1. Clipless Dual-Space Bounds for Faster Stochastic Rasterization Samuli Laine Timo Aila Tero Karras Jaakko Lehtinen NVIDIA Research

5. (x,y)

6. (x,y,u,v,t)

7. Motion Blur

8. t=0t=1

9. Motion Blur

10. t Accumulation Buffer [Haeberli ‘90]

11. t InterleaveUVT [Fatahalian ‘09]

12. t

13. t

14. t

15. 4 samples/pixel (16 UVT triples)16 samples/pixel (64 UVT triples) Scene: Assassin’s Creed, courtesy of Ubisoft InterleaveUVT [Fatahalian ‘09]

16. Unique UVTs 4 samples/pixel, unique UVTs16 samples/pixel, unique UVTs Scene: Assassin’s Creed, courtesy of Ubisoft

17. 5D Rasterization t=0t=1 t

18. 5D Rasterization t=0t=1 t

19. 5D Rasterization t=0t=1 t

20. 5D Rasterization t

21. t=0t=1 t ?

22. 5D Rasterization t=0t=1 t

23. 5D Rasterization t=0t=1 t ?

24. 5D Rasterization t=0t=1 t ?

25. Pixar Algorithm t=0t=1 t t=.5

26. Pixar Algorithm t=0t=1 t t=.5 XX

27. Pixar Algorithm t=0t=1 t t=.5 XX

28. Our Method t=0t=1 t

29. Our Method t=0t=1 t

30. Our Method t=0t=1 t XXX t range computed for pixel

31. Our Method  Determine pixels potentially covered by triangle  For each pixel  Compute time bounds t min,t max  Enumerate samples where t min ≤ t ≤ t max  For each such sample, perform 5D coverage test  Same for lens bounds u min,u max and v min,v max

32. Bound Computation  Lens bounds computed in screen space  Time bounds computed in dual space

33. Lens Bounds x y u=0u= –1u= +1 film lens focal plane u screen-space x is linear with u

34. Lens Bounds x y u= –1u= +1 screen-space x is linear with u

35. Lens Bounds x y u=au=b screen-space x is linear with u u a b

36. Time Bounds  World-space affine motion  Not affine in screen space, but affine in clip space  Perspective causes singularities in screen space  Operate in dual space

37. Clip Space and Dual Space x w t=0 t=1

38. Clip Space and Dual Space x w γ δ γ= –1 γ= +1

39. Clip Space and Dual Space x w γ δ δ { γ= –0.5

40. Clip Space and Dual Space x w γ δ

41. x w γ δ

42. x w γ δ

43. x w γ δ δ is linear in x and w δ = x – wγ x and w are linear in t δ is linear in t t=0 t=1 t=0 t=1

44. Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1

45. Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1

46. Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1 t=a t

47. Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1 t=a t a

48. Time Bounds  Compute separately for x and y  Intersect resulting spans  If intersection is empty, skip pixel

49. Recap  For each triangle  For each pixel  Compute t, u, v bounds  Cull samples outside bounds  Profit

50. Results  Measure sample test efficiency (STE)  Compare against methods that allow arbitrary sampling patterns # samples tested with full 5D test # samples hit STE =

51. Results Scene: Age of Conan PC MMO, courtesy of Funcom Bbox scan Pixar Our method 41664 static23.6 motion2.79.517.721.923.7 motion x 21.36.014.620.924.0 defocus1.74.48.813.923.1 defocus x 20.71.84.48.821.9 both0.71.22.64.35.6 both x 20.40.61.12.02.9 STE in %, scene Conan

52. Results Scene: Assassin’s Creed, courtesy of Ubisoft Bbox scan Pixar Our method 41664 static23.2 motion10.819.522.423.123.4 motion x 24.314.821.223.023.6 defocus9.515.119.021.123.2 defocus x 24.39.515.119.023.0 both4.56.87.210.114.1 both x 21.32.13.96.76.9 STE in %, scene Assassin

53. Results Bbox scan Pixar Our method 41664 static8.598.608.598.608.59 motion0.502.976.438.028.63 motion x 20.141.274.707.408.69 defocus0.190.591.533.138.57 defocus x 20.050.190.591.538.51 both0.120.250.491.084.51 both x 20.030.070.160.392.42 STE in %, scene Cars

54. Conclusions  Each triangle processed once  Arbitrary sampling patterns  High STE  Future work  Combined motion + defocus case

55. Thank You