CS39 Sculpture Generator I Carlo H Squin University

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

Brent Collins “Genesis” – Brent Collins at BRIDGES 2000

Brent Collins: Early Sculptures All photos by Phillip Geller

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”

Brent Collins: Stacked Saddles All photos by Phillip Geller

Leonardo -- Special Issue On Knot-Spanning Surfaces: Illustrated Essay on Topological Art With an Artist’s Statement by Brent Collins George K. Francis with Brent Collins

The Math in Collins’ Sculptures u Collins works with rulers and compasses; any math in his early work is intuitive. u He is inspired by nature, e. g. soap films (= minimal area surfaces). u Prof. George Francis: “Connection to math. Minimal Surfaces!”

Scherk’s 2 nd Minimal Surface (1834) u The central part of this is a “Scherk Tower. ”

Generalizing the “Scherk Tower” Normal “biped” saddles “Scherk Tower” Generalization to higher-order saddles (“Monkey saddle”)

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

Brent Collins: Hyperbolic Hexagon (1993) Six balanced saddles in a circular ring. Inspired by the shape of a soap film suspended in a wire frame. = Curved “Scherk Tower” (with 6 stories).

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

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. u A big investment of effort !

Collins’ Fabrication Process Layered laminated main shape Detailed pattern cut from main shape Example: “Vox Solis”

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 ?

“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.

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

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

A Plethora of Shapes

Edge Treatment square, flat cut semi-circular bulging out

Embellishment of Basic Shape color texture background

Sculpture Generator 1, GUI

Some of the Parameters in “SG 1”

Generated Scherk-Collins Shapes

Base Geometry: One “Scherk Story” u Taylored hyperbolas, hugging a circle Hyperbolic Slices Triangle Strips Pre-computed -- then warped into toroid

Shapes from Sculpture Generator 1

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

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

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

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

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 = 8 u detail = 12

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

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)

“Hyperbolic Hexagon II” (wood) Brent Collins 1997

Profiled Slice through “Heptoroid” u One thick slice thru sculpture, from which Brent can cut boards and assemble a rough shape. u Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board.

Emergence of the Heptoroid (1) Assembly of the precut boards

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

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

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

Fused Deposition Modeling (FDM)

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

“Scherk-Collins” Sculptures (FDM)

“Cohesion” (SIGGRAPH’ 2003 Art Gallery) Cast by Reinmuth Bronze Studio, Eugene, OR

Hyper-Sculpture: Family of 12 Trefoils W=2 W=1 B=2 B=3 B=4

Going more than once around the loop W = 380° W = 560° W = 720° … results in an interwoven structure.

11 Stories, Monkey-Saddles, W=2: cross–eye stereo picture

9 -story Intertwined Double Toroid Bronze investment casting from wax original made on 3 D Systems’ “Thermojet”

Extension of Concept Allow different kinds of “stretching” …

Extending the Paradigm: Totem 3 Bronze Investment Cast

Stepwise Expansion of Horizon u Playing with many different shapes and u experimenting at the limit of the domain of the sculpture generator, u stimulates new ideas for alternative shapes and generating paradigms. Swiss Mountains

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

12 -Story Scherk-Collins Toroid 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

David Lynn, Nova Blue Studio Arts u http: //sites. google. com/site/novabluestudioarts/

Master Module for “Millennium Arch”

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

Two Times Three Modules

Merging the Two Half-Circles

Brent Collins and David Lynn

“Millennium” Arch by Night

Millennium Man Vitruvian Man by Leonardo

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

Yet Another Medium: Stone Progress picture from Dingli Stone Carving Art Co. , SE China

Spring, 2012

QUESTIONS ? ?