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SIGGRAPH 2004, OZONE

SIGGRAPH 2004, OZONE. Turning a Snowball Inside Out: Mathematical Visualization at the 12-foot Scale. Alex Kozlowski & Carlo H. Séquin: U.C. Berkeley Dan Schwalbe: ComSquared Systems, Eagan, MN Stan Wagon: Macalester College, St. Paul, MN John M. Sullivan, Tech. University, Berlin.

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SIGGRAPH 2004, OZONE

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  1. SIGGRAPH 2004, OZONE Turning a Snowball Inside Out: Mathematical Visualization at the 12-foot Scale Alex Kozlowski & Carlo H. Séquin: U.C. Berkeley Dan Schwalbe: ComSquared Systems, Eagan, MN Stan Wagon: Macalester College, St. Paul, MN John M. Sullivan, Tech. University, Berlin

  2. “Whirled White Web” 3D-Print

  3. Day 1: The “Monolith” Cut away prisms …

  4. End of Day 2 The Torus

  5. Day 3, pm: Flanges, Holes

  6. Day 4: Geometry Refinement

  7. “House Cleaning”

  8. Memories of 2003

  9. 12:40 pm -- 42° F

  10. 12:41 pm -- 42° F

  11. The Winners 1st: Canada – B.C., 2nd: USA – Minnesota, 3rd: USA – Breckenridge “… sacred geometry … very intricate … very 21st century !”

  12. “WWW” Wins Silver Medal

  13. What Are We Going To Do For 2004 ? “Turning a Snowball Inside Out” Making a Model of the Half-way Pointof the Sphere Eversion Process

  14. Sphere Eversion is Possible ! PINCH • First proven by Steve Smale around 1960from complex topological arguments. • But he could not say HOW it can be done … ! • Surface may pass through itself, • but no ripping, puncturing, creasing allowed,e.g., this is not an acceptable solution:

  15. Sphere Eversion Process • A few years later Bernard Morin, a blind mathematician, figured out how to do it. • In his honor, the half-way point,where half each of the inside and outside of the sphere shell can be seen, is called the Morin surface.

  16. Sphere Eversion Process • You need a rather contorted move to achieve the desired goal. • Bernard Morin figured out one such path. • Charles Pugh made models from chicken wire. • Nelson Max made a first computer simulation.

  17. Optimal Sphere Eversion • In the 1990’s John Sullivan found the most efficient way (using the least surface bending)to accomplish this eversion,and made a beautiful movie of it. From: John Sullivan: “The Optiverse”

  18. The Simplest Polyhedral Model Partial cardboard model based on cuboctahedron eversion by Apéry & Denner.

  19. Shape Adaption for Snow Sculpture Restructured Morin surface to fit block size: (10’ x 10’ x 12’)

  20. Make Surface “Transparent” • Realize surface as a grid. • Draw a mesh of smooth lines onto the surface …

  21. Gridded Models for Transparency SLIDE virtual model 3D-Print from Zcorp

  22. “Turning a Snowball Inside-Out” Carlo H. Séquin, Alex Kozlowski, John Sullivan Dan Schwalbe, Stan Wagon

  23. The Final Model

  24. Morin’s Surface Eversion

  25. The Half-way Point

  26. Finish the Process

  27. Computer Projections

  28. Horizontal Slices and Projections

  29. Practice Block (Stan Wagon)

  30. First Night

  31. Working Out Plan B

  32. Working on the Grid

  33. Day 1 Day 1

  34. Day 1

  35. Shovels, Drills, Pick-axes ...

  36. End of Day 1

  37. Day 2 A Template for the “ear”

  38. Day 2

  39. Day2

  40. End of Day 2

  41. Day 3

  42. Defining the Grid

  43. Carving the Grid

  44. Cleaning Out the Cross-Tunnel

  45. Day3

  46. End of Day 3

  47. Day 4

  48. Day 4

  49. Day 5 End of Day 4

  50. Day 5

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