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CONTACT, March. 21-23, 2003

CONTACT, March. 21-23, 2003. Art, Math, Computers, and Creativity. Carlo Séquin, University of California, Berkeley. I am a Designer …. CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994. RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000. Focus of Talk.

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CONTACT, March. 21-23, 2003

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  1. CONTACT, March. 21-23, 2003 Art, Math, Computers, and Creativity Carlo Séquin, University of California, Berkeley

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

  3. Focus of Talk The role of the computer in: • aesthetic optimization, • the creative process.

  4. Brent Collins “Hyperbolic Hexagon II”

  5. Leonardo -- Special Issue On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art With an Artist’s Statement by Brent Collins George K. Francis with Brent Collins

  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 • 6 saddles in a ring • 6 holes passing through symmetry plane at ±45º • “wound up” 6-story Scherk tower • What would happen, • if we added more stories ? • or introduced a twist before closing the ring ?

  9. Closing the Loop straight or twisted

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

  11. “Sculpture Generator I”, GUI

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

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

  14. 1-story Scherk Tower • branches = 5 • stories = 1 • height = 1.35 • flange = 1.00 • thickness = 0.04 • rim_bulge = 0 • warp = 58.0 • twist = 37.5 • azimuth = 0 • textr_tiles = 8 • detail = 6

  15. 180º Arch = Half a Scherk Toroid • branches = 8 • stories = 1 • height = 5 • flange = 1.00 • thickness = 0.06 • rim_bulge = 1.25 • warp = 180 • twist = 0 • azimuth = 0 • textr_tiles = e • detail = 12

  16. V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen

  17. How to Obtain a Real Sculpture ? • Prepare a set of cross-sectional blue printsat equally spaced height intervals,corresponding to the board thicknessthat Collins is using for the construction.

  18. Collins’ Fabrication Process Wood master patternfor sculpture Layered laminated main shape Example: “Vox Solis”

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

  20. Profiled Slice through the Sculpture • One thick slicethru “Heptoroid”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, 3/4of one board.

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

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

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

  24. The Finished “Heptoroid” • at Fermi Lab Art Gallery (1998).

  25. SFF (Solid Free-form Fabrication) Monkey- Saddle Cinquefoil

  26. Fused Deposition Modeling (FDM)

  27. Zooming into the FDM Machine

  28. Various “Scherk-Collins” Sculptures

  29. Part II Developing Parameterized Sculpture Families (Extending a Paradigm)

  30. Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4

  31. Close-up of Some Trefoils B=1 B=2 B=3 Varying the number of branches, the order of the saddles.

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

  33. Exploring New Ideas: W=2 • Going around the loop twice ... … resulting in an interwoven structure.

  34. 9-story Intertwined Double Toroid Bronze investment casting fromwax original made on3D Systems’“Thermojet”

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

  36. Note: The computer becomesan amplifier / acceleratorfor the creative process.

  37. Séquin’s “Minimal Saddle Trefoil” • bronze cast, gold plated

  38. Minimal Trefoils -- cast and finished by Steve Reinmuth

  39. Steve Reinmuth

  40. Brent Collins’ “Pax Mundi” A new inspiration

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

  42. Part III The “Least Understood” Step (Capturing a Paradigm)

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

  44. 2-period Gabo Curve • Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.

  45. 4-period Gabo Curve Same construction as for a 2-period curve

  46. “Pax Mundi” Revisited • Can be seen as:Amplitude modulated, 4-period Gabo curve

  47. SLIDE-UI for “Pax Mundi” Shapes

  48. “Viae Globi” Family (Roads on a Sphere) L2 L3 L4 L5

  49. Via Globi 3 (Stone) Wilmin Martono

  50. Via Globi 5 (Wood) Wilmin Martono

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