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CS285

CS285. Sculpture Generator I Carlo H. Séquin University of California, Berkeley In Collaboration with B rent Collins Gower, Missouri. Brent Collins. “Genesis” – Brent Collins at BRIDGES 2000. Leonardo -- Special Issue. On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art

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CS285

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  1. CS285 Sculpture Generator I Carlo H. Séquin University of California, Berkeley In Collaboration with Brent Collins Gower, Missouri

  2. Brent Collins “Genesis” – Brent Collins at BRIDGES 2000

  3. 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

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

  5. 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”

  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. 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 !

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

  12. 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 !

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

  14. The Need for a Prototyping Tool Intriguing Conceptual Idea: “Turn the Hyperbolic Hexagon into a Heptagon” • Goals:Give it more variety; • Make different hole-angles visible from one direction by adding twist before closure. • Results:Surface becomes single-sided; • The four separate edges join into a torus knot. Question: Will it look beautiful ? • What can we do if it doesn’ t ? • Perhaps more twist can save it ? • What is the best size for the holes, the flanges ? • How can we find out quickly ?

  15. “Sculpture Generator I” Prototyping 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.

  16. Generated Scherk-Collins Shapes

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

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

  19. A Plethora of Shapes

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

  21. Embellishment of Basic Shape color texture background

  22. Sculpture Generator, GUI

  23. Some of the Parameters in “SC1”

  24. 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.

  25. Base Geometry: One Scherk Story • Hyperbolic Slices ==> Triangle Strips • Pre-computed -- then warped into toroid

  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. 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.

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

  33. 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.

  34. 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)

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

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

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

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

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

  40. “Heptoroid”

  41. 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

  42. Sculpture Design • branches = 4 • storeys = 11 • height = 1.55 • flange = 1.00 • thickness = 0.06 • rim_bulge = 1.00 • warp = 330.00 • twist = 247.50 • azimuth = 56.25 • mesh_tiles = 0 • textr_tiles = 1 • detail = 8 • bounding box: • xmax= 6.01, • ymax= 1.14, • zmax= 5.55, • xmin= -7.93, • ymin= -1.14, • zmin= -8.41

  43. FDM Maquette of Solar Arch

  44. Breckenridge Competition • 2nd place

  45. We Can Try Again … in L.A.

  46. … or in Washington D.C.

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

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

  49. Various “Scherk-Collins” Sculptures

  50. Fused Deposition Modeling (FDM)

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