1. Stackabilization Honghua Li, Ibraheem Alhashim, Hao Zhang, Ariel Shamir, Daniel Cohen-Or

2. Stacking 2

3. Goal: stackabilize shapes 3

4. Challenge-1 geometrically understand stacking 4

5. Challenge-2 space saving vs. shape preserving 5 Original SqueezedCone-like Balanced ?

6. Related work Shape optimization 6 [Mitra et al. 2007] [Hoppe et al. 1993] Low levelHigh level

7. Related work 2D Tiling 7 Escherization [Kaplan and Salesin 2000]

8. Our approach Define stackability measure Automatically improve stackability Contact driven deformation Structure preserving Greedy optimization Allow designers to control the process 8

9. Stackability

10. The measure 10 high low medium

11. Stacking measure 11

12. Stacking measure 12

13. Stacking measure 13 offset

14. Upper & Lower Envelopes 14 Upper envelope Lower envelope

15. Gap function 15

16. Gap function 16 offset

17. Gap function 17

18. Improve stackability 18

19. Slight shape changes 19

20. Slight shape changes 20 Gap function

21. Slight shape changes 21

22. Interesting shape changes 22

23. Contact regions 23

24. Contact driven deformation 24

25. Contact driven deformation 25

26. Algorithm

27. Deformation model Component-wise controller [Zheng et al. 2011] Cuboid Cylinder Generalized Cylinder 27

28. Deformation model Structure preserving Symmetries Point joints Line joints 28

29. Search space is huge Optimization problem 29 TranslationRotationScaling Controller

30. Optimization problem Find the best shape deformation Improves the stackability Preserves shape structure and minimizes distortion 30 Shape distortionStackability improved

31. Optimization Greedy approach 31 Input Contact driven deformation Best candidate Candidates Target is met? Output Yes No Target stackability

32. Optimization 32

33. Optimization 33

34. Optimization 34

35. Optimization 35

36. Optimization 36

37. Optimization 37

38. Optimization 38

39. Optimization 39

40. Optimization 40

41. Optimization 41

42. Optimization 42

43. Optimization 43

44. Implementation

45. Prerequisites Segmentation and Controllers 45 Cuboid Generalized Cylinder

46. Prerequisites Symmetry and joint detection 46

47. Results

48. Results 48

49. Results 49

50. Results 50

51. Results 51

52. Conclusion, limitations and future work 52

53. Conclusion Defined a measure for stackability Analyze and optimize geometry of the shape to increase its stackability 53

54. Limitation Deformation model is limited 54

55. Limitation Stability of stack 55

56. Future work Partition + stackabilization 56

57. Future work Partition + stackabilization 57

58. Future work Partition + stackabilization 58

59. Future work Folding + stacking 59

60. Future work Other deformation models 60

61. Thank you code.google.com/p/stacker 61