1. A Hierarchical Splitting Scheme to Reveal Insight into Highly Self-Occluded Integral Surfaces Andrea Brambilla Ivan Viola Helwig Hauser University of Bergen www.ii.uib.no/vis

2. Andrea Brambilla 1 of 19 Flow Phenomena and Visualization Wikipedia

3. Andrea Brambilla Raw Data Wikipedia 2 of 19

4. Andrea Brambilla Flow Features Vortex Saddle Wikipedia 3 of 19

5. Andrea Brambilla Integral Structures Wikipedia 2 of 19

6. Andrea Brambilla Integral Structures Streamline Path line Streak lines Time line Wikipedia 3 of 19

7. Andrea Brambilla 3 of 19 Integral Structures Streamline Path line Streak lines Time line Stream surface Path surface Time surface Wikipedia

8. Andrea Brambilla 3 of 19 Integral Structures Streamline Path line Streak lines Time line Stream surface Path surface Time surface Wikipedia

9. Andrea Brambilla 4 of 19 Integral Surfaces

10. Andrea Brambilla 4 of 19 Integral Surfaces

11. Andrea Brambilla 4 of 19 Integral Surfaces

12. Andrea Brambilla 5 of 19 Cluttering & Self Occlusion

13. Andrea Brambilla 6 of 19 Surface Splitting

14. Andrea Brambilla 6 of 19 Surface Splitting

15. Andrea Brambilla 6 of 19 Surface Splitting

16. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Importance Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction

17. Importance Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction

18. Importance Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure CUT! Visualization and User Interaction

19. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction Importance

20. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction Importance

21. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction Importance

22. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction

23. Andrea Brambilla 7 of 19 A Generic Splitting Framework Surface Pieces Importance Cut Space Cut Selection and Splitting Complexity Measure Visualization and User Interaction

24. Andrea Brambilla 8 of 19 Existing Approaches Li et al. 08: - building blocks - blocks relationships Karpenko et al. 08: - parallel planes - symmetries Bruckner and Gröller 06: - user defined cuts - view dep. occlusion

25. Andrea Brambilla 8 of 19 Existing Approaches Li et al. 08: - building blocks - blocks relationships Karpenko et al. 08: - parallel planes - symmetries Ruiz et al. 08: parallel planes - information theory Bruckner et al. 06: - user defined cuts - view dep. occlusion

26. Andrea Brambilla 9 of 19 Cut Space: Surface Parameterization No building blocks

27. Andrea Brambilla 9 of 19 Cut Space: Surface Parameterization No building blocks Arbitrary cuts not effective

28. Andrea Brambilla 9 of 19 Cut Space: Surface Parameterization No building blocks Arbitrary cuts not effective

29. Andrea Brambilla 9 of 19 Cut Space: Surface Parameterization No building blocks Arbitrary cuts not effective Parameterization seeding point integration time Cut space given by stream / path lines time lines (s p, t p ) (s p, 0)

30. Andrea Brambilla 9 of 19 Cut Space: Surface Parameterization No building blocks Arbitrary cuts not effective Parameterization seeding point integration time Cut space given by stream / path lines time lines Preserve surface semantic

31. p1p1 pivot Andrea Brambilla 10 of 19 Surface Complexity How much a point «occludes» the rest of the surface Visualization tools typically employ polar view p2p2

32. p1p1 pivot Andrea Brambilla 10 of 19 Surface Complexity p2p2 X1X1 X2X2 cpx(p 1 ) = 3cpx(p 2 ) = 2 For every point p How much a point «occludes» the rest of the surface Visualization tools typically employ polar view cpx(p) = | X |

33. Andrea Brambilla 11 of 19 Surface Complexity

34. cpx(p) = | X | p1p1 pivot Andrea Brambilla 12 of 19 Surface Complexity p2p2 X1X1 X2X2 cpx(p 1 ) = 3cpx(p 2 ) = 2 Including the importance cpx(p) = = ∑ x ∈ X importance(x) For every point p How much a point «occludes» the rest of the surface Visualization tools typically employ polar view

35. Andrea Brambilla 13 of 19 Cut Selection and Splitting Choose the cut Ω that reduce occlusion the most

36. Andrea Brambilla 13 of 19 Cut Selection and Splitting Choose the cut Ω that reduce occlusion the most CPX(Ω) = length(Ω) -1 ∙ ∫ Ω cpx(p)dp p1p1 p2p2 p3p3 p4p4 p5p5 p6p6 p8p8 p9p9 p7p7

37. Andrea Brambilla 13 of 19 Cut Selection and Splitting Choose the cut Ω that reduce occlusion the most Complexity already computed for every point p Average complexity over potential cuts The cut with the highest complexity is chosen The (piece of) surface is cut CPX(Ω) = length(Ω) -1 ∙ ∫ Ω cpx(p)dp

38. Andrea Brambilla 14 of 19 Surface Splitting

39. Andrea Brambilla 14 of 19 Surface Splitting Cut Space Complexity Cut Space Complexity

40. Andrea Brambilla 14 of 19 Surface Splitting

41. Andrea Brambilla 14 of 19 Surface Splitting

42. Andrea Brambilla 15 of 19 Interaction

43. Andrea Brambilla 15 of 19 Interaction

44. Andrea Brambilla 15 of 19 Interaction

45. Andrea Brambilla 16 of 19 Results - Gas Leak

46. Andrea Brambilla 17 of 19 Results - Gas Leak

47. Andrea Brambilla 18 of 19 Summary & Future Work So what? the proposed generic framework can help designing succesful splitting and explosion algorithms our splitting approach is the first which can effectively subdivide integral surfaces the complexity measure adequatly approximate the degree of self-occlusion of a surface And then? extend the approach to path and other kinds of surfaces (or even volumes) improve the versatility of the visualization system boost performances via a GPU implementation

48. Andrea Brambilla Thanks for your attention! Questions? Thanks to GexCon AS and AVL providing the datasets The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number 226042. andrea.brambilla@uib.no www.ii.uib.no/vis 19 of 19

49. A. Brambilla 19 of 19 Flow in a Box

50. Andrea Brambilla 19 of 19 Surface Splitting

51. Andrea Brambilla 19 of 19 Surface Splitting

52. Andrea Brambilla 19 of 19 Surface Splitting

53. Andrea Brambilla 19 of 19 Interaction

54. Andrea Brambilla 19 of 19 Interaction

55. Andrea Brambilla 19 of 19 Interaction

56. Andrea Brambilla 19 of 19 Gas Leak

57. Andrea Brambilla 19 of 19 Gas Leak

58. Andrea Brambilla 19 of 19 Gas Leak - Right Vortex

59. A. Brambilla 19 of 19 Thanks for your attention! Questions? Thanks to GexCon AS and AVL providing the datasets The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number 226042. andrea.brambilla@uib.no www.ii.uib.no/vis

60. p Andrea Brambilla Surface Complexity How much a point «occludes» the rest of the surface Precise evaluation not feasible!

61. Andrea Brambilla Surface Complexity

62. Andrea Brambilla Surface Complexity p1p1 pivot p2p2 p3p3 cpx(p) = ∑ x ∈ X importance(x) ∙ abs( nrm(p) ● r / |r| )