usf -- may 2004 esthetic engineering or art and math in snow carlo h. séquin university of...
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USF -- May 2004USF -- May 2004
Esthetic Engineeringor
Art and Math in Snow
Carlo H. Séquin
University of California, Berkeley
I am a Designer …I am a Designer …
CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994
RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000
Focus of TalkFocus of Talk
The role of the computer in:
aesthetic optimization,
the creative process.
Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
““Hyperbolic Hexagon” by B. CollinsHyperbolic Hexagon” by B. Collins
6 saddles in a ring
6 holes passing through symmetry plane at ±45º
= “wound up” 6-story Scherk tower
Discussion: What if … we added more stories ?
or introduced a twist before closing the ring ?
Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
Collins’ Fabrication ProcessCollins’ Fabrication Process
Example: “Vox Solis”
Layered laminated main shapeWood master pattern
for sculpture
Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”
50% 10%23%30%
45% 5%20%27%
35% 2%15%25%
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.
Profiled Slice through “Heptoroid”Profiled Slice through “Heptoroid”
Hyper-Sculpture: “Family of 12 Trefoils”Hyper-Sculpture: “Family of 12 Trefoils”
W=2
W=1
B=1 B=2 B=3 B=4
Stan Wagon, Stan Wagon, Macalester College, St. Paul, MNMacalester College, St. Paul, MN
Leader of Team “USA – Minnesota”
Breckenridge, Breckenridge, 20022002
Bathsheba Grossman:
“A Twist in Time”
Honorable Mention
“Expressive Impact”
Snow-Sculpting, Breckenridge, 2003Snow-Sculpting, Breckenridge, 2003
Brent Collins and Carlo Séquin
are invited to join the team
and to provide a design.
Other Team Members:
Stan Wagon, Dan Schwalbe, Steve Reinmuth
(= Team “Minnesota”)
Collins’ Initial Suggestion: Minimal TrefoilCollins’ Initial Suggestion: Minimal Trefoil
Stan’s Objection: “Too simple …– we know we can do this.
No risk – no fun !”
Name, StoryName, Story
“Snow Flower, Winter Rose, Winter Whirl, Wild White Whirl, Webbed Wild Whirl, Whirled Wild Web …”
finally the perfect homonym:
“Whirled White Web”
Like this global network, the ridges of our sculpture span the outer perimeters of the whole “globe,” and at the same time come close together in the central hole. It illustrates how the WWW can link together people from all over the world.
Plan of AttackPlan of Attack
Cut away 2 large triangular prisms;
Hang plastic template (12’x18’) over slab;
Mark projections of holes, flanges;
Drill, carve, refine …(using maquette for reference)
Try this first on a smaller practice block!
The WinnersThe Winners
1st: Canada – B.C., 2nd: USA – Minnesota, 3rd: USA – Breckenridge
“… sacred geometry … very intricate … very 21st century !”
What Are We Going To Do For 2004 ?What Are We Going To Do For 2004 ?
“Turning a Snowball Inside Out”
Sphere EversionSphere Eversion
~ 1960, the blind mathematician B. Morin, (born 1931) conceived of a way how a sphere can be turned inside-out:
Surface may pass through itself,
but no ripping, puncturing, creasing allowed,e.g., this is not an acceptable solution:
PINCH
Sphere Eversion ProcessSphere Eversion Process But there are more contorted paths
that can achieve the desired goal.
Bernard Morin figured out one such path.
Charles Pugh made models from chicken wire.
Nelson Max made a first computer simulation.
Morin SurfaceMorin Surface
Another view of the half-way point,
from: John Sullivan: “The Optiverse”
(surface of minimum bending energy).
Simplest ModelSimplest Model
Partial cardboard model based on the simplest polyhedral sphere (= cuboctahedron) eversion.
Gridded Models for TransparencyGridded Models for Transparency
3D-Print from Zcorp SLIDE virtual model
Restructured Morin surface to fit block size: (10’ x 10’ x 12’)
Shape Adaption for Snow SculptureShape Adaption for Snow Sculpture
Make Surface “Transparent”Make Surface “Transparent”
Realize surface as a grid.
Draw a mesh of smooth lines onto the surface …
Conclusions (1)Conclusions (1)
Interactive computer graphics is a novel (to artists) medium that can play an important role -- even for traditional artists.
Virtual Prototyping can save time and can tackle sculptures of a complexitythat manual techniques could not conquer.