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VSMM -- October 2001

VSMM -- October 2001. Sculpture Design Carlo H. Séquin University of California, Berkeley. Focus of Talk. How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?. Outline.

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VSMM -- October 2001

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  1. VSMM -- October 2001 Sculpture Design Carlo H. Séquin University of California, Berkeley

  2. Focus of Talk • How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?

  3. Outline • Background (Why?) • Collaboration with Brent Collins • Parameterized Sculpture Families • Sculpture Optimization

  4. I am a Designer …

  5. Roots of My Passion for Sculpture My love for geometry and abstract sculptureemerged long long before I learned to play with computers. Thanks to:Alexander Calder, Naum Gabo,Max Bill, M.C. Escher, Frank Smullin, ...

  6. 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

  7. Brent Collins: Early Sculptures All photos by Phillip Geller

  8. Collins’ Abstract Geometric Art • Beautiful symmetries • Graceful balance of the saddle surfaces • Superb craftsmanship • Intriguing run of the edges • What type of knot is formed ? • Mystery: one-sided or two-sided ? ==> Focus on “Chains of Saddles”

  9. “Hyperbolic Hexagon II” (wood) Brent Collins

  10. Brent Collins: Stacked Saddles

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

  12. “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 ?

  13. Closing the Loop straight or twisted

  14. Collins - Séquin Collaboration • Discuss ideas on the phone • Exchange sketches • Vary the topological parameters • But how do you know whether it is beautiful ? Need visual feedback. • Making models from paper strips is not good enough. • A key problem is making the sculpture look good from all sides !

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

  16. Collins’ Fabrication Process Building the final sculpture (2-3 months): • Take measurements from mock-up model,transfer parallel contours to 1” boards. • Roughly precut boards, leaving registration marksand contiguous pillars for gluing boards together. • Stack and glue together precut boards,remove auxiliary struts. • Fine-tune overall shape,sand and polish the surface. A big investment of effort !

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

  18. “Sculpture Generator I” Prototyping & Visualization tool forScherk-Collins Saddle-Chains. • Slider control for this one shape-family, • Control of about 12 parameters. • Main goal: Speed for interactive editing. • Geometry part is about 5,000 lines of C; • 10,000 lines for display & user interface.

  19. Scherk-Collins Sculptures

  20. The Basic Element Scherk’s 2ndminimal surface 3-story tower,trimmed, thickened 180 degreesof twist added

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

  22. A Plethora of Shapes

  23. Edge Treatment square, flat cut semi-circular bulging out

  24. Embellishment of Basic Shape color texture background

  25. Sculpture Generator, GUI

  26. 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

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

  28. 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

  29. 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

  30. 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

  31. Main Goal in Sculpture Generator I Real-time Interactive Speed ! • Can’t afford surface optimizationto obtain true minimal surfaces; • also, this would be aesthetically too limited.  Use closed-form hyperbolic approximation.

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

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

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

  35. 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.

  36. Our First “Joint” Sculpture Six monkey saddles in a ring with no twist (like Hyperbolic Hexagon) azimuth = –30°, flange 1.5 (aesthetics) size, thickness (fabrication consideration)

  37. Another Joint Sculpture • Heptoroid

  38. Heptoroid ( from Sculpture Generator I ) Cross-eye stereo pair

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

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

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

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

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

  44. Various “Scherk-Collins” Sculptures

  45. Fused Deposition Modeling (FDM)

  46. Looking into the FDM Machine

  47. Zooming into the FDM Machine

  48. Séquin’s “Minimal Saddle Trefoil” • Stereo-lithography master

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

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

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