Tubular Sculptures A 3D Sketchbook of Ideas

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Tubular SculpturesA 3D Sketchbook of Ideas

• Carlo H. Séquin, EECS U.C. Berkeley

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Dedication toFrank Smullin (1943 1983)
Creator of tubular sculptures
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Frank Smullin keynote speaker at the Design
Automation Conference, Nashville, 1981
Centerpiece Fit to be Tied 9 sections of
metal pipe joined by bolted flanges, gradually
being transformed from a straight pipe into a
tight knot.

• The defining moment of my initiation to 3D
  graphics and geometrical sculpture.

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Gradual Tying of a Knot
?

• Basic Operation

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Frank Smullins CAD Techniques

• Tubular sculpturesFigure-8 Knot at Duke U.
• Apple II program for calculating intersections

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Frank Smullin (Nashville, 1981)

• The Granny-knot has more artistic merits than
  the square knot because it is more 3Dits ends
  stick out in tetrahedral fashion...

Granny Knot
Square Knot
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Granny-Knot as a Building Block
Smullin TetraGranny Core of
Granny-Knot

• Four tetrahedral links, like a carbon atom, can
  be assembled into diamond-lattice ...

... leads to the Granny-Knot-Lattice ?
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Strands in the Granny-Knot-Lattice
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Granny-Knot-Lattice (Séquin, 1981)
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Graduate course, Fall 1983Creative Geometric
Modeling
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My First Art Show, Fall 1983

• Tubular center piece

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Large-scale Free-form Sculpture
Pax Mundi II Hyperbolic Hexagon
II

• is expensive

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Charles PerryEquinoxDallas, TX
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Tubular Sculpture

• Steam Pipe Sculptureby shade

Ribbed Maceby Charles Perry
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Joining Tubular Elements . . .

• Gas-Welding Classby Michael Rivera

Multipolygonal SpiralsJavier Carvajal
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Exploration and Review

• What artistic possibilities do tubes provide ?
• What have artists done with tubular elements ?
• Is there a role for CAD in this type of
  sculptures ?

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PART I Just Cylinders !

• Cant go much simpler than this !

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The Cylinder in Architecture
Chapel at MIT
La Défense, France
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Cylinders as Sculptures
Max Bill
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Cylindrical Anamorphic Art
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Multiple Cylinders
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Roger Berry Rising Wave, Oyster Bay
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FUNtain Hydraulophone, Ontario
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Alexander Liberman Gate of Hope

• COE, Univerity of Hawaii at Manoa

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Alexander Liberman Olympic Iliad
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Cassini

• Cassini
• Charles Perry

Mini-Cassini Carlo Séquin
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Rinus Roelofs Bar Tetrahedron
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Mitering Becomes an Issue !
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Branching Tubes
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Max Bill (1938-39) Construction with 30 Similar
Elements
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A Modular Type of Tube Junctions
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A Particularly Ingenious Type of Tube Junction

• Marc PelletierBridges 2002

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Stephen Adams

• Bad Plumbing (2003) Copper
  Figure (2004)

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Buffalo Bayou Art Park in Houston, TX
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Art or Just Bad Plumbing ?

• From Dark Roasted Blend, Weird Wonderful
  Things
• http//www.darkroastedblend.com/2008/03/disturbing
  -wiring-part-3.html

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Elegant Home Appliances

• Water Faucet by Water Decor Inc.
• Based on mitered cylindrical elements

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Is There a Role for the Computer ?
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PART II Symmetrical Tangles
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George Hart 72 Pencils CMYK
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G4G8
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Akio Hisume Spaceball
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Séquin Skewed Tangle of 12 Cylinders

• Forming four symmetrically interlinked triangles

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Jack Snoeyink 30 Aluminium Tubes

• Five interlinked, skewed tetrahedra,a grouping
  that cannot be taken apart with 2 hands

