1. Graphics Lunch, March 1, 2007 CAD / CAM for Geometric Sculpture Carlo H. Séquin University of California, Berkeley

2. Collaboration with Brent Collins, Steve Reinmuth The Making of “Pax Mundi II”

3. Brent Collins “Hyperbolic Hexagon II”

4. Brent Collins: Stacked Saddles

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

6. “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 ?

7. Closing the Loop straight or twisted

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

9. “Sculpture Generator I”, GUI

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

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

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

13. 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”

14. Emergence of the “Heptoroid” (1) Assembly of the precut boards

15. Emergence of the “Heptoroid” (2) Forming a continuous smooth edge

16. Emergence of the “Heptoroid” (3) Smoothing the whole surface

17. The Finished “Heptoroid” u at Fermi Lab Art Gallery (1998).

18. Various “Scherk-Collins” Sculptures

19. Fused Deposition Modeling (FDM)

20. Zooming into the FDM Machine

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

22. Cohesion SIGGRAPH’2003 Art Gallery

23. Extending the Paradigm: Totem 3 u Add affine stretching

24. Another Inspiration: Brent Collins’ Pax Mundi

25. Keeping up with Brent... u Sculpture Generator I can only do warped Scherk towers, not able to describe a shape like Pax Mundi. u Need a more general approach ! u Use the SLIDE modeling environment (developed at U.C. Berkeley by J. Smith) to capture the paradigm of such a sculpture in a procedural form. l Express it as a computer program l Insert parameters to change salient aspects / features of the sculpture u First: Need to understand what is going on   

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

27. 2-period “Gabo Curve” u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used (symmetry!).

28. 4-period “Gabo Curve” Same construction as for as for 2-period curve

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

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

31. 2-period Gabo sculpture

32. Via Globi 5 (Wood) Wilmin Martono

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

34. Towards More Complex Pathways u Tried to maintain high degree of symmetry, u but wanted more highly convoluted paths … u Not as easy as I thought ! u Tried to work with splines whose control vertices were placed at the vertices or edge mid-points of a Platonic or Archimedean polyhedron. u Tried to find Hamiltonian paths on the edges of a Platonic solid, but had only moderate success. u Used free-hand sketching on a sphere …

35. Conceiving “Viae Globi” u Sometimes I started by sketching on a tennis ball !

36. More CAD/CAM Tools... u A way to make nice curvy paths on the surface of a sphere: ==> Circle-splines. u A way to sweep interesting cross sections along these spherical paths: ==> SLIDE. u A way to fabricate the resulting designs: ==> Our FDM machine.

37. Interpolating Circle-Splines Carlo Séquin Jane Yen on the plane -- and on the sphere

38. Maloja -- FDM part u A rather winding Swiss mountain pass road in the upper Engadin.

39. Stelvio u An even more convoluted alpine pass in Italy.

40. Altamont u Celebrating American multi-lane highways.

41. Altamont (Bronze)

42. Maloja

43. Lombard u A very famous crooked street in San Francisco u Note that I switched to a flat ribbon.

44. Extending the Paradigm: Aurora-M u Same path on sphere, u but more play with the swept cross section. u This is a Moebius band. u It is morphed from a concave shape at the bottom to a flat ribbon at the top of the flower.

45. Music of the Spheres (Collins) Sweep path no longer confined to a sphere

46. Large Sculpture... a dream of every artist ! Many new problems: u How to scale-up the design u How to manufacture it u Installation problems u Maintenance u Liability u...

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

48. Maquette for “Whirled White Web” 3D-Print

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

50. Removing lots of snow … Day 1

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

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

54. Chipping away …

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

56. End of Day 2 The Torus

57. Day 3, am: Drawing Flanges

58. Day 3, pm: Flanges, Holes

59. Day 4: Geometry Refinement

61. End of Day 4: Desired Geometry

62. Day 5, am: Surface Refinement

63. “House Cleaning”

64. “Whirled White Web”

66. Official Team Photo

67. 12:40 pm -- 42° F

68. 12:41 pm -- 42° F

69. “WWW” Wins Silver Medal

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

71. 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

72. Target Geometry

73. Emulation u Use smoother quintic spline u Make 4 identical parts (needs extra control point) u Add a few “warp” parameters

74. The Master Pattern u Master to make a mold from. u Use 4 copies.

75. Model of Master Part Made with FDM u 4 pieces make the whole sculpture

76. Model of Pax Mundi 2 Assembled

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

78. Design of Two-Part Master u Alignment tabs for easy assembly

79. Model of the 2 Master Segments

80. Machined Master Pattern #2

81. Steve Reinmuth, Bronze Studio, Eugene OR

82. Master  Silicone Rubber Mold

83. Mold  Several (4) Wax Copies

84. Spruing the Wax Parts for Casting

85. Ceramic Slurry Shell Around Wax Part

86. Shell Ready for Casting

87. Casting with Liquid Bronze

88. Bronze Cast Slowly Cooling Off

89. Cracking the Ceramic Shell

90. The Freed Bronze Cast

91. Final Steps for Pax Mundi II u Removing sprues and runners u Sand-blasting the 20 cast pieces u Welding the pieces together u Cutting off clamping tabs u Smoothing the surface u Applying a patina u Installation

92. Assembly of Pieces

93. The Single Support Point

94. The Assembly is Too Squat !!

95. Changing the Curvature

96. Grinding the Welded Seams, Polishing the Surface

97. Applying Patina

98. Ready for Shipping

99. Pax Mundi II on the Loading Dock

100. The Move Around the Building (Jan.18)

101. Front Door H&R Block Building

102. Scaffolding with Crane

103. The Final Destination

104. Technical Problems

105. Steve Tightening the Bolts

106. Brent Polishing Our Baby