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Image Synthesis

Image Synthesis. Basics of global illumination. Global illumination. Global illumination. Photorealistic image synthesis. Photorealistic image synthesis. Photorealistic image synthesis. Photorealistic image synthesis. Radiometric quantities. Strahlungsenergie: radiant energy

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Image Synthesis

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  1. Image Synthesis Basics of global illumination

  2. Global illumination

  3. Global illumination

  4. Photorealistic image synthesis

  5. Photorealistic image synthesis

  6. Photorealistic image synthesis

  7. Photorealistic image synthesis

  8. Radiometric quantities Strahlungsenergie: radiant energy Qin Joule [J] Strahlungsleistung oder -fluss: radiant fluxin Watt [W=J/s] Einfallende Flussdichte: irradiance (incident) power per area in [W/m2] ausgehende Flussdichte: radiosity (radiant exitance)power per area in [W/m2]

  9. Radiometric quantities Strahlungsintensitätpower per solid angle in [W/sr]

  10. d N  dA dN dA Strahldichte: Radiance Combination of flux and intensity Strahldichte = Radiance Central quantity in physics based images synthesis Units: [W/(m2sr)] Power per unit solid angle per projected unit area

  11. Radiance Relation between irradiance and radiance

  12. BRDF BRDF Bidirectional reflection distribution function Proportionality constant fr(i ,x, r ) [1/sr]

  13. Reflection equation Differential reflected radiance from incoming radiance using BRDF Integration over all directions Integral equation for one unknown based on relation between Li(i) and Lr(r)

  14. Radiosity Radiosity equation Form factors Solution methods

  15. Solving the rendering equation • Monte-Carlo techniques • See course Computer Graphics • Finite-Elemente techniques • Radiosity technique • Projection of equations with infinite dimension onto functions space with finite dimension • Results in a linear system of equations • Efficient for smooth illumination and reflection

  16. Example

  17. Example

  18. Example

  19. Considerations

  20. Considerations Subdivision of the scene into planar patches Diffuse Reflection (Lambertian reflector)

  21. N Li Lr BRDF: Diffuse Reflection Radiosity and reflectance from radiance we get

  22. y x Continuous radiosity equation From rendering equation Assumption: diffuse Reflection Integration over outgoing directions from

  23. y x Continuous radiosity equation Radiosity equation with new geometry factor

  24. Classical radiosity equation Radiosity equation Assumption: surface-patches i with constant Bi(x) Averaging: integration of all Bi and division through Ai

  25. Classical radiosity equation Classical discrete Radiosity equation Form factors Fraction of energy that leaves element i and directly arrives at element j

  26. “Direction” of Form factors Fraction of energy that leaves element i and directly arrives at element j

  27. Form factor computation Form factor computation methods

  28. Pj Pi Form factors Nusselt-Analog • Geometric interpretation of form factorsfrom differential area dAi to element Aj • Proportional to the area of doubleprojection onto base of hemisphere • First projection: • Second projection: Projectiononto hemisphere Cylinder projectiononto circle area

  29. Form factors

  30. Form factor computation

  31. Form factor computation • The hemicube algorithm • Fij = q Fq

  32. Form factor computation

  33. z A A x Form factor computation • Hemicube method

  34. Form factor computation

  35. Form factor computation Hemicube-Verfahren: Simulated Steel Mill (Feldman, Wallace)55 000 Patches, gerechnet auf VAX 8700

  36. Computing the radiosity

  37. Computing the radiosity Be>0

  38. Smooth solution Solution yields constant radiosities per patch Solution is independent of view point Interpolate per-vertex values Gouraud-Shading for interactive walk-throughs Alternatively: Radiosity-Texture

  39. Radiosity solution techniques • Classical radiosity (often Ei instead of Bie) Material Geometry

  40. Radiosity solution techniques • Direct solution • Gauß elimination: matrix inversion • complexity = O(n3) for n patches

  41. Linear system of equations For n patches: a system for n unknowns Bi n2 matrix elements from form factors Matrix elements (1-T)ij,i!=j = 0, if V(i,j) = 0

  42. Iterative solution methods B = E + TB = E + T(E+TB) = E + TE + T2B = ... = T0E + T1E + T2E + T3E + ... = B(0) + B(1) + B(2) + B(3) + ... 2-times reflectedlight 1-times reflectedlight 0-time reflectedlight

  43. Jacobi iteration Iteration 0

  44. Jacobi iteration Iteration 1

  45. Jacobi iteration Iteration 2

  46. Jacobi iteration Iteration 3

  47. Gathering One step gathers energy from all other patches and generates one new value Select patches consecutively independent of their contribution Physical interpretationof Gauß-Seidel

  48. Shooting Select patches with regard to importance, distribute energy to all others, shot „unshot“ radiosity

  49. Solution methods summary

  50. Radiosity vs. ray-tracing

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