CONTACT, March' 2123, 2003

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CONTACT, March. 21-23, 2003

• Art, Math, Computers,
• and Creativity

Carlo Séquin, University of California,
Berkeley
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I am a Designer
CCD Camera, Bell Labs, 1973 Soda Hall,
Berkeley, 1994
RISC chip, Berkeley, 1981 Octa-Gear,
Berkeley, 2000
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Focus of Talk

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

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Brent Collins
Hyperbolic Hexagon II
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Leonardo -- Special Issue
On Knot-Spanning Surfaces An Illustrated Essay
on Topological Art With an Artists Statement by
Brent Collins
George K. Francis with Brent Collins
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Brent Collins Stacked Saddles
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Scherks 2nd Minimal Surface
Normal biped saddles
Generalization to higher-order saddles(monkey
saddle)
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Hyperbolic Hexagon by B. Collins

• 6 saddles in a ring
• 6 holes passing through symmetry plane at 45º
• wound up 6-story
  Scherk tower
• What would happen,
• if we added more stories ?
• or introduced a twist before closing the ring ?

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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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A Simple Scherk-Collins Toroid

• Parameters(genome)
• branches 2
• stories 1
• height 5.00
• flange 1.00
• thickness 0.10
• rim_bulge 1.00
• warp 360.00
• twist 90
• azimuth 90
• textr_tiles 3
• detail 8

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A Scherk Tower (on its side)

• branches 7
• stories 3
• height 0.2
• flange 1.00
• thickness 0.04
• rim_bulge 0
• warp 0
• twist 0
• azimuth 0
• textr_tiles 2
• detail 6

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1-story Scherk Tower

• branches 5
• stories 1
• height 1.35
• flange 1.00
• thickness 0.04
• rim_bulge 0
• warp 58.0
• twist 37.5
• azimuth 0
• textr_tiles 8
• detail 6

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180º Arch Half a Scherk Toroid

• branches 8
• stories 1
• height 5
• flange 1.00
• thickness 0.06
• rim_bulge 1.25
• warp 180
• twist 0
• azimuth 0
• textr_tiles e
• detail 12

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V-art
VirtualGlassScherkTowerwith MonkeySaddles(R
adiance 40 hours) Jane Yen
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How to Obtain a Real Sculpture ?

• Prepare a set of cross-sectional blue printsat
  equally spaced height intervals,corresponding
  to the board thickness that Collins is using
  for the construction.

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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 the Sculpture

• One thick slicethru Heptoroidfrom 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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SFF (Solid Free-form Fabrication)
Monkey- Saddle Cinquefoil
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Fused Deposition Modeling (FDM)
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Zooming into the FDM Machine
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Various Scherk-Collins Sculptures
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Part II
Developing Parameterized Sculpture
Families (Extending a Paradigm)
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Family of Symmetrical Trefoils
W2
W1
B1 B2 B3
B4
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Close-up of Some Trefoils
B1 B2
B3
Varying the number of branches, the order of the
saddles.
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Higher-order Trefoils (4th order saddles)
W1 (Warp)
W2 ?
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Exploring New Ideas W2

• Going around the loop twice ...

resulting in an interwoven structure.
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9-story Intertwined Double Toroid
Bronze investment casting from wax original
made on 3D SystemsThermojet
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Stepwise Expansion of Horizon

• Playing with many different shapes and
• experimenting at the limit of the domain of the
  sculpture generator,
• stimulates new ideas for alternative shapes and
  generating paradigms.

Swiss Mountains
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Note
The computer becomesan amplifier /
acceleratorfor the creative process.
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Séquins Minimal Saddle Trefoil

• bronze cast, gold plated

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Minimal Trefoils -- cast and finished by Steve
Reinmuth
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Steve Reinmuth
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Brent Collins Pax Mundi
A new inspiration
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Keeping up with Brent ...

• Sculpture Generator I can only do warped Scherk
  towers,not able to describe a shape like Pax
  Mundi.
• Need a more general approach !
• Use the SLIDE modeling environment(developed at
  U.C. Berkeley by J. Smith)to capture the
  paradigm of such a sculpturein a procedural
  form.
• Express it as a computer program
• Insert parameters to change salient aspects /
  features of the sculpture
• First Need to understand what is going on ?

