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Southern Oregon University, May 2003

Explore the role of computers in creative design and aesthetic optimization with examples of geometric sculptures and minimal surfaces. Discover the process of parameterized shape generation and realization through layered manufacturing.

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Southern Oregon University, May 2003

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  1. Southern Oregon University, May 2003 Surface Optimization and Aesthetic Engineering 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: • the creative process, • aesthetic optimization.

  4. Outline • Collaboration with Brent Collins • Parameterized Shape Generation • Realization by Layered Manufacturing • Geometric Sculptures in Snow • Aesthetics of Minimal Surfaces • Sphere Inversion as a Challenge • Search for a “Beauty Functional” • CAD Tools that We Are Lacking

  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 “Hyperbolic Hexagon II”

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

  8. Brent Collins: Stacked Saddles

  9. “Hyperbolic Hexagon” by B. Collins • 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 ?

  10. Closing the Loop straight or twisted

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

  12. “Sculpture Generator I”, GUI

  13. 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

  14. 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

  15. A Virtual Sculpture (1996)

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

  17. Minimal Surfaces At all surface points, Minimal Surfaceshave equal and opposite principal curvatures. Catenoid

  18. Main Goal in Sculpture Generator 1 Real-time Interactive Speed ! • Can’t afford real surface optimizationto obtain true minimal surfaces (too slow); • also, this would be aesthetically too limited.  Make closed-form hyperbolic approximation.

  19. Hyperbolic Cross Sections

  20. Base Geometry: One Scherk Story • Hyperbolic Slices  Triangle Strips • precomputed  then warped into toroid

  21. The Basic Saddle Element with surface normals

  22. Hyperbolic Contour Lines On a straight tower and on a toroidal ring

  23. Part IIIHow 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.

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

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

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

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

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

  29. Fused Deposition Modeling (FDM)

  30. Zooming into the FDM Machine

  31. Various “Scherk-Collins” Sculptures

  32. Part IV But what, if we want to make a really large sculpture ?

  33. 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”)

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

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

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

  37. Monkey Saddle Trefoil from Sculpture Generator I

  38. The Poor Man’s Opportunity: Snow-Sculpting!Annual Championships in Breckenridge, CO

  39. “Whirled White Web”

  40. 12:40 pm -- 42° F

  41. 12:40:01 Photo: StRomain

  42. 12:41 pm -- 42° F

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

  44. 4 pm

  45. Snow Sculpting • More on the construction and drama of our snow sculpture tonight at 7pm. • Also, pictures of some of the other snow sculptures.

  46. Part V DISCUSSION: Aesthetics of Minimal Surfaces

  47. “Whirled White Web” Séquin 2003 Maquette made with Sculpture Generator I Minimal surface spanning three (2,1) torus knots

  48. “Tightest Saddle Trefoil” Séquin 1997 Shape generated with Sculpture Generator 1 Minimal surface spanning one (4,3) torus knots

  49. “Atomic Flower II” by Brent Collins Minimal surface in smooth edge(captured by John Sullivan)

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