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Genesis: Abstract Geometric Art Sculpture Generator

Explore the beautiful symmetries and graceful balance of saddle surfaces in Brent Collins' early sculptures. Witness intriguing edge runs and mysteries of one-sided or two-sided knots in his stunning creations. Delve into the world of topological art with Brent Collins and George K. Francis. Discover the intricate details and superb craftsmanship of Scherk towers, hyperbolic shapes, and the Scherk-Collins toroids. Experience the prototyping process and fabrication techniques behind these unique sculptures. Immerse yourself in the artistry of Collins' sculptural designs, from simple toroids to complex monkey saddles and heptagons. Witness the emergence of the Heptoroid and the Cohesion sculpture, extending the paradigm of geometric art. Join the journey through sculptural transformations and the creation of masterpieces like the Millennium Arch.

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Genesis: Abstract Geometric Art Sculpture Generator

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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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