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Part III
The Least Understood Step (Capturing a
Paradigm)
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Sculptures by Naum Gabo

• Pathway on a sphere
• Edge of surface is like seam of tennis ball
• ? 2-period Gabo curve.

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2-period Gabo Curve

• Approximation with quartic B-splinewith 8
  control points per period,but only 3 DOF are
  used.

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4-period Gabo Curve

• Same construction as for a 2-period curve

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Pax Mundi Revisited

• Can be seen as Amplitude modulated, 4-period
  Gabo curve

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SLIDE-UI for Pax Mundi Shapes
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Viae Globi Family (Roads on a Sphere)
L2 L3 L4
L5
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Via Globi 3 (Stone)
Wilmin Martono
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Via Globi 5 (Wood)
Wilmin Martono
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Extending the Paradigm

• Try to Expand the Sculpture Family
• Aim for more highly convoluted paths,
• maintain high degree of symmetry.
• Need a better tool to draw on sphere

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Circle Splines on the Sphere

• Examples from Jane Yens Editor Program
• ( another piece of scaffolding)

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Via Globi -- Virtual Design
Wilmin Martono
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Maloja (FDM part)

• A rather winding Swiss mountain pass road in the
  upper Engadin.

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Stelvio

• An even more convoluted alpine pass in Italy.

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Altamont

• Celebrating American multi-lane highways.

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Lombard

• A very famous crooked street in San Francisco
• Note that I switched to a flat ribbon.

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Part IV

• How to make a really large sculpture ?
• Scaling-up problems
• Production problems
• Engineering problems
• Installation problems
• Maintenance problems
• Insurance problems
• ? Need a Commission !

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International Snow-sculpting Championships,
Breckenridge, 2003

• Brent Collins and Carlo Séquin
• are invited to provide a design
• for Team USA Minnesota
• Other Team Members
• Stan Wagon, Dan Schwalbe, Steve Reinmuth

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Stan Wagon, Macalester College, St. Paul, MN

• Leader of Team USA Minnesota

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Breckenridge, 1999

• Helaman Ferguson Invisible Handshake

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Breckenridge, 2000

• Robert Longhurst
• Rhapsody in White
• 2nd Place

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Breckenridge, 2002

• Bathsheba Grossman
• A Twist in Time
• Honorable Mention
• Expressive Impact

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Monkey Saddle Trefoil

• from Sculpture Generator I

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Maquettes

• 3D-Print FDM

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Name, 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.

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ACCEPTED !

• Now how do we get this design into a
  10x10x12 block of snow ?

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Construction Drawings

• Top View Side View
  Axial View

Remove these prisms first!
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Day 1
Removing lots of snow
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Day 1 The Monolith

• Cut away prisms

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Day 2 Making a Torus

• Mark center, circles
  Bulls-eye !

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Chipping away
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End of Day 2

• The Torus

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Day 3, am Drawing Flanges
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Day 3, pm Flanges, Holes
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Day 4 Geometry Refinement
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End of Day 4 Desired Geometry
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Day 5, am Surface Refinement
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House Cleaning
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Whirled White Web
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Official Team Photo
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Part V

• DISCUSSION
• How much of this process could have been done
  by a computer alone
• ?

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The Starting Point

• In many instances my work started from one of
  Brent Collins sculptures.
• Where did Brent get his ideas from ?(? Forms
  found in nature )
• How soon will we able to say
• Computer, make me something like that !
• Make me a few more in the same style !
• (1) Capturing a Paradigm.
• (2) Extending a Paradigm.

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Capturing a Paradigm

• What made me think of Naum Gabo, when I tried to
  understand Collins Pax Mundi?
• How did I know that it was a good match ?
• ? I needed to understand
• It is a sweep,
• Path lies on a sphere and
• has some regularity to its undulations

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Extending a Paradigm

• A paradigm expressed, so that a computer can
  deal with it, is typically an algorithmand
  this program will have some variables, some of
  which can be used as parameters.
• It takes some informed judgment to decide
  which ones will actually work as parameters,
  and what their useful value range should be.
• Also, when is it appropriate / productive to
  extend the range of a parameter?

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Is It Art ?

• Can it be art, -- if it is created by a computer
  ?
• Who judges which parameters to pick ?-- what are
  successful combinations ?
• How many cultures (today in the future) would
  recognize these shapes as being something
  special ?

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QUESTIONS ?DISCUSSION ?