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Innovations in Stackabilization: Enhancing Shape Stability through Geometry Optimization

This paper explores the concept of stackabilization, focusing on the challenge of stacking shapes while addressing both space-saving and shape-preserving aspects. The proposed method includes defining a stackability measure, automatically enhancing it through contact-driven deformation techniques, and utilizing greedy optimization strategies. The approach aims to balance structural integrity with aesthetic design, ensuring that slight shape modifications do not compromise overall stability. Key advancements in algorithms and deformation models are detailed, aiming to assist designers in optimizing their creations for better stackability.

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Innovations in Stackabilization: Enhancing Shape Stability through Geometry Optimization

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

  2. Stacking

  3. Goal: stackabilize shapes

  4. Challenge-1 geometrically understand stacking

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

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

  7. Related work • 2D Tiling 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

  9. Stackability

  10. The measure low high medium

  11. Stacking measure

  12. Stacking measure

  13. Stacking measure offset

  14. Upper & Lower Envelopes Upper envelope Lower envelope

  15. Gap function Gap function

  16. Gap function offset

  17. Gap function

  18. Improve stackability

  19. Slight shape changes

  20. Slight shape changes Gap function

  21. Slight shape changes

  22. Interesting shape changes

  23. Contact regions

  24. Contact driven deformation

  25. Contact driven deformation

  26. Algorithm

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

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

  29. Optimization problem • Search space is huge Translation Rotation Scaling Controller

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

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

  32. Optimization

  33. Optimization

  34. Optimization

  35. Optimization

  36. Optimization

  37. Optimization

  38. Optimization

  39. Optimization

  40. Optimization

  41. Optimization

  42. Optimization

  43. Optimization

  44. Implementation

  45. Prerequisites • Segmentation and Controllers Generalized Cylinder Cuboid

  46. Prerequisites • Symmetry and joint detection

  47. Results

  48. Results

  49. Results

  50. Results

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