CS 184, 5/11/2009 My Own Use of Computer Graphics Carlo H. Séquin University of California, Berkeley

Brent Collins “Hyperbolic Hexagon II”

Brent Collins: Stacked Saddles

“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 Discussion: What if … l we added more stories ? l or introduced a twist before closing the ring ?

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

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

Sculpture Generator 1, GUI

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

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. Profiled Slice through Heptoroid

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).

Various “Scherk-Collins” Sculptures

Rapid Prototyping with FDM

A Look Into the FDM Machine Galapagos 6 sculpture in progress 2 NOZZLES

Extending the Paradigm: Totem 3 Bronze Investment Cast

The Team: “Whirled White Web” (C. Séquin, S. Wagon, D. Schwalbe, B. Collins, S. Reinmuth) Snowsculpting Championships 2003

Removing lots of snow … Day 1

Day 2: Making a Torus

Day 3, pm: Carving Flanges, Holes

Day 4: Geometry Refinement “Devil’s Toothbrush”

Day 5, am: Surface Refinement

12:40 pm -- 42° F

12:41 pm -- 42° F

“WWW” Wins Silver Medal

Brent Collins’ Pax Mundi 1997: wood, 30”diam. 2006: Commission from H&R Block, Kansas City to make a 70”diameter version in bronze. My task: to define the master geometry. CAD tools played important role.

Emulation; Define Master Pattern u Use 4 copies. u Master to make a mold from. Alignment tab

Design of Two-Part Master u Alignment tabs for easy assembly

Subdivide into Two Master Segments

Joe Valasek’s CNC Milling Machine u Styrofoam milling machine

Machined Master Pattern #2

(Cut) Master  Silicone Rubber Mold

Mold  Several (4) Wax Copies

Spruing the Wax Parts for Casting

Ceramic Slurry Shell Around Wax Part

Shell Ready for Casting

Casting with Liquid Bronze

The Freed Bronze Cast

Assembling the Segments

The “Growing” Ribbon

Applying Patina

Front Door of the... H&R Block Building

The Final Destination

Steve Reinmuth Tightening the Bolts

Brent Collins Polishing Our Baby

Thanks to Steve Reinmuth... u for creating the beautiful patinas, u for the fabrication photographs.

Questions ?