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CSCE 441 Computer Graphics: Radiosity

CSCE 441 Computer Graphics: Radiosity. Jinxiang Chai. Rendering: Illumination Computing. Direct ( local ) illumination Light directly from light sources No shadows Indirect ( global ) illumination Transparent, reflective surfaces, and hard shadows (Ray tracing)

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CSCE 441 Computer Graphics: Radiosity

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  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/power per unit area leaving a surface.

  15. Radiosity • Model light effects by considering the physical laws governing the radiant energy transfer; • 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 Ax from Ay Radiant energy leaving Ay in all directions 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!

  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 • Visibility • - if not visible, receive zero power

  35. Form Factors for Subdivided Patches • Visibility • - if not visible, receive zero power

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

  37. Form Factor: Analytical

  38. Form Factor: How to compute? • Closed Form • - analytical • 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: Nusselt Analog So how can we use Nusselt Analog to compute the form factor?

  43. Form Factor: Nusselt Analog So how can we use Nusselt Analog to compute the form factor? - answer: precomputing

  44. Form Factor: HemiCube

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

  46. Precomputing Form Factor How to calculate the form factor for each cell?

  47. Delta Form Factor: Top Face Top of hemicube

  48. Delta Form Factors: Side Faces Side of hemicube

  49. The Hemicube in Action

  50. Form Factors: HemiCube

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