1. G.I.
•
•
•
•
• MLT, unbiased MC

2. G.I.
• ->
• ->
• ->
• ->
• MLT, unbiased MC -> ?
• maxwellrender, fryrender, indigo,
Kerkythea, etc.

3. MC rendering
•
• diffuse
• irradiance cache? final gather?
• MC
.

4. • MC
• ~
• Analytic
• !=

5. “Analytic”
• Closed-form
• MC
•
•

6. • 90
• Arvo, INRIA, multipole light expansion,
spherical harmonics Durand 2005
• duffse +

7. Analytic rendering
• visibility
•
•
• ~

8. ,

9. A First Order Analysis of Lighting, Shading, and Shadows

10. • (gradient)

11. •
•
•

12. Contribution
•
•
•
•
•

13. •
• spatial angular

14. •

15. • B=
• ∇B^V = B

16. •V Heaviside formalize
w < a(x)
1( ),
w > a(x)
0( )

17. • Heaviside

18. •B angular V
. T = L x BRDF x cos

19. •
•
• Bx
• Bx

20. • , V
(discontinuity) (
)

21. V
•
•
• (semi-analytic)
•
• ?

22. αe
αs
x
support line OK

23. 0 1 1
0
0
1
1
1
x
V

24. 2D

25. • :
• :

26. 3D

27. • 1/10
• 1/100
• Visibility gradient
• theta=100, phi=100
• 1 pixel 100

28. •
•
miss
• The 3D visibility complex[Durand 2002]
• Guided visibility sampling[Wonka 2006]
?

29. • Heaviside
•
• V
•
•
• additional
• V

30. • diffuse
• specular
• opaque glossy
• ( )
?
• ” ”

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. 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