Princeton, March 2003

1
Princeton, 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.

4
Background

• My love for geometry and abstract
  sculptureemerged long long before I learned to
  play with computers.
• Thanks to Alexander Calder, Naum Gabo,Max
  Bill, M.C. Escher, Frank Smullin, ...

5
Outline

• Parameterized Shape Generators
• Sculpture Families (Group Technology)
• Creativity Capturing a Paradigm
• LARGE Sculptures (in Snow!)
• CAD Tools for Conceptual Design

6
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
7
Brent Collins
Hyperbolic Hexagon II
8
Scherks 2nd Minimal Surface
Normal biped saddles
Generalization to higher-order saddles(monkey
saddle)
9
Brent Collins Stacked Saddles
10
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 ?

11
Closing the Loop
straight or twisted
12
Brent Collins Prototyping Process
Mockup for the "Saddle Trefoil"
Armature for the "Hyperbolic Heptagon"
Time-consuming ! (1-3 weeks)
13
Sculpture Generator I, GUI
14
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

15
Also a Scherk-Collins Toroid

• branches 1
• stories 5
• height 1.00
• flange 1.00
• thickness 0.04
• rim_bulge 1.01
• warp 360
• twist 900
• azimuth 90
• textr_tiles 1
• detail 20

16
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

17
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

18
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

19
V-art
VirtualGlassScherkTowerwith MonkeySaddles(R
adiance 40 hours) Jane Yen
20
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.

21
Collins Fabrication Process
Wood master patternfor sculpture
Layered laminated main shape
Example Vox Solis
22
Slices through Minimal Trefoil
50
10
23
30
45
5
20
27
35
2
15
25
23
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.

24
Emergence of the Heptoroid (1)
Assembly of the precut boards
25
Emergence of the Heptoroid (2)
Forming a continuous smooth edge
26
Emergence of the Heptoroid (3)
Smoothing the whole surface
27
The Finished Heptoroid

• at Fermi Lab Art Gallery (1998).

28
SFF (Solid Free-form Fabrication)
Monkey- Saddle Cinquefoil
29
Fused Deposition Modeling (FDM)
30
Zooming into the FDM Machine
31
Various Scherk-Collins Sculptures
32
Part II
Developing Parameterized Sculpture
Families (Extending a Paradigm)
33
Family of Symmetrical Trefoils
W2
W1
B1 B2 B3
B4
34
Close-up of Some Trefoils
B1 B2
B3
Varying the number of branches, the order of the
saddles.
35
Higher-order Trefoils (4th order saddles)
W1 (Warp)
W2 ?
36
Exploring New Ideas W2

• Going around the loop twice ...

resulting in an interwoven structure.
37
9-story Intertwined Double Toroid
Bronze investment casting from wax original
made on 3D SystemsThermojet
38
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
39
Note
The computer becomesan amplifier /
acceleratorfor the creative process.
40
Séquins Minimal Saddle Trefoil

• bronze cast, gold plated

41
Minimal Trefoils -- cast and finished by Steve
Reinmuth
42
Steve Reinmuth
43
Brent Collins Pax Mundi
A new inspiration
44
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 ?

45
Part III
The Creative Step (Capturing a Paradigm)
46
Sculptures by Naum Gabo

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

47
2-period Gabo Curve

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

48
4-period Gabo Curve

• Same construction as for a 2-period curve

49
Pax Mundi Revisited

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

50
SLIDE-UI for Pax Mundi Shapes
51
Viae Globi Family (Roads on a Sphere)
L2 L3 L4
L5
52
Via Globi 3 (Stone)
Wilmin Martono
53
Via Globi 5 (Wood)
Wilmin Martono
54
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

55
Circle Splines on the Sphere

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

56
Via Globi -- Virtual Design
Wilmin Martono
57
Maloja (FDM part)

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

58
Stelvio

• An even more convoluted alpine pass in Italy.

59
Altamont

• Celebrating American multi-lane highways.

60
Lombard

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

61
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 !