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Akio Hisume Sunflower-Tower

• Fairchild Tropical Garden, Miami, Florida
• using 300 4m bamboo poles, (1986-2003)

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Kenneth Snelson Needle Tower

• Self-similar tapered tensegrity structure

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Impossible Cylinder

• original drawing by Istvan Orosz
• computer image by Gershon Elber

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Realization of Impossible Cylinder

• This cylinder is a double-twisted band

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Allow the Tube to Bend !
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PART III Tori and Chain Links

• Bend cylinder into a closed loop

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Oldest Artistic Torus ? (ca. 3000 BC)

• Seen in Science Museum in Vienna, Sept. 2008

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John Robinson Bonds of Friendship
1979
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Helaman Ferguson Two Canoes
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Helaman Ferguson Two Canoes

• Original model by Helaman Ferguson, 1995

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Helaman Ferguson Two Canoes

• How it was assembled

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Proposed Torus Sculpture
Torus! Torus! inflatable structure by Joseph
Huberman
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Three Tori

• Borromean Rings by Alex Feingold

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Carlo Séquin Borromean Tangle 5

• No two loops are pair-wise interlinked !

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Nobbly Wobblys

• Doggie Solutions, http//www.doggiesolutions.co.uk
  
• Every two loops pair-wise interlink !

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Orderly Tangles

• 20 interlinked triangles Geoff Wyvill
  Nova Plexus
• More Orderly Tangles in the book by Alan Holden

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Chain Links
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Forming Linear Chains
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Chainmaille
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Carlo Séquin Defying Gravity
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PART IV Iterated Cylinders and Tori? Ribbed
Surfaces

• Iterating thin tubular elements in space with
  small variations in shape and placement leads to
  ribbed transparent surfaces which is a nice
  sculptural paradigm.

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Ribbed Surfaces for Visualization
Mathematicians Models and Sculptures
A ruled surface Single-shell hyperboloid
String art by
Ray Schechter
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Non-Orientable 4D Cells(Mathematical
Visualization)

• Hemi-cube ( 4 quadrilaterals )

Hemi-dodecahedron( 6 pentagons )
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Iterated Hula-Hoops

• Cross-cap model Twisted
  Goblet

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Iterated Tubular Segments
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Charles Perry Harmony (Hartford, CT)

• Two semi-circular guide rails.
• Four ribbed surfaces.
• Ribs are of varying curvature.

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Charles Perry Solstice (Tampa, FL)
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Parameterization of Solstice

• (3, 2) torus knot
• Curved ribs in nearlytriangular configuration

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Parameterization of Solstice

• 3 major elements to control

Staggering of ribsrib offset alongguide rail
Rib shapes concave hyperbolic triangles
Guide rail (3, 2) torus knot
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Solstice and its Emulation
Emulation (3, 2) knot
Solstice (3, 2) knot
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Solstice and Variations
Modified (2, 3) knot
Solstice (3, 2) knot
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Solstice and Variations
Modified (4, 3) knot
Solstice (3, 2) knot
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(4, 3) Torus Knot

• Convex ribs to show torus

Concave ribs ? Solstice
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Sweeping Ribs
Single rail 0, 0.5) ? 0.5, 1.0)
Two rails 0, 0.5 ? 0.0, 1.0
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Application-Specific Guide Rails

• For Solstice we use(p, q) torus knots

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Sweeping Rib Offset
Rib Offsets
0
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303
360
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Rib Shape Parameterization

• Cubic Hermite
• Tangent directions and magnitudes at both ends

• Circular Arcs
• Embedding plane
• Turning angle

Rails
Rails
?
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Cubic Hermite Ribs

• End tangents specified in terms of Frenet
  frames of guide rails.

n
b
t
V
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Symmetric, Planar Cubic Hermite Ribs

• Constrain ribs to be symmetric, planar.
• Select a plane through chord with an angle
  against rail tangent.
• Rib tangent angles are offset from chordor a
  curve offset dfrom chord is set.

