2. USF -- May 2004 Esthetic Engineering or Art and Math in Snow Carlo H. Séquin University of California, Berkeley

3. I am a Designer … CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994 RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000

4. Focus of Talk The role of the computer in: u aesthetic optimization, u the creative process.

5. Brent Collins “Hyperbolic Hexagon II”

6. Brent Collins: Stacked Saddles

7. Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle)

8. “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 ?

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. Various “Scherk-Collins” Sculptures

21. Fused Deposition Modeling (FDM)

22. Zooming into the FDM Machine

23. Hyper-Sculpture: “Family of 12 Trefoils” W=2 W=1 B=1 B=2 B=3 B=4

24. “Cohesion” SIGGRAPH’2003 Art Gallery

25. Stan Wagon, Macalester College, St. Paul, MN u Leader of Team “USA – Minnesota”

26. Stan Wagon u Skier – Mountaineer – Snow Sculptor

27. Dan Schwalbe u Software Engineer – Snow Sculptor

28. Helaman Ferguson Umbilic Torus Costa Surface

29. Breckenridge, 1999 Helaman Ferguson: “Invisible Handshake”

30. Breckenridge, CO, 1999 Helaman Ferguson: “Invisible Handshake”

31. Robert Longhurst Moebius Band Enneper Surface

32. Breckenridge, 2000 Robert Longhurst: “Rhapsody in White” 2 nd Place

33. Breckenridge, 2001 Robert Longhurst: “White Narcissus”

34. Batsheba Grossman Antipot Antichron

35. Breckenridge, 2002 Bathsheba Grossman: “A Twist in Time” Honorable Mention “Expressive Impact”

36. Snow-Sculpting, Breckenridge, 2003 Brent Collins and Carlo Séquin are invited to join the team and to provide a design. Other Team Members: Stan Wagon, Dan Schwalbe, Steve Reinmuth (= Team “Minnesota”)

37. Steve Reinmuth

38. Collins’ Initial Suggestion: Minimal Trefoil Stan’s Objection: “Too simple … – we know we can do this. No risk – no fun !”

39. Monkey Saddle Trefoil from Sculpture Generator I

40. Maquettes 3D-Print FDM

41. Name, Story u “Snow Flower, Winter Rose, Winter Whirl, Wild White Whirl, Webbed Wild Whirl, Whirled Wild Web …” u finally the perfect homonym: “Whirled White Web” u Like this global network, the ridges of our sculpture span the outer perimeters of the whole “globe,” and at the same time come close together in the central hole. It illustrates how the WWW can link together people from all over the world.

42. ACCEPTED ! Now – how do we get this design into a 10’x10’x12’ block of snow ?

43. Construction Drawings Top View Side View Axial View

44. Plan of Attack u Cut away 2 large triangular prisms; u Hang plastic template (12’x18’) over slab; u Mark projections of holes, flanges; u Drill, carve, refine … (using maquette for reference) u Try this first on a smaller practice block!

45. 1:1 Templates Magnified from computer prints with the classical grid method

46. Practice Block (1) Template transfer Reference holes

47. Practice Block (2) Free-hand carving  Irregular ribs

48. Practice Block (3)  Need new plan !

50. Removing lots of snow … Day 1

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

52. Day 2: Making a Torus Mark center, circles … Bull’s-eye !

54. Chipping away …

56. Tools, Templates

57. Making a Torus Use of template Need for a sun shield

58. End of Day 2 The Torus

59. Day 3, am: Drawing Flanges

60. Day 3, pm: Flanges, Holes

61. End of Day 3: Proper Topology

62. Day 4: Geometry Refinement

64. End of Day 4: Desired Geometry

65. Day 5, am: Surface Refinement

66. “House Cleaning”

67. “Whirled White Web”

69. Official Team Photo

70. 12:40 pm -- 42° F

71. 12:41 pm -- 42° F

72. 12:40:01 Photo: StRomain

73. 12:50 pm

74. 3 pm

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

77. “WWW” Wins Silver Medal

78. British Columbia: “Winter Comes”

80. Day 2 Day 3

81. Breckenridge: “A Fishing Tail”

82. Mexico City: “Capilla Posa”

83. China: “The Love of Mother”

84. Quebec: “Rève’Olution”

85. Manitoba: “Birth of a Nation”

86. USA – New York: “94 Hour Photo”

88. What Are We Going To Do For 2004 ? “Turning a Snowball Inside Out”

89. Sphere Eversion u ~ 1960, the blind mathematician B. Morin, (born 1931) conceived of a way how a sphere can be turned inside-out: l Surface may pass through itself, l but no ripping, puncturing, creasing allowed, e.g., this is not an acceptable solution: PINCH

90. Sphere Eversion Process u But there are more contorted paths that can achieve the desired goal. u Bernard Morin figured out one such path. u Charles Pugh made models from chicken wire. u Nelson Max made a first computer simulation.

91. Morin Surface Another view of the half-way point, from: John Sullivan: “The Optiverse” (surface of minimum bending energy).

92. Simplest Model Partial cardboard model based on the simplest polyhedral sphere (= cuboctahedron) eversion.

93. Gridded Models for Transparency 3D-Print from ZcorpSLIDE virtual model

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

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

96. The Final Model

97. Day1

98. Day2

99. Day3

100. Day 4

101. Day4

102. Day5 Honorable Mention: Most Ambitious Design

103. “Paradigm Shift” (British Columbia)

104. “Year of the Dragon” USA - Tennessee

105. Conclusions (1) u Interactive computer graphics is a novel (to artists) medium that can play an important role -- even for traditional artists. u Virtual Prototyping can save time and can tackle sculptures of a complexity that manual techniques could not conquer.

106. Conclusions (2) u The computer is not only a great visualization and prototyping tool, u It also is a generator for new ideas and u an amplifier for an artist’s inspiration.