CSCE 441 Computer Graphics: Radiosity

1. CSCE 441 Computer Graphics: Radiosity Jinxiang Chai

2. Rendering: Illumination Computing • Direct (local) illumination • Light directly from light sources • No shadows • Indirect (global) illumination • Transparent, reflective surfaces, and hard shadows (Ray tracing) • Diffuse interreflections, color bleeding, and soft shadow (radiosity)

3. Rendering: Illumination Computing • Direct (local) illumination • Light directly from light sources • No shadows • Indirect (global) illumination • Transparent, reflective surfaces, and hard shadows (Ray tracing) • Diffuse interreflections, color bleeding, and soft shadow (radiosity)

4. Review: Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources)

5. Review: Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources)

6. Review: Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object)

7. Review: Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)

8. Review: Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)

9. Ray Tracing Assumption The illumination of a point is determined by - illumination/shadow ray (direct lighting from light sources) - reflection ray (light reflected by an object) - transparent ray (light passing through an object)

10. Pros and Cons of Ray Tracing Advantages of ray tracing All the advantages of the local illumination model Also handles shadows, reflection, and refraction Disadvantages of ray tracing Computational expense No diffuse inter-reflection between surfaces (i.e., color bleeding) Not physically accurate Radiosity handles these shortcomings for diffuse surfaces!

11. Radiosity vs. Local Illumination

12. Radiosity

13. Physical Image vs. Radiosity Rendering

14. Radiostiy • Definition: The radiant (luminous) exitance is the radiant flux per unit area leaving a surface.

15. Radiosity • The radiosity model computes radiant-energy interactions between all the surfaces in a scene

16. Radiosity: Key Idea #1

17. Diffuse Surface

18. Radiosity: Key Idea #2

19. Constant Surface Approximation

20. Radiosity Equation

21. Radiosity Equation

22. Radiosity Algorithm

23. Energy Conservation Equation

24. Energy Conservation Equation The total rate of radiant energy leaving surface i per unit square

25. Energy Conservation Equation The rate of energy emitted from surface i per unit area - zero if surface i is not a light source

26. Energy Conservation Equation Reflectivity factor Percent of incident light that is reflected in all directions

27. Energy Conservation Equation Form factor Fractional amount of radiant energy from surface j that reaches surface i

28. Compute Form Factors The form factor specifies the fraction of the energy leaving one patch and arriving at the other. In other words, it is an expression of radiant exchange between two surface patches!

29. Compute Form Factors Radiant energy reaching Ay from Ax Radiant energy leaving Ax in all directions The form factor specifies the fraction of the energy leaving one patch and arrives at the other. In other words, it is an expression of radiant exchange between two surface patches!

30. Form Factor: Reciprocity

31. Radiosity Equation • Radiosity for each polygon • Linear system: • - : radiosity of patch I (unknown) • - : emission of patch I (known) • - : reflectivity of patch I (known) • - : form-factor (known)

32. Linear System X = B A

33. Radiosity Algorithm

34. Form Factors for Infinitesimal Surfaces

35. Form Factors for Subdivided Patches

36. Form Factor: How to compute? • Closed Form • - anlytical • Hemicube

37. Form Factor: Analytical

38. Form Factor: How to compute? • Closed Form • - anlytical • Hemicube

39. Form Factor: Nusselt Analog Nusselt developed a geometric analog which allows the simple and accurate calculation of the form factor between a surface and a point on a second surface. 3D diagram

40. Form Factor: Nusselt Analog The form factor is, then, the area projected on the base of the hemisphere divided by the area of the base of the hemisphere, or (A/B) A B 2D diagram

41. Form Factor: Nusselt Analog

42. Form Factor: HemiCube

43. Form Factor: HemiCube • Project path on hemicube • Add hemicube cells to compute form factors A B 2D diagram

44. Delta Form Factor: Top Face Top of hemicube

45. Delta Form Factors: Side Faces Side of hemicube

46. The Hemicube in Action

47. Form Factors: HemiCube

48. Form Factors

49. Radiosity Algorithm

50. How to Solve Linear System? • Matrix conversion • Iterative approaches • - Jacobian (gathering) • - Gauss-Seidel (gathering) • - progressive refinement (shooting)