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Connecting Computers and Creativity: Art, Math, and Sculpture

Explore the intersection of art, math, and sculpture through computer-aided design. Discover the beauty of abstract geometric art and the intricate designs of Brent Collins. Experience the process of prototyping and fabrication, and learn how technology is revolutionizing the world of sculpture. Join us on this creative journey where computers and art collide.

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Connecting Computers and Creativity: Art, Math, and Sculpture

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  1. USF -- February 2001 Art, Math, and Sculpture Connecting Computers and Creativity Carlo H. Séquin University of California, Berkeley

  2. My Professional Focus Computer-Aided Design • Design useful and beautiful objectswith the help of computers. • Develop (interactive) computer programsto make these tasks easier.

  3. Computer-Aided Design I : Integrated Circuits: “RISC I” chip (1981)

  4. Computer-Aided Design II :Mathematical Models “Granny Knot” Lattice Berkeley UniGrafix (1982)

  5. Computer-Aided Design III : Buildings Soda Hall, CS Dept. Berkeley (1992)

  6. Computer-Aided Design IV : Mechanical Parts Octahedral Gear Design (1985) Realization (FDM) (2000)

  7. Computer-Aided Design V : Abstract Sculpture (virtual) (Since 1995)

  8. Computer-Aided Design V : Abstract Sculpture (virtual) Scherk-Collins Tower

  9. Computer-Aided Design V : Abstract Sculpture (virtual) Doubly-looped Scherk-Collins saddle-chain

  10. Computer-Aided Design V : Abstract Sculpture (real) “Bonds of Friendship”(2001) Fabricated by: Fused Deposition Modeling Currently in S.F.:at Gallery 650,Delancy/Brannan

  11. 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, ...

  12. 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

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

  14. My Fascination with... Brent 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”

  15. Brent Collins: Stacked Saddles

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

  17. “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 ?

  18. Closing the Loop straight or twisted

  19. 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.

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

  21. 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 !

  22. Collins’ Fabrication Process Lamination process to make an overall shape that withincontains the final sculpture. Example: “Vox Solis”

  23. “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. ==> VIDEO

  24. Scherk-Collins Sculptures

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

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

  27. A Plethora of Shapes

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

  29. Embellishment of Basic Shape color texture background

  30. === VIDEO === • 6 min

  31. A Simple Scherk-Collins Toroid • branches = 2 • storeys = 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

  32. Also a Scherk-Collins Toroid • branches = 1 • storeys = 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

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

  34. 1-story Scherk Tower • branches = 5 • storeys = 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

  35. 180º Arch = Half a Scherk Toroid • branches = 8 • storeys = 1 • height = 5 • flange = 1.00 • thickness = 0.06 • rim_bulge = 1.25 • warp = 180 • twist = 0 • azimuth = 0 • textr_tiles = e • detail = 12

  36. 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. > Make closed-form hyperbolic approximation.

  37. Hyperbolic Cross Sections

  38. Base Geometry: One Scherk Story • Hyperbolic Slices ==> Triangle Strips • precomputed -- then warped into toroid

  39. The Basic Saddle Element with surface normals

  40. Hyperbolic Contour Lines On a straight tower and on a ring

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

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

  43. 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.

  44. 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)

  45. “Hyperbolic Hexagon II” (wood)

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

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

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

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

  50. 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

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