62
The Poor Mans Opportunity Snow-Sculpting!Annua
l Championships in Breckenridge, CO
63
Stan Wagon, Macalester College, St. Paul, MN

• Leader of Team USA Minnesota

64
Stan Wagon

• Skier Mountaineer Snow Sculptor

65
Helaman Ferguson

• Umbilic Torus Costa Surface

66
Breckenridge, 1999

• Helaman Ferguson Invisible Handshake

67
Robert Longhurst

• Moebius Band Enneper Surface

68
Breckenridge, 2000

• Robert Longhurst
• Rhapsody in White
• 2nd Place

69
Breckenridge,2001

• Robert Longhurst
• White Narcissus

70
Batsheba Grossman

• Antipot Antichron

71
Breckenridge, 2002

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

72
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

73
Collins Initial Suggestion Minimal Trefoil

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

74
Monkey Saddle Trefoil

• from Sculpture Generator I

75
Maquettes

• 3D-Print FDM

76
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.

77
ACCEPTED !

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

78
Construction Drawings

• Top View Side View
  Axial View

79
11 Templates

• Magnified from computer prints with the
  classical grid method

80
Plan of Attack

• Cut away 2 large triangular prisms
• Hang plastic template (12x18) over slab
• Mark projections of holes, flanges
• Drill, carve, refine (using maquette for
  reference)
• Try this first on a smaller practice block!

81
Practice Block (1)

• Template transfer Reference holes

82
Practice Block (2)

• Free-hand carving ? Irregular
  ribs

? Need new plan !
83
Day 1
Removinglots of snow
84
Day 1 The Monolith

• Cut away prisms

85
Day 2 Making a Torus

• Mark center, circles
  Bulls-eye !

86
(No Transcript)
87
Chipping away
88
(No Transcript)
89
Tools, Templates
90
Making a Torus

• Use of template Need for a sun shield

91
End of Day 2

• The Torus

92
Day 3, am Drawing Flanges
93
Day 3, pm Flanges, Holes
94
End of Day 3 Proper Topology
95
Day 4 Geometry Refinement
96
(No Transcript)
97
End of Day 4 Desired Geometry
98
Day 5, am Surface Refinement
99
House Cleaning
100
Whirled White Web
101
(No Transcript)
102
Official Team Photo
103
1240 pm
104
1241 pm
105
1250 pm
106
3 pm
107
The Winners

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

sacred geometry very intricate very 21st
century !
108
(No Transcript)
109
4 pm
110
British Columbia Winter Comes
111
(No Transcript)
112
Team Breckenridge (3rd Place)
Day 2 Day
3
113
Team Breckenridge A Fishing Tail
114
Mexico City Capilla Posa
115
China The Love of Mother
116
Quebec RèveOlution
117
Manitoba Birth of a Nation
118
USA New York 94 Hour Photo
119
(No Transcript)
120
Part V

• DISCUSSION
• State of the Art of CAD-tools
• for creative / aesthetic design.

121
Visualization / Evaluation

• High-quality computer renderings.
• Well- established programsinternal
  walk-through,external terrain fly-over,hybrid
  city exploration.
• Good interactive controls,good rendering of
  scene.
• Technology is driven by video games!

122
Conceptual Design (3D Sketching)

• E.g. creating a new form ( a Moebius bridge )
• CAD Tools are totally inadequate.
• Effective design ideation involves more than just
  the eyes and perhaps a (3D?) stylus.
• WANTEDfull-hand haptics (palm and fingers),
  whole body gestures,group interactions,

123
The Holy Grail of a CAD System (for abstract,
geometric sculpture design)

• Combines the best of physical / virtual worlds
• No gravity ? no scaffolding needed
• Parts have infinite strength ? dont break
• Parts can be glued together and taken apart
• Beams may bend like perfect splines (or MVC)
• Surfaces may stretch like soap films (or MVS)
• Parts may emulate materials properties (sound).

124
QUESTIONS ?DISCUSSION ?
125
Question for General Audience

• If a computer did it can it still be art ?

126
SPARE SLIDES
127
CONTACT, March. 21-23, 2003

• Art, Math, Computers,
• and Creativity

Carlo Séquin, University of California,
Berkeley