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CSCE 641 Computer Graphics: Radiosity

CSCE 641 Computer Graphics: Radiosity. Jinxiang Chai. Rendering: Illumination Computing. Direct ( local ) illumination Light directly from light sources No shadows. Local Illumination. I r = k a I a + I i (k d (n.l) + k s (h.n) m ). ambient. diffuse. specular. Local Illumination.

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CSCE 641 Computer Graphics: Radiosity

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  1. CSCE 641 Computer Graphics: Radiosity Jinxiang Chai

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

  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

  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

  6. Direct and Indirect Light

  7. 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)

  8. Radiosity vs. Local Illumination

  9. Radiosity

  10. Physical Image vs. Radiosity Rendering

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

  12. Radiosity • Radiosity computes the rendering equation for 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. Energy Conservation Equation

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

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

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

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

  25. Compute Form Factors 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 patchesl

  26. 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 patchesl

  27. 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)

  28. Linear System X = B A

  29. Radiosity Algorithm

  30. Form Factors

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

  32. Form Factor: Analytical

  33. Form Factor: How to compute? • Closed Form • - anlytical • Hemicube: precomputation!!!

  34. Form Factor: Nusselt Analog

  35. Form Factor: Nusselt Analog

  36. Form Factor: Nusselt Analog So how can use Nusselt analog for form factor calculation?

  37. Form Factor: HemiCube

  38. Delta Form Factor: Top Face Top of hemicube

  39. Delta Form Factors: Side Faces Side of hemicube

  40. The Hemicube in Action

  41. Form Factors: HemiCube

  42. Form Factors

  43. Radiosity Algorithm

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

  45. Matrix Conversion - Computational cost: O(N3) - Very slow for a large set of polygons

  46. Iterative Approaches

  47. Jacobian Iterations • For all patches i, i=1,…,N, • While not converged: • for all patches i=1,…,N

  48. Jacobian Iterations • For all patches i, i=1,…,N, • While not converged: • for all patches i=1,…,N Update of one patch requires evaluation of N Form Factors What’s the computational cost?

  49. Successive Approximation

  50. Rendering • - The final Φi's can be used in place of intensities in a standard renderer (Gouraud) • - Radiosities are constant over the extent of a patch • - A standard renderer requires vertex intensities (or radiosities) • - If the radiosities of surrounding patches are know, vertex radiosities can be estimated using bilinear interpolation

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