OZONE Meeting, SIGGRAPH 2003

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OZONE Meeting, SIGGRAPH 2003

• mathematics art

Carlo H. Séquin U.C. Berkeley
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I am a Designer, Engineer
CCD Camera, Bell Labs, 1973 Soda Hall,
Berkeley, 1994
RISC chip, Berkeley, 1981 Octa-Gear,
Berkeley, 2000
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Artistic Geometry

• The role of the computer in
• the creative process,
• aesthetic optimization.
• Collaboration with

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Virtual Model Making for Mathematically Inspired
SculpturesArt-Math'97, SUNY, Albany, 1997.
Hyperbolic Hexagon II
B. Collins
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Closing the Loop
straight or twisted
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Brent Collins Prototyping Process
Mockup for the "Saddle Trefoil"
Armature for the "Hyperbolic Heptagon"
Time-consuming ! (1-3 weeks)
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Sculpture Generator I, GUI
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V-art
VirtualGlassScherkTowerwith MonkeySaddles(R
adiance 40 hours) Jane Yen
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Art, Math, and ComputersBRIDGES98, Winfield KS,
July 29, 1998
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Virtual Prototyping of Geom. Sculptures
Computers Sculpture, Chicago,1998.

• Solar Arch (with Brent Collins)

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Collins Fabrication Process
Wood master patternfor sculpture
Layered laminated main shape
Example Vox Solis
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Slices through Minimal Trefoil
50
10
23
30
45
5
20
27
35
2
15
25
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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.

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Emergence of the Heptoroid (1)
Assembly of the precut boards
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Emergence of the Heptoroid (2)
Forming a continuous smooth edge
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Emergence of the Heptoroid (3)
Smoothing the whole surface
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The Finished Heptoroid

• at Fermi Lab Art Gallery (1998).

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Various Scherk-Collins Sculptures
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Hyper-Sculpture Family of 12 Trefoils
W2
W1
B1 B2 B3
B4
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Computer-Augmented InspirationISAMA 99, San
Sebastian, 1999.

• Doubly-wound Scherk-Collins Toroid

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Cohesion

• SIGGRAPH2003 Art Gallery

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Analogies from 2D to 3D Exercises in
Disciplined Creativity BRIDGES, Winfield KS,
1999.

• 3D Yin-Yang

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Turning Math Models into Sculptures MOSAIC 2000,
Seattle, 2000.

• Triply Twisted Figure-8 Klein Bottle

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Symmetries on the SphereISIS Symmetry Congress,
Sydney, 2001.

• 60 Butterflies

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Viae Globi - Pathways on a Sphere Mathematics
and Design, Geelong, 2001.
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Sculpture Design Virtual Systems
Multimedia,Berkeley, 2001

• Galapagos (version 5), inspired by Brent Collins

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3D Visualization Models of the Regular Polytopes
in ? 4 DBRIDGES_5, Towson MD, 2002.

• 4D 120-Cell

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Volutions EvolutionMeeting Alhambra, Granada,
2003
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Modular Minimal Surfaces of Increasing Genus,
Embedded in a Cube

• Volution_0 Volution_5

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Whirled White Web Art Math in
SnowSnow-sculpting, Breckenridge, CO, 2003
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The Winners

• 1st Canada B.C., 2nd USA
  Minnesota, 3rd USA Breckenridge

sacred geometry very intricate very 21st
century !