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CS 284

CS 284. 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. Brent Collins: Early Sculptures. All photos by Phillip Geller. Collins’ Abstract Geometric Art.

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CS 284

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  1. CS 284 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. Brent Collins: Early Sculptures All photos by Phillip Geller

  4. 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 ?

  5. Leonardo -- Special Issue On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art 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) “Scherk Tower”

  8. 2nd and 3rd Order “Scherk Towers”

  9. “Hyperbolic Hexagon” by B. Collins • 6 saddles in a ring • = “wound up” 6-story Scherk tower • 6 holes passing through symmetry plane at ±45º • Discussion: What if … • we added more stories ? • or introduced a twist before closing the ring ?

  10. Closing the Loop straight or twisted “Scherk Tower” “Scherk-Collins Toroids”

  11. “Hyperbolic Heptagon” - Paper Skeleton

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

  13. Sculpture Generator 1, GUI

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

  15. Some of the Parameters in “SC1”

  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. 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

  23. 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

  24. 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

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

  26. 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.

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

  28. “Vox Solis” by Brent Collins

  29. 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)

  30. Brent Collins “Hyperbolic Hexagon II”

  31. Inauguration Sutardja Dai Hall 2/27/09

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

  33. Profiled Slice through “Heptoroid” • One thick slicethru sculpture,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. Emergence of the Heptoroid (1) Assembly of the precut boards

  35. Emergence of the Heptoroid (2) Forming a continuous smooth edge

  36. Emergence of the Heptoroid (3) Smoothing the whole surface

  37. The Finished Heptoroid • at Fermi Lab Art Gallery (1998).

  38. Extending the Paradigm: “Totem 3” Bronze Investment Cast

  39. “Cohesion” SIGGRAPH’2003 Art Gallery

  40. 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

  41. Two Modules Assembled

  42. Master Module for “Millennium Arch”

  43. Fabrication of “Millennium Arch” The mold for the key module A polyester segment cast

  44. Two Times Three Modules

  45. Merging the Two Half-Circles

  46. Brent Collins with “Millennium Arch”

  47. “Millennium” Arch by Night

  48. Sculpture Generator #2

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