First Order

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First Order

  1. 1. G.I. • • • • • MLT, unbiased MC
  2. 2. G.I. • -> • -> • -> • -> • MLT, unbiased MC -> ? • maxwellrender, fryrender, indigo, Kerkythea, etc.
  3. 3. MC rendering • • diffuse • irradiance cache? final gather? • MC .
  4. 4. • MC • ~ • Analytic • !=
  5. 5. “Analytic” • Closed-form • MC • •
  6. 6. • 90 • Arvo, INRIA, multipole light expansion, spherical harmonics Durand 2005 • duffse +
  7. 7. Analytic rendering • visibility • • • ~
  8. 8. ,
  9. 9. A First Order Analysis of Lighting, Shading, and Shadows
  10. 10. • (gradient)
  11. 11. • • •
  12. 12. Contribution • • • • •
  13. 13. • • spatial angular
  14. 14.
  15. 15. • B= • ∇B^V = B
  16. 16. •V Heaviside formalize w < a(x) 1( ), w > a(x) 0( )
  17. 17. • Heaviside
  18. 18. •B angular V . T = L x BRDF x cos
  19. 19. • • • Bx • Bx
  20. 20. • , V (discontinuity) ( )
  21. 21. V • • • (semi-analytic) • • ?
  22. 22. αe αs x support line OK
  23. 23. 0 1 1 0 0 1 1 1 x V
  24. 24. 2D
  25. 25. • : • :
  26. 26. 3D
  27. 27. • 1/10 • 1/100 • Visibility gradient • theta=100, phi=100 • 1 pixel 100
  28. 28. • • miss • The 3D visibility complex[Durand 2002] • Guided visibility sampling[Wonka 2006] ?
  29. 29. • Heaviside • • V • • • additional • V
  30. 30. • diffuse • specular • opaque glossy • ( ) ? • ” ”
  31. 31. References 1/2 • [Ramamoorthi 2007] A First Order Analysis of Lighting, Shading, and Shadows • http://www1.cs.columbia.edu/~ravir/papers/firstorder/index.html • [Durand 2002] The 3D visibility complex : a new approach to the problems of accurate visibility. • [Durand 2005] A Frequency analysis of Light Transport • http://people.csail.mit.edu/fredo/ • [Durand 1997] The Visibility Skeleton: A Powerful And Efficient Multi- Purpose Global Visibility Tool • [Wonka 2006] Guided Visibility Sampling • [Mattausch 2006] Adaptive Visibility-Driven View Cell Construction
  32. 32. References 2/2 • [Arvo 1997] The Irradiance Jacobian for Partially Occluded Polyhedral Sources • [Arvo 2002] Closed-Form Expressions for Irradiance from Non-Uniform Lambertian Luminaire. Part 1 & II • [Arvo 2000] Perterbation Methods for Interactive Specular Reflections • http://www.ics.uci.edu/~arvo/papers.html

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