1 / 50

Sculpture Generator: Crafting Geometric Art with Superb Symmetries

Discover the fascinating world of Brent Collins' abstract geometric sculptures, including the graceful balance of saddle surfaces and the mystery of their one-sided or two-sided nature. Explore his collaboration with Séquin, prototype processes, and the intricate fabrication methods behind these masterpieces. Delve into the innovative Sculpture Generator I tool, allowing for real-time interactive editing and customization of Scherk-Collins shapes with various parameters. Unravel the artistry behind creating beautiful sculptures that captivate from all angles.

riggsk
Download Presentation

Sculpture Generator: Crafting Geometric Art with Superb Symmetries

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS_39 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. V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen

  46. Fused Deposition Modeling (FDM)

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

  48. Various “Scherk-Collins” Sculptures

  49. Note: The computer becomesan amplifier / acceleratorfor the creative process.

  50. Questions ? THE END

More Related