1. EECS Computer Science Division University of California, Berkeley
Florida 1999
CAD 2007, Honolulu, Hawaii
Computer-Aided Design and Realization of Geometrical Sculptures Carlo H. Séquin
EECS Computer Science Division
University of California, Berkeley

2. Brent Collins, Wood Sculptor, 1996
Florida 1999
Brent Collins, Wood Sculptor, 1996
For whom I designed certain shapes on the computer which he then built in wood.
... my main “artist-collaborator” since 1994

3. Brent Collins: Stacked Saddles

4. Hyperbolic Hexagon II – our first collaborative piece
Florida 1999
Hyperbolic Hexagon II – our first collaborative piece
For whom I designed certain shapes on the computer which he then built in wood.
Brent Collins, 1997

5. Hyperbolic Hexagon (B. Collins, 1994)
6 saddles in a ring
6 holes passing through symmetry plane at ±45º
= “wound up” 6-story Scherk tower
Discussion: What if …
we added more stories ?
or introduced a twist before closing the ring ?

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

7. Closing the Loop straight or twisted
Adding smooth geometric deformations: Bending, Twisting

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
Creates a family of highly specialized, parameterized shapes

10. Base Geometry: One “Scherk Story”
Taylored hyperbolas, hugging a circle
Hyperbolic Slices  Triangle Strips

11. The Basic Saddle Element
with surface normals
precomputed -- then warped into toroid

12. Shape Generation: by stacking this basic hyperbolic element,
twisting that stack along z-axis,
bending (warping) it into an arch or loop.

13. Toroidal Warp into Collins Ring
8-story tower
warped into a ring
360º twist added

14. A Plethora of Shapes

15. Some of the Parameters in “SG1”

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

17. True Minimal Surfaces ?
Not a true “minimal surface” (like a soap film)!

18. Ken Brakke’s Surface Evolver
For approximating minimal surfaces:
Start with a crude
polyhedral object
Subdivide triangles
Optimize vertices
Repeat the process

19. Shape Comparison Minimal Trefoil from Sculpture Generator I
Minimal surface from Brakke’s Surface Evolver

20. Volution Surfaces (twisted shells)
Florida 1999
Volution Surfaces (twisted shells)
Costa Cube Ico-Vol Here, minimal surfaces seem aesthetically optimal.

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

22. Profiled Slice through Heptoroid
Florida 1999
Profiled Slice through Heptoroid
One thick slice thru sculpture, from which Brent can cut boards and assemble a rough shape.
Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board.
From these Collins will precut boards
then assemble the complete shape
and fine tune and polish it.

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

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

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

26. Various “Scherk-Collins” Sculptures

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

28. Rapid Prototyping with FDM

29. A Look Into the FDM Machine
2 NOZZLES
Galapagos 6 sculpture in progress

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

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

32. 9-story Intertwined Double Toroid
Bronze
investment
casting from wax original made on 3D Systems’ “Thermojet”

33. Extending the Paradigm: Totem 3
Bronze Investment Cast

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

35. Snowsculpting Championships 2003
The Team: “Whirled White Web” (C. Séquin, S. Wagon, D. Schwalbe, B. Collins, S. Reinmuth)

36. Day 1
Removing lots of snow …

37. Day 2: Making a Torus

38. Day 3, pm: Carving Flanges, Holes

39. Day 4: Geometry Refinement

40. Day 5, am: Surface Refinement

41. 12:40 pm ° F

42. 12:41 pm ° F

43. “WWW” Wins Silver Medal

44. Every Artist’s Dream: Large and Durable Sculpture !
Need a material more permanent than snow ...

45. Brent Collins’ Pax Mundi 1997: wood, 30”diam.
2006: Commission from
H&R Block, Kansas City
to make a 70”diameter version in bronze.
My task: to define the master geometry.
CAD tools played important role.

46. How to Model Pax Mundi ... Already addressed that question in 1998:
Pax Mundi could not be done with Sculpture Generator I
Needed a more general program !
Used the Berkeley SLIDE environment.
First: Needed to find the basic paradigm   

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

48. 2-period “Gabo Curve”
Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used (symmetry!).

49. 4-period “Gabo Curve”
Same construction as for as for 2-period curve

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

51. SLIDE-GUI for “Pax Mundi” Shapes
Florida 1999
Good combination of interactive 3D graphics and parameterizable procedural constructs.
Good combination of interactive 3D graphics and parameterizable procedural constructs.

52. 2-period Gabo sculpture
Tennis ball – or baseball – seam used as
sweep curve.

53. Viae Globi Family (Roads on a Sphere)
periods

54. Via Globi 5 (Virtual Wood)
Wilmin Martono

55. Modularity of Gabo Curve Generator
Sweep Curve Generator:
Gabo Curves as B-splines
Cross Section Fine Tuner:
Paramererized shapes
Sweep / Twist Controller

56. Sweep / Twist Control
How do we orient, move, morph ... the cross section along the sweep path ?
Natural orientation with Frenet frame
Torsion Minimization: Azimuth: tangential / normal
900° of twist added.

57. Extension: Free-form Curve on a Sphere
Spherical Spline Path Editor (Jane Yen)
Nice smooth interpolating curves through sparse data points

58. Many Different Viae Globi Models

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

60. Allows Knotted Sweep Paths
Chinese Button Knot

61. Really Free-form 3D Space Curves
Figure-8 knot

62. Using Another Cross Section
Galapagos 6

63. Target Geometry Constraints: Bronze, 70” diameter
Less than 1500 pounds
Less than $50’000
Maintain beauty, strength
Minimize master geometry

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

65. Emulation; Define Master Pattern
Master to make a mold from.
Alignment tab
Use 4 copies.

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

67. Joe Valasek’s CNC Milling Machine
Styrofoam milling machine

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

69. Subdivide into Two Master Segments

70. Machined Master Pattern #2

71. (Cut) Master  Silicone Rubber Mold

72. Mold  Several (4) Wax Copies

73. Spruing the Wax Parts for Casting

74. Ceramic Slurry Shell Around Wax Part

75. Shell Ready for Casting

76. Casting with Liquid Bronze

77. The Freed Bronze Cast

78. Assembling the Segments

79. The “Growing” Ribbon

80. The Assembly is Too Squat !!

81. Changing the Curvature
PHYSICS is important too ... not just Geometry !

82. Grinding the Welded Seams, Polishing the Surface

83. Applying Patina

84. Front Door of the ...
H&R Block Building

85. The Final Destination

86. Steve Reinmuth Tightening the Bolts

87. Brent Collins Polishing Our Baby

88. Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin

89. Our Next Commission 10 ft diameter amber-tinted polyester resin
to be hung in an atrium below skylight

90. QUESTIONS ? ?