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CPSC 641 Computer Graphics: Radiosity

Learn about the limitations of local illumination in rendering and explore the concept of radiosity for indirect illumination in computer graphics. Discover the radiosity equation, form factor computation, and the use of techniques like Hemicube and Monte Carlo.

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CPSC 641 Computer Graphics: Radiosity

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  1. CPSC 641 Computer Graphics: Radiosity Jinxiang Chai

  2. Local Illumination Ir = kaIa + Ii (kd (n.l) + ks(h.n)m ) ambient diffuse specular

  3. Local Illumination Ir = kaIa + Ii (kd (n.l) + ks(h.n)m ) ambient diffuse specular

  4. Local Illumination Ir = kaIa + Ii (kd (n.l) + ks(h.n)m ) ambient diffuse specular • if there are multiple lights there is a sum of the specular and diffuse components for each light

  5. Local Illumination Ir = kaIa + Ii (kd (n.l) + ks(h.n)m ) ambient diffuse specular • if there are multiple lights there is a sum of the specular and diffuse components for each light What are limitations of local illumination?

  6. Rendering: Illumination Computing • Direct (local) illumination • Light directly from light sources • No shadows

  7. Direct and Indirect Light

  8. Rendering: Illumination Computing • Direct (local) illumination • Light directly from light sources • No shadows • Indirect (global) illumination • Hard and soft shadows • Diffuse interreflections (radiosity) • Glossy interreflections (caustics)

  9. Early Radiosity

  10. Consolation Room

  11. Challenge • To evaluate the reflection equation • the incoming radiance must be known • To evaluate the incoming radiance • the reflected radiance must be known

  12. Radiosity • Only consider inter-reflections between diffuse surfaces!

  13. Radiosity: Key Idea #1

  14. Diffuse Surface

  15. Radiosity: Key Idea #2

  16. Constant Surface Approximation

  17. Radiosity Equation

  18. Radiosity Equation

  19. Radiosity Algorithm

  20. Radiosity Algorithm

  21. Energy Conservation Equation

  22. Energy Conservation Equation Form factor

  23. Compute Form Factors

  24. Compute Form Factors Radiant energy reaching Ay from Ax Radiant energy leaving Ax in all directions

  25. Form Factor: Reciprocity

  26. Radiosity Equation

  27. Linear System

  28. Radiosity Algorithm

  29. Form Factors

  30. Form Factor: How to compute? • Closed Form • - anlytical • Hemicube • Monte Carlo

  31. Form Factor: Analytical

  32. Form Factor: How to compute? • Closed Form • - anlytical • Hemicube • Monte Carlo

  33. Form Factor: Nusselt Analog

  34. Form Factor: Nusselt Analog Why is it true?

  35. Form Factor: Nusselt Analog

  36. Form Factor: Nusselt Analog How can we use this property?

  37. Form Factor: Nusselt Analog How can we use this property? - Speed up form-factor evaluation

  38. Form Factor: HemiCube

  39. Delta Form Factor: Top Face Top of hemicube

  40. Delta Form Factors: Side Faces Side of hemicube

  41. The Hemicube in Action

  42. Form Factor: HemiCube

  43. Form Factors

  44. Radiosity Algorithm

  45. How to Solve Linear System? • Matrix conversion • Iterative approaches • - Jacobian • - Gauss-Seidel

  46. Matrix Conversion

  47. Iterative Approaches

  48. Jacobian

  49. Successive Approximation

  50. Gauss-Seidel

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