush with wall? • is the carpet and wood supposed to be this dark?

20. Radiosity – today’s topic Indirect lighting affects realism. • room has a corner • window has depth • carpet and wood on table is lighter • walls look more pink

21. The Rendering Equation – Graph Style p’ p p’’ Reflectance from Surfaces Light passing from p’ to p Emission (light source) Visibility (shadows)

23. Diffuse Interreflections - Radiosity • Consider lambertian surfaces and sources. • Radiance independent of viewing direction. • Consider total power leaving per unit area of a surface. • Can simulate soft shadows and color bleeding • from diffuse surfaces. • Used abundantly in heat transfer literature

24. Irradiance, Radiosity • Irradiance E is the power received per unit surface area • Units: W/m2 • Radiosity • Power per unit area leaving the surface (like irradiance)

25. Planar piecewise constancy assumption • Subdivide scene into small “uniform” polygons

26. Power Equation • Power from each polygon: • Linear System of Equations:

29. Form Factors Invariant

30. Form Factor Computation • Schroeder and Hanrahan derived an analytic expression for polygonal surfaces. • In general, computing double integral is hard. • Use Monte Carlo Integration.

31. Form Factor Computation

32. Form Factor Computation

34. Linear System of Radiosity Equations Known Known Unknown • Matrix Inversion to Solve for Radiosities.

36. Doug James

37. Wireframe

38. Classical Approach • No Interpolation

39. Wireframe

40. Classical Approach • Low Res

41. Classical Approach • High Res • More accurate

42. Classical Approach • High Res • Interpolated

44. Sample Scenes

45. Sample Scenes

46. Sample Scenes

47. Sample Scenes

48. Sample Scenes

49. Summary

50. Interreflections : The Inverse Problem Thanks to Shree Nayar, Seitz et al, Levoy et al, David Kriegman