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kd-trees using the RTSAH Matthias Moulin, Niels Billen and Philip - PowerPoint PPT Presentation

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Efficient visibility heuristics for kd-trees using the RTSAH Matthias Moulin, Niels Billen and Philip Dutr Department of Computer Science KU Leuven, Belgium kd-trees Matthias Moulin, Niels Billen and Philip Dutr 2 kd-trees Recursively

  1. Efficient visibility heuristics for kd-trees using the RTSAH Matthias Moulin, Niels Billen and Philip Dutré Department of Computer Science KU Leuven, Belgium

  2. kd-trees Matthias Moulin, Niels Billen and Philip Dutré 2

  3. kd-trees Recursively split 3D space Matthias Moulin, Niels Billen and Philip Dutré 3

  4. kd-trees Recursively split 3D space Matthias Moulin, Niels Billen and Philip Dutré 4

  5. kd-trees Recursively split 3D space Matthias Moulin, Niels Billen and Philip Dutré 5

  6. kd-trees Recursively split 3D space Matthias Moulin, Niels Billen and Philip Dutré 6

  7. kd-trees Trace rays front to back Matthias Moulin, Niels Billen and Philip Dutré 7

  8. kd-trees Trace rays front to back Matthias Moulin, Niels Billen and Philip Dutré 8

  9. kd-trees Trace rays front to back Matthias Moulin, Niels Billen and Philip Dutré 9

  10. kd-trees Trace rays front to back Matthias Moulin, Niels Billen and Philip Dutré 10

  11. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 11

  12. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 12

  13. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 13

  14. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 14

  15. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 15

  16. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 16

  17. kd-trees Problem: where to put the splitting planes? Matthias Moulin, Niels Billen and Philip Dutré 17

  18. Literature • Surface Area Heuristic [Goldsmith & Salmon 1987], [MacDonald & Booth 1990] • Optimizations • 𝒫(𝑂 log(𝑂)) build procedure [Wald & Havran 2006] • Mail-boxing [Hunt 2008] • Alternative build heuristics • Interior rays [Fabianowski et al. 2009] • Actual ray distribution [Havran & Bittner 1999], [Bittner & Havran 2009] • Non-uniform ray distribution [Choi et al. 2012] • Blocking factors [Reinhard et al. 1996], [Havran 2000] Matthias Moulin, Niels Billen and Philip Dutré 18

  19. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 19

  20. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 20

  21. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 21

  22. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 22

  23. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 23

  24. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑞 L 𝐷 L + 𝑞 R 𝐷 R Matthias Moulin, Niels Billen and Philip Dutré 24

  25. Surface Area Heuristic Where to put the splitting plane? → Try to minimize the ray tracing cost! 𝐷 SAH 𝑊 = 𝐷 t + 𝑇𝐵 L 𝐷 L + 𝑇𝐵 R 𝐷 R 𝑇𝐵 Tot 𝑇𝐵 Tot Matthias Moulin, Niels Billen and Philip Dutré 25

  26. Surface Area Heuristic ― Problems SAH assumes that rays do not terminate within a voxel Matthias Moulin, Niels Billen and Philip Dutré 26

  27. Surface Area Heuristic ― Problems SAH assumes that rays do not terminate within a voxel Matthias Moulin, Niels Billen and Philip Dutré 27

  28. Surface Area Heuristic ― Problems SAH assumes that rays do not terminate within a voxel Contribution: 𝒲 L→R = unblocked rays from left to right Matthias Moulin, Niels Billen and Philip Dutré 28

  29. Surface Area Heuristic ― Problems SAH assumes that rays do not terminate within a voxel Contribution: 𝒲 R→L = unblocked rays from right to left Matthias Moulin, Niels Billen and Philip Dutré 29

  30. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L [Ize et al. 2011] Matthias Moulin, Niels Billen and Philip Dutré 30

  31. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 31

  32. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 32

  33. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 33

  34. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 34

  35. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 35

  36. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 36

  37. Ray Termination Surface Area Heuristic 𝐷 RTSAH = 𝐷 t + 𝑞 jL 𝐷 L + 𝑞 jR 𝐷 R + 𝑞 L→R 𝐷 L + 𝒲 L→R 𝐷 R + 𝑞 R→L 𝐷 R + 𝒲 R→L 𝐷 L Matthias Moulin, Niels Billen and Philip Dutré 37

  38. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 38

  39. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 39

  40. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 40

  41. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 41

  42. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 42

  43. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 43

  44. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 44

  45. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 45

  46. RASTERIZED Approximation Projects all primitives orthogonally on the splitting plane Matthias Moulin, Niels Billen and Philip Dutré 46

  47. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 47

  48. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 48

  49. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 49

  50. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 50

  51. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 51

  52. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 52

  53. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 53

  54. AVERAGED approximation 1 average projected surface area = 4 surface area Matthias Moulin, Niels Billen and Philip Dutré 54

  55. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 55

  56. Visibility Estimation Error Matthias Moulin, Niels Billen and Philip Dutré 56

  57. Results Sponza (512spp) Whitted Ray Tracer Matthias Moulin, Niels Billen and Philip Dutré 57

  58. SAH Diff (RASTERIZED, SAH) Diff (AVERAGED, SAH) Low High #INTERSECTION tests for PRIMARY rays Matthias Moulin, Niels Billen and Philip Dutré 58

  59. SAH Diff (RASTERIZED, SAH) Diff (AVERAGED, SAH) Less More -12.5% -25.5% #INTERSECTION tests for PRIMARY rays Matthias Moulin, Niels Billen and Philip Dutré 59

  60. SAH Diff (RASTERIZED, SAH) Diff (AVERAGED, SAH) Low High #INTERSECTION tests for SHADOW rays Matthias Moulin, Niels Billen and Philip Dutré 60

  61. SAH Diff (RASTERIZED, SAH) Diff (AVERAGED, SAH) Less More -3.1% -22.1% #INTERSECTION tests for SHADOW rays Matthias Moulin, Niels Billen and Philip Dutré 61

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