1 / 68

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 Indirect ( global ) illumination Transparent, reflective surfaces, and hard shadows (Ray tracing)

sherryunderwood
Download Presentation

CSCE 641 Computer Graphics: Radiosity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSCE 641 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. Radiosity • The radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces.

  15. Radiosity • The radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces. • Techniques of modeling the transfer of energy between surfaces based upon radiosity were first used in analyzing heat transfer between surfaces in an enclosed environment. The same techniques can be used to analyze the transfer of radiant energy between surfaces in computer graphics.

  16. Radiosity • The radiostiy of a surface is the rate at which energy leaves that surface (energy per unit time per unit area). It includes the energy emitted by a surface as well as the energy reflected from other surfaces. • Techniques of modeling the transfer of energy between surfaces based upon radiosity were first used in analyzing heat transfer between surfaces in an enclosed environment. The same techniques can be used to analyze the transfer of radiant energy between surfaces in computer graphics. • Radiosity methods allows the intensity of radiant energy arriving at a surface to be computed. These intensities can then be used to determine the shading of the surface.

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

  18. Radiosity: Key Idea #1

  19. Diffuse Surface

  20. Radiosity: Key Idea #2

  21. Constant Surface Approximation

  22. Radiosity Equation

  23. Radiosity Equation

  24. Radiosity Algorithm

  25. Energy Conservation Equation

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

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

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

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

  30. 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!

  31. 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!

  32. Form Factor: Reciprocity

  33. 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)

  34. Linear System X = B A

  35. Radiosity Algorithm

  36. Form Factors for Infinitesimal Surfaces

  37. Form Factors for Subdivided Patches

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

  39. Form Factor: Analytical

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

  41. 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

  42. 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

  43. 3D diagram How to speed up the form-factor calculation? Nusselt analogy allows us to calculate the form factor conveniently - But it is still computationally expensive. - Can we speed up the process?

  44. 3D diagram Speedup via Precomputation! Nusselt analogy allows us to calculate the form factor conveniently - But it is still computationally expensive. - Can we speed up the process? Yes

  45. Form Factor: Nusselt Analog

  46. Form Factor: HemiCube

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

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

  49. Form Factor: HemiCube (x,y) So how can we calculate the form factor between tiny patch on hemicube and the point?

  50. Delta Form Factor: Top Face Top of hemicube

More Related