YLEM, March 2003

1
YLEM, March 2003

• Art, Math, and Sculpture

Carlo Séquin, University of California,
Berkeley
2
I am a Designer
CCD Camera, Bell Labs, 1973 Soda Hall,
Berkeley, 1994
RISC chip, Berkeley, 1981 Octa-Gear,
Berkeley, 2000
3
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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Note
The computer becomesan amplifier /
acceleratorfor the creative process.
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Another Extension

• Allow different kinds of stretching

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Totem_2
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Cohesion

• Use more durable materials bronze !

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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 Creative 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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Via Globi 3 (Stone)
Wilmin Martono
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Via Globi 5 (Wood)
Wilmin Martono
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Viae Globi Family (Roads on a Sphere)
L2 L3 L4
L5
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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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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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Another Extension

• Using different cross sections for the sweep.

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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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The Poor Mans Opportunity Snow-Sculpting!Annua
l Championships in Breckenridge, CO
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Stan Wagon, Macalester College, St. Paul, MN

• Leader of Team USA Minnesota

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Helaman Ferguson

• Umbilic Torus Costa Surface

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Breckenridge, 1999

• Helaman Ferguson Invisible Handshake

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Robert Longhurst

• Moebius Band Enneper Surface

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Breckenridge, 2000

• Robert Longhurst
• Rhapsody in White
• 2nd Place

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Breckenridge,2001

• Robert Longhurst
• White Narcissus

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Batsheba Grossman

• Antipot Antichron

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Breckenridge, 2002

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

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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

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Collins Initial Suggestion Minimal Trefoil

• Stans Objection Too simple we know we can
  do this.No risk no fun !

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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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Tools, Templates
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Making a Torus

• Use of template Need for a sun shield

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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 Carving the Flanges, Holes
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End of Day 3 Proper Topology
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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
Ready for inspection, judging
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Official Team Photo
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1240 pm
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1241 pm
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1250 pm
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3 pm
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The Winners

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

sacred geometry very intricate very 21st
century !
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4 pm
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British Columbia Winter Comes
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Team Breckenridge (3rd Place)
Day 2 Day
3
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Team Breckenridge A Fishing Tail
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Mexico City Capilla Posa
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China The Love of Mother
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Quebec RèveOlution
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Manitoba Birth of a Nation
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USA New York 94 Hour Photo
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