CHS UCB CS39 Sculpture Generator I Carlo H

CHS UCB CS_39 Sculpture Generator I Carlo H. Séquin University of California, Berkeley In Collaboration with Brent Collins Gower, Missouri

CHS UCB Brent Collins “Genesis” – Brent Collins at BRIDGES 2000

CHS UCB 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

CHS UCB Brent Collins: Early Sculptures All photos by Phillip Geller

CHS UCB Collins’ Abstract Geometric Art u Beautiful symmetries u Graceful balance of the saddle surfaces u Superb craftsmanship u Intriguing u What run of the edges type of knot is formed ? u Mystery: one-sided or two-sided ? ==> Focus on “Chains of Saddles”

CHS UCB Brent Collins: Stacked Saddles

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

CHS UCB “Hyperbolic Hexagon” by B. Collins u 6 saddles in a ring u 6 holes passing through symmetry plane at ± 45º u “wound up” 6 -story Scherk tower u What would happen, l if we added more stories ? l or introduced a twist before closing the ring ?

CHS UCB Closing the Loop straight or twisted

CHS UCB Collins - Séquin Collaboration u Discuss ideas on the phone u Exchange u Vary sketches the topological parameters u But how do you know whether it is beautiful ? Need visual feedback. u Making models from paper strips is not good enough. u. A key problem is making the sculpture look good from all sides !

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

CHS UCB Collins’ Fabrication Process Building the final sculpture (2 -3 months): u Take measurements from mock-up model, transfer parallel contours to 1” boards. u Roughly precut boards, leaving registration marks and contiguous pillars for gluing boards together. u Stack and glue together precut boards, remove auxiliary struts. u Fine-tune overall shape, sand polish the surface. A big investment of effort !

CHS UCB Collins’ Fabrication Process Layered laminated main shape Wood master pattern for sculpture Example: “Vox Solis”

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

CHS UCB “Sculpture Generator I” Prototyping tool for Scherk-Collins Saddle-Chains. u Slider control for this one shape family, u Control u Main of about 12 parameters. goal: Speed for interactive editing. u Geometry u 10, 000 part is about 5, 000 lines of C; lines for display & user interface.

CHS UCB Generated Scherk-Collins Shapes

CHS UCB The Basic Element Scherk’s 2 nd minimal surface 3 -story tower, trimmed, thickened 180 degrees of twist added

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

CHS UCB A Plethora of Shapes

CHS UCB Edge Treatment square, flat cut semi-circular bulging out

CHS UCB Embellishment of Basic Shape color texture background

CHS UCB Sculpture Generator, GUI

CHS UCB Some of the Parameters in “SC 1”

CHS UCB Main Goal in Sculpture Generator I Real-time Interactive Speed ! u Can’t afford surface optimization to obtain true minimal surfaces; u also, this would be aesthetically too limited. Use closed-form hyperbolic approximation.

CHS UCB Base Geometry: One Scherk Story u Hyperbolic Slices ==> Triangle Strips u Pre-computed -- then warped into toroid

CHS UCB A Simple Scherk-Collins Toroid Parameters: (genome) u branches = 2 u stories = 1 u height = 5. 00 u flange = 1. 00 u thickness = 0. 10 u rim_bulge = 1. 00 u warp = 360. 00 u twist = 90 u azimuth = 90 u textr_tiles = 3 u detail = 8

CHS UCB Also a Scherk-Collins Toroid u branches = 1 u stories = 5 u height = 1. 00 u flange = 1. 00 u thickness = 0. 04 u rim_bulge = 1. 01 u warp = 360 u twist = 900 u azimuth = 90 u textr_tiles = 1 u detail = 20

CHS UCB A Scherk Tower (on its side) u branches = 7 u stories = 3 u height = 0. 2 u flange = 1. 00 u thickness = 0. 04 u rim_bulge = 0 u warp = 0 u twist = 0 u azimuth = 0 u textr_tiles = 2 u detail = 6

CHS UCB 1 -story Scherk Tower u branches = 5 u stories = 1 u height = 1. 35 u flange = 1. 00 u thickness = 0. 04 u rim_bulge = 0 u warp = 58. 0 u twist = 37. 5 u azimuth = 0 u textr_tiles = 8 u detail = 6

CHS UCB 180º Arch = Half a Scherk Toroid u branches = 8 u stories = 1 u height = 5 u flange = 1. 00 u thickness = 0. 06 u rim_bulge = 1. 25 u warp = 180 u twist = 0 u azimuth = 0 u textr_tiles = e u detail = 12

CHS UCB How to Obtain a Real Sculpture ? u Prepare a set of cross-sectional blue prints at equally spaced height intervals, corresponding to the board thickness that Brent is using for the construction.

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

CHS UCB Profiled Slice through the Sculpture u One thick slice thru “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, 3/4 of one board.

CHS UCB 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)

CHS UCB “Hyperbolic Hexagon II” (wood) Brent Collins

CHS UCB Heptoroid ( from Sculpture Generator I ) Cross-eye stereo pair

CHS UCB Emergence of the “Heptoroid” (1) Assembly of the precut boards

CHS UCB Emergence of the “Heptoroid” (2) Forming a continuous smooth edge

CHS UCB Emergence of the “Heptoroid” (3) Smoothing the whole surface

CHS UCB “Heptoroid”

CHS UCB Advantages of CAD of Sculptures u Exploration u Instant visualization of results u Eliminate u Create u More need for prototyping virtual reality pictures u Making u Better of a larger domain more complex structures optimization of chosen form precise implementation u Rapid prototyping of maquettes

CHS UCB Sculpture Design u u u 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 u u u u bounding box: xmax= 6. 01, ymax= 1. 14, zmax= 5. 55, xmin= -7. 93, ymin= -1. 14, zmin= -8. 41

CHS UCB FDM Maquette of Solar Arch

CHS UCB Breckenridge Competition u 2 nd place

CHS UCB V-art Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

CHS UCB Fused Deposition Modeling (FDM)

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

CHS UCB Various “Scherk-Collins” Sculptures

CHS UCB Note: The computer becomes an amplifier / accelerator for the creative process.

CHS UCB Questions ? THE END