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3D Cubic Hermite Ribs

• A combination of the previous two approaches.
• Uses rail tangent,chord direction, and their
  cross product.

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Rib Shape Modification in Solstice
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Solstice and Variations
Modified (4, 5) knot
Solstice_2 (3, 2) knot (with denser ribs)
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Charles Perry Early Mace (Atlanta)
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Charles Perry Early Mace
Emulation
Variation with straight ribs
Variation with convex ribs
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Ribbed Figure-8 Knot
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C. PerryEclipseHyatt, S.F.
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C. PerryEclipseHyatt, S.F.
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PART V Free-form Tubular Elements

• Bent or flexiblepipes or tubes . . .

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José de Rivera

• Construction 5B Construction
  35

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José de Rivera
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Mike Oldfield Tubular Bells
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Mike Oldfield Tubular Bells
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Cosimo Cavallaro Knot (1996)

• DeCordova Museum and Sculpture Park, Lincoln, MA

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Richard Zawitz Statue of Infinity (2003)
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Richard Zawitz Museum Tangle (1982)

• A deformable unit with 18 quarter-circle segments

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Naef Wooden Toys (flexible) Ellipso
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Naef Wooden ToysCaterpillar
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Turbo Charger
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Functional Appliance AND Art
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Richard Serra Lead Piece
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Collins Double-Tube Sculptures
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Carlo Séquin Galapagos 6
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PART VI Knotty Sculptures

• Clearly we can bend tubes into knots
• We can use these knots as modular elements

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Knots
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MoreKnots
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Hilbert Cube from Plastic Pipe Ellbows
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PART VII 3D Calligraphy

• Just lines in space ?

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Neon Calligraphy

• Russ RuBertPositronic Neural Net

Jeppe Hein Changing Neon Sculpture
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Bill Culberts Sky Blues
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Michael Hayden Skys the Limit
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PART VIII Beyond Strictly Tubular

• In the last knot sculpture, diameter already
  changes dramatically can no longer be done in a
  modular way or just bending pipes or tubes

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Tubular People
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John T. Unger Oh, Beautiful Life!Curious
Child
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1994 Ad Absolut Scudera Vodka
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Jonathan BorofskyDancers

• Denver Center for the Performing Arts, Sculpture
  Park

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Tony Cragg Statue

• www.sapagroup.com/en/Company-sites/Sapa-RC-Profile
  s/About-us/Sculpture/

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Claire Ochsner
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Brancusi Bird in Space

• Looks deceptively simple from a distance, but is
  a rather complex free-form surface when viewed
  closer. Hard to fabricate !

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MODULARITY

• Brancusi Endless Column

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QUESTIONS?
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S P A R E S
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Emulation
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Variation

• (3,2) Torus Knot (2,3) Torus Knot

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A Building Block for Eclipse II ?
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• Houston plumbing cube

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Hilbert Cube 512, 3D
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The Use of Figure-8 Knots

• Figure-8 knot can also have 4 lobes
• sticking out in tetrahedral directions.

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Figure-8 Knots in Diamond Lattice Cell
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A Denser Lattice of Figure-8 Knots
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Dense Figure-8 Knot Lattice

• Model made with selective laser sintering.

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My Conceptual 3D-CAD Tools
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Recursive Figure-8 Knot

• Recursion step

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Recursive Figure-8 Knot

• Scale stroke-width proportional to recursive
  reduction

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2.5D Recursive (Fractal) Knot
Trefoil Recursion

• Robert Fathauer Recursive Trefoil Knot

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Recursion on a 7-crossing Knot
...
Map the whole thing into all meshes of similar
shape

• Robert Fathauer, Bridges Conference, 2007

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From 2D Drawings to 3D Sculpture

• Too flat ! Switch plane
  orientations

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Recursive Figure-8 Knot 3D

• Maquette emerging from FDM machine

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Recursive Figure-8 Knot

• 9 loop iterations