1. CHS UCB BID 02/02/02 Parameterized Sculpture Design Carlo H. Séquin University of California, Berkeley

2. CHS UCB Designs I worked on:

3. CHS UCB Sculpture Design u How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?

4. CHS UCB “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 What would happen, l if we added more stories ? l or introduced a twist before closing the ring ?

5. CHS UCB “Hyperbolic Hexagon II” (wood) Brent Collins

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

7. CHS UCB Closing the Loop straight or twisted

8. CHS UCB Sculpture Generator, GUI

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

10. CHS UCB A Simple Scherk-Collins Toroid Parameters: (genome) u branches = 2 u stories = 1 u height = 5.00 u flange = 1.00 u thickness = 0.10 u rim_bulge = 1.00 u warp = 360.00 u twist = 90 u azimuth = 90 u textr_tiles = 3 u detail = 8

11. CHS UCB Also a Scherk-Collins Toroid u branches = 1 u stories = 5 u height = 1.00 u flange = 1.00 u thickness = 0.04 u rim_bulge = 1.01 u warp = 360 u twist = 900 u azimuth = 90 u textr_tiles = 1 u detail = 20

12. CHS UCB A Scherk Tower (on its side) u branches = 7 u stories = 3 u height = 0.2 u flange = 1.00 u thickness = 0.04 u rim_bulge = 0 u warp = 0 u twist = 0 u azimuth = 0 u textr_tiles = 2 u detail = 6

13. CHS UCB 180º Arch = Half a Scherk Toroid u branches = 8 u stories = 1 u height = 5 u flange = 1.00 u thickness = 0.06 u rim_bulge = 1.25 u warp = 180 u twist = 0 u azimuth = 0 u textr_tiles = e u detail = 12

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

15. CHS UCB Séquin’s “Minimal Saddle Trefoil” u Stereo- lithography master

16. CHS UCB Minimal Trefoils -- cast and finished by Steve Reinmuth

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

18. CHS UCB Emergence of the “Heptoroid” (1) Assembly of the precut boards

19. CHS UCB Another Joint Sculpture u “Heptoroid” carved by Brent Collins

20. CHS UCB Advantages of CAD of Sculptures u Exploration of a larger domain u Instant visualization of results u Eliminate need for prototyping u Create virtual reality pictures u Making more complex structures u Better optimization of chosen form u More precise implementation u Rapid prototyping of maquettes

21. CHS UCB Rapid Prototyping by FDM

22. CHS UCB Various “Scherk-Collins” Sculptures

23. CHS UCB Parameterized Sculpture Families Within the domain of a sculpture generator, vary selectively 1 to 3 parameters, and create the resulting instances: u Scherk Collins toroids  “Trefoil Family” u Pax Mundy  “Viae Globi”

24. CHS UCB Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4

25. CHS UCB Close-up of Some Trefoils B=1 B=2 B=3 Varying the number of branches B (the order of the saddles).

26. CHS UCB Higher-order Trefoils (4th order saddles) W=1 (Warp)W=2 

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

28. CHS UCB Inspiration: Brent Collins’ “Pax Mundi”

29. CHS UCB Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball;  2-period Gabo curve.

30. CHS UCB 2-period Gabo curve u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used.

31. CHS UCB 4-period Gabo curve Same construction as for as for 2-period curve

32. CHS UCB “Pax Mundi” Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

33. CHS UCB SLIDE-UI for “Pax Mundi” Shapes

34. CHS UCB Parameterized Sculpture Design 3 Phases: l Discover and distill out the key paradigm l Define the most appropriate set of parameters l Develop generalizations of the paradigm  The Program is the Design, is the Artwork!

35. CHS UCB Via Globi 3 (Stone) Wilmin Martono

36. CHS UCB “Maloja” -- FDM part u A rather winding Swiss mountain pass road in the upper Engadin.

37. CHS UCB “Stelvio” u An even more convoluted alpine pass in Italy.

38. CHS UCB “Altamont” u Celebrating American multi-lane highways.

39. CHS UCB “Lombard” u A very famous crooked street in San Francisco

40. CHS UCB Conclusions Design as an aesthetic optimization in the purely geometrical realm. The computer can also be an amplifier / accelerator for the creative process.

41. CHS UCB Questions ? THE END

42. CHS UCB EXTRAS

43. Another Inspiration by B. Collins

44. CHS UCB Collin’s Conceptual Design SWEEP CURVE (FOR DOUBLE CYLINDER) IS COMPOSED OF 4 IDENTICAL SEGMENTS, FOLLOWS THE SURFACE OF A SPHERE.

45. CHS UCB Reconstruction / Analysis (v1) AWKWARD ALIGNMENT FROM THE FDM MACHINE

46. CHS UCB Further Explorations (v2: add twist)

47. CHS UCB A More Complex Design (v3)

48. CHS UCB Fine-tuned Final(?) Version (v5)

49. CHS UCB Galapagos-6 (v6)

50. CHS UCB Circle Splines on the Sphere Examples from Jane Yen’s Editor Program