1. ETH, July 21, 2008 Scherk’s 2 nd Minimal Surface, Snowsculpting, EuroGraphics Award Carlo H. Séquin University of California, Berkeley

2. Brent Collins Hyperbolic Hexagon II

3. Brent Collins: Stacked Saddles

4. Scherk’s 2 nd Minimal Surface

5. Normal “biped” saddles Generalization to higher-order saddles (monkey saddle)

6. Scherk Tower Scherk Tower u 5-story core u Monkey saddles u Thick surface u “Flare” added

7. Hyperbolic Hexagon by B. Collins u 6 saddles in a ring u 6 holes passing through symmetry plane at ±45º u = “wound up” 6-story Scherk tower u Discussion: What if … l we added more stories ? l or introduced a twist before closing the ring ?

8. Solar Arch u 12 stories u 4 th -order saddles u 270° twist

9. Closing the Loop straight or twisted

10. Brent Collins’ Prototyping Process Armature for the Hyperbolic Heptagon Mockup for the Saddle Trefoil Time-consuming ! (1-3 weeks)

11. Sculpture Generator I, GUI

12. V-art Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

13. Collins’ Fabrication Process Example: Vox Solis Layered laminated main shape Wood master pattern for sculpture

14. Slices through Minimal Trefoil 50%10%23%30% 45%5%20%27% 35%2%15%25%

15. u One thick slice thru sculpture, from which Brent can cut boards and assemble a rough shape. u Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board. Profiled Slice through Heptoroid

16. Emergence of the Heptoroid (1) Assembly of the precut boards

17. Emergence of the Heptoroid (2) Forming a continuous smooth edge

18. Emergence of the Heptoroid (3) Smoothing the whole surface

19. The Finished Heptoroid u at Fermi Lab Art Gallery (1998)

20. “Scherk-Collins” Sculptures (FDM)

21. Hypersculpture: Family of 12 Trefoils W=2 W=1 B=1 B=2 B=3 B=4

22. Extending the Notion of a “Saddle” B=1 B=2 B=3 B = number of branches = the order of the saddles. B = 1: A “one-leg saddle”?  just a simple band.

23. Another Extension … Allow different kinds of “stretching” …

24. Extending the Paradigm: Totem 3 Bronze Investment Cast

25. Cohesion SIGGRAPH’2003 Art Gallery

26. Going more then once around the loop... … results in an interwoven structure. w =380° w =560° w =720°

27. 11 Stories, Monkey-Saddles, w=2: cross – eye stereo picture

28. 9-story Intertwined Double Toroid Bronze investment casting from wax original made on 3D Systems’ Thermojet

29. Stepwise Expansion of Horizon u Playing with many different shapes and u experimenting at the limit of the domain of the sculpture generator, u stimulates new ideas for alternative shapes and generating paradigms. Swiss Mountains

30. Sculpture Generator 1 as a Playground The computer becomes an amplifier / accelerator for the creative process. Another occasion where Sculpture Generator 1 became invaluable...

31. Silver Medal Winner: “Whirled White Web” (C. Séquin, S. Wagon, D. Schwalbe, B. Collins, S. Reinmuth) Snowsculpting Championships 2003

32. Removing lots of snow … Day 1

34. Day 2: Making a Torus

35. End of Day 2 The Torus

36. Day 3, am: Drawing Flanges

37. Day 3, pm: Carving Flanges, Holes

38. Day 4: Geometry Refinement

40. End of Day 4: Desired Geometry

41. Day 5, am: Surface Refinement

42. Official Team Photo

43. Judgement Time: Whirled White Web

44. 12:40 pm -- 42° F

45. 12:41 pm -- 42° F

46. “WWW” Wins Silver Medal

47. Large and Durable Sculpture ! u Need a material more permanent than snow...

48. Another Inspiration: Brent Collins’ Pax Mundi (1997)

49. Keeping up with Brent... u Pax Mundi cannot be done with Sculpture Generator I u Needs a more general program ! u First: Need to understand what is going on  

50. Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis- or base-ball; ==> 2-period Gabo curve.

51. 2-period “Gabo Curve” u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used (symmetry!).

52. 4-period “Gabo Curve” Same construction as for as for 2-period curve

53. Pax Mundi Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

54. SLIDE-GUI for “Pax Mundi” Shapes Good combination of interactive 3D graphics and parameterizable procedural constructs.

55. 2-period Gabo Sculpture Tennis ball – or baseball – seam used as sweep curve.

56. Viae Globi Family (Roads on a Sphere) Viae Globi Family (Roads on a Sphere) 2 3 4 5 periods

57. Via Globi 5 (Virtual Wood) Wilmin Martono

58. Extension: Free-form Curve on a Sphere Carlo Séquin Jane Yen (2001) on the plane -- and on the sphere Interpolating Circle Splines

59. Many Different Viae Globi Models

60. Paradigm Extension: Sweep Path is no longer confined to a sphere! Music of the Spheres (Brent Collins)

61. 2006: Commission for a Big Sculpture! u Scale up original “Pax Mundi” (to 6ft diam.) u Less than 1500 pounds u Budget 50’000 $ u Due in 4 months (  Nov. 2006) u Collaboration: Collins, Reinmuth, Séquin u My task: Create the digital file for a mold master

62. Target Geometry

63. Emulation; Define Master Pattern u Use 4 copies. u Master to make a mold from.

64. Subdivide into Two Master Segments

65. Joe Valasek’s CNC Milling Machine u Styrofoam milling machine

66. Machined Master Pattern #2

67. (Cut) Master  Silicone Rubber Mold

68. Mold  Several (4) Wax Copies

69. Spruing the Wax Parts for Casting

70. Ceramic Slurry Shell Around Wax Part

71. Shell Ready for Casting

72. Casting with Liquid Bronze

73. Bronze Cast Slowly Cooling Off

74. Cracking the Ceramic Shell

75. The Freed Bronze Cast

76. Assembly of Pieces

77. Grinding the Welded Seams, Polishing the Surface

78. Applying Patina

79. Front Door H&R Block Building

80. The Final Destination

81. Steve Tightening the Bolts

82. Brent Polishing Our Baby

85. Motif Selected for EuroGraphics Award 3D-Print

86. Splitting the Wheel

87. The Components

88. Creating the Half-Wheel Mold

89. Dimpling the Clay Master

90. Preparing the Last Piece of the Mold

91. Pouring the “Top” Mold Piece

92. Anatomy of the Mold Master and the 3 small silicone rubber pieces The large silicone rubber piece Hydrostone mother mold (for rigidity)

93. Assembling the Mold

94. Filling Mold with Wax

95. Extracting the Wax Cast

96. Wax Copy and FDM Master Wax-coated FDM masterWax copy from mold

97. 7 Secondary Copies in Wax

98. Application of Ceramic Slurry

99. Various Ceramic Shells

100. Bronze Casting

101. Breaking the Ceramic Shell

102. Many Cast Pieces

103. Cleaning Up the Cast Bronze Pieces

104. Assemblies With Different Patinas Eurographics Awards

105. Thanks to Steve Reinmuth... u for creating the beautiful patinas, u for the fabrication photographs.

106. The Four Awards Handed Out April ‘08