0
G.I.
•
•
•
•
• MLT, unbiased MC
G.I.
•           ->

•                ->

•           ->

•                   ->

• MLT, unbiased MC ->           ?

  • m...
MC rendering
•
•                            diffuse



• irradiance cache? final gather?
 •                                ...
• MC
 •           ~

• Analytic
 •           !=
“Analytic”

•           Closed-form

    • MC
•
    •
•                                     90



• Arvo, INRIA, multipole light expansion,
    spherical harmonics Durand 2005
...
Analytic rendering
•                  visibility




    •
        •
    •       ~
,
A First Order Analysis of Lighting, Shading, and Shadows
•   (gradient)
•

    •
    •
Contribution
•
    •
•
•
•
•

    •   spatial   angular
•
• B=
• ∇B^V =   B
•V   Heaviside   formalize




                   w < a(x)
                     1(       ),
                   w > a(x)
  ...
• Heaviside
•B   angular     V
     . T = L x BRDF x cos
•

    •

        •   Bx


        •        Bx
•                         ,       V
        (discontinuity)       (


    )
V

•
    •
•       (semi-analytic)

    •
    •                     ?
αe

    αs



         x
support line   OK
0 1 1
                0
            0
        1
    1
1




                          x
                V
2D
•   :

•       :
3D
•   1/10



    •   1/100

    •           Visibility gradient

•   theta=100, phi=100

    •       1 pixel           100
•

    •
         miss

    • The 3D visibility complex[Durand 2002]
    • Guided visibility sampling[Wonka 2006]
        ?
•                        Heaviside

    •
        •            V

    •
•
    •   additional

    •   V
• diffuse
• specular
•         opaque           glossy



•                      (            )
                          ...
References 1/2
•   [Ramamoorthi 2007] A First Order Analysis of Lighting, Shading, and
    Shadows

    •   http://www1.cs...
References 2/2
• [Arvo 1997] The Irradiance Jacobian for
  Partially Occluded Polyhedral Sources
• [Arvo 2002] Closed-Form...
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First Order

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Transcript of "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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