Embed Size (px)
Citation preview
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.
Brent CollinsBrent Collins
“Hyperbolic Hexagon II”
Brent Collins: Stacked SaddlesBrent Collins: Stacked Saddles
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 ?
Closing the LoopClosing the Loop
straight
or
twisted
Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
““Sculpture Generator I”, GUI Sculpture Generator I”, GUI
V-artV-art
VirtualGlassScherkTowerwithMonkeySaddles
(Radiance 40 hours)
Jane Yen
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”
Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)
Assembly of the precut boards
Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)
Smoothing the whole surface
The Finished The Finished “Heptoroid”“Heptoroid”
at Fermi Lab Art Gallery (1998).
Various “Scherk-Collins” SculpturesVarious “Scherk-Collins” Sculptures
Fused Deposition Modeling (FDM)Fused Deposition Modeling (FDM)
Zooming into the FDM MachineZooming into the FDM Machine
Hyper-Sculpture: “Family of 12 Trefoils”Hyper-Sculpture: “Family of 12 Trefoils”
W=2
W=1
B=1 B=2 B=3 B=4
““Cohesion”Cohesion”
SIGGRAPH’2003 Art Gallery
Stan Wagon, Stan Wagon, Macalester College, St. Paul, MNMacalester College, St. Paul, MN
Leader of Team “USA – Minnesota”
Stan WagonStan Wagon
Skier – Mountaineer – Snow Sculptor
Dan SchwalbeDan Schwalbe
Software Engineer – Snow Sculptor
Helaman FergusonHelaman Ferguson
Umbilic Torus Costa Surface
Breckenridge, 1999Breckenridge, 1999
Helaman Ferguson: “Invisible Handshake”
Breckenridge, CO, 1999Breckenridge, CO, 1999
Helaman Ferguson: “Invisible Handshake”
Robert LonghurstRobert Longhurst
Moebius Band Enneper Surface
Breckenridge, Breckenridge, 20002000
Robert Longhurst:
“Rhapsody in White”
2nd Place
Breckenridge,Breckenridge,20012001
Robert Longhurst:
“White Narcissus”
Batsheba GrossmanBatsheba Grossman
Antipot Antichron
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”)
Steve ReinmuthSteve Reinmuth
Collins’ Initial Suggestion: Minimal TrefoilCollins’ Initial Suggestion: Minimal Trefoil
Stan’s Objection: “Too simple …– we know we can do this.
No risk – no fun !”
Monkey Saddle TrefoilMonkey Saddle Trefoil
from Sculpture Generator I
MaquettesMaquettes
3D-Print FDM
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.
ACCEPTED !ACCEPTED !
Now – how do we get this design into a 10’x10’x12’ block of snow ?
Construction DrawingsConstruction Drawings
Top View Side View Axial View
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!
1:1 Templates1:1 Templates
Magnified from computer prints with the classical grid method
Practice Block (1)Practice Block (1)
Template transfer Reference holes
Practice Block (2)Practice Block (2)
Free-hand carving Irregular ribs
Practice Block (3)Practice Block (3)
Need new plan !
Removing lots of snow …
Day 1Day 1
Day 1: The “Monolith”Day 1: The “Monolith”
Cut away prisms …
Day 2: Making a TorusDay 2: Making a Torus
Mark center, circles … Bull’s-eye !
Chipping away …Chipping away …
Tools, TemplatesTools, Templates
Making a TorusMaking a Torus
Use of template Need for a sun shield
End of Day 2End of Day 2
The Torus
Day 3, am: Drawing FlangesDay 3, am: Drawing Flanges
Day 3, pm: Flanges, Holes Day 3, pm: Flanges, Holes
End of Day 3: Proper TopologyEnd of Day 3: Proper Topology
Day 4: Geometry RefinementDay 4: Geometry Refinement
End of Day 4: Desired GeometryEnd of Day 4: Desired Geometry
Day 5, am: Surface RefinementDay 5, am: Surface Refinement
““House Cleaning”House Cleaning”
““Whirled White Web”Whirled White Web”
Official Team PhotoOfficial Team Photo
12:40 pm -- 4212:40 pm -- 42° F° F
12:41 pm -- 4212:41 pm -- 42° F° F
12:40:0112:40:01
Photo:StRomain
12:50 pm12:50 pm
3 pm3 pm
The WinnersThe Winners
1st: Canada – B.C., 2nd: USA – Minnesota, 3rd: USA – Breckenridge
“… sacred geometry … very intricate … very 21st century !”
““WWW” Wins Silver MedalWWW” Wins Silver Medal
British Columbia: “Winter Comes” British Columbia: “Winter Comes”
Day 2 Day 3
Breckenridge: “A Fishing Tail”Breckenridge: “A Fishing Tail”
Mexico City: “Capilla Posa”Mexico City: “Capilla Posa”
China: “The Love of Mother”China: “The Love of Mother”
Quebec: “RQuebec: “Rèève’Olution”ve’Olution”
Manitoba: “Birth of a Nation”Manitoba: “Birth of a Nation”
USA – New York: “94 Hour Photo”USA – New York: “94 Hour Photo”
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 …
The Final ModelThe Final Model
Day1Day1
Day2Day2
Day3Day3
Day 4Day 4
Day4Day4
Day5Day5
Honorable Mention:
Most AmbitiousDesign
““Paradigm Shift” (British Columbia)Paradigm Shift” (British Columbia)
““Year of the Dragon” USA - TennesseeYear of the Dragon” USA - Tennessee
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.
Conclusions (2)Conclusions (2)
The computer is not only a great visualization and prototyping tool,
It also is a generator for new ideas and
an amplifier for an artist’s inspiration.
