USF -- February 2001

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USF -- February 2001

• Art, Math, and Sculpture
• Connecting Computers and Creativity
• Carlo H. Séquin
• University of California, Berkeley

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My Professional Focus

• Computer-Aided Design
• Design useful and beautiful objectswith the help
  of computers.
• Develop (interactive) computer programsto make
  these tasks easier.

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Computer-Aided Design I Integrated Circuits

• RISC I chip (1981)

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Computer-Aided Design II Mathematical Models

• Granny Knot Lattice
• Berkeley UniGrafix (1982)

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Computer-Aided Design III Buildings
Soda Hall, CS Dept. Berkeley (1992)
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Computer-Aided Design IV Mechanical Parts
Octahedral Gear

• Design (1985) Realization (FDM) (2000)

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Computer-Aided Design V Abstract Sculpture
(virtual)
(Since 1995)
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Computer-Aided Design V Abstract Sculpture
(virtual)

• Scherk-Collins Tower

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Computer-Aided Design V Abstract Sculpture
(virtual)

• Doubly-looped Scherk-Collins saddle-chain

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Computer-Aided Design V Abstract Sculpture
(real)

• Bonds of Friendship(2001)
• Fabricated by Fused Deposition Modeling
• Currently in S.F.at Gallery 650,Delancy/Brannan

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Roots of My Passion for Sculpture

• 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, ...

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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 Early Sculptures
All photos by Phillip Geller
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My Fascination with...
Brent Collins Abstract Geometric Art

• Beautiful symmetries
• Graceful balance of the saddle surfaces
• Superb craftsmanship
• Intriguing run of the edges
• What type of knot is formed ?
• Mystery one-sided or two-sided ?
• gt Focus on Chains of Saddles

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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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Collins - Séquin Collaboration

• Discuss ideas on the phone
• Exchange sketches
• Vary the topological parameters
• But how do you know whether it is beautiful ?
  Need visual feedback.
• Making models from paper strips is not good
  enough.

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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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Collins Fabrication Process

• Building the final sculpture (2-3 months)
• Take measurements from mock-up model,transfer
  parallel contours to 1 boards.
• Roughly precut boards, leaving registration
  marksand contiguous pillars for gluing boards
  together.
• Stack and glue together precut boards,remove
  auxiliary struts.
• Fine-tune overall shape,sand and polish the
  surface.
• A big investment of effort !

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Collins Fabrication Process
Lamination process to make an overall shape that
withincontains the final sculpture. Example
Vox Solis
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Sculpture Generator I

• Prototyping Visualization tool
  forScherk-Collins Saddle-Chains.
• Slider control for this one shape-family,
• Control of about 12 parameters.
• Main goal Speed for interactive editing.
• Geometry part is about 5,000 lines of C
• 10,000 lines for display user interface.
• gt VIDEO

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Scherk-Collins Sculptures
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The Basic Element
Scherks 2ndminimal surface
3-story tower,trimmed, thickened
180 degreesof twist added
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Toroidal Warp into Collins Ring
8-story tower
warped into a ring
360º twist added
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A Plethora of Shapes
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Edge Treatment
square, flat cut
semi-circular
bulging out
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Embellishment of Basic Shape
color
background
texture
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VIDEO

• 6 min

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A Simple Scherk-Collins Toroid

• branches 2
• storeys 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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Also a Scherk-Collins Toroid

• branches 1
• storeys 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

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A Scherk Tower (on its side)

• branches 7
• storeys 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
• storeys 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
• storeys 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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Main Goal in Sculpture Generator I

• Real-time Interactive Speed !
• Cant afford surface optimizationto obtain true
  minimal surfaces
• also, this would be aesthetically too limited.
• gt Make closed-form hyperbolic approximation.

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Hyperbolic Cross Sections
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Base Geometry One Scherk Story

• Hyperbolic Slices gt Triangle Strips
• precomputed -- then warped into toroid

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The Basic Saddle Element

• with surface normals

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Hyperbolic Contour Lines

• On a straight tower and on a ring

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How to Obtain a Real Sculpture ?

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

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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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Our First Joint Sculpture

• Six monkey saddles in a ring with no twist
• (like Hyperbolic Hexagon)
• azimuth 30, flange 1.5
• (aesthetics)
• size, thickness
• (fabrication consideration)

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Hyperbolic Hexagon II (wood)
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Heptoroid ( from Sculpture Generator I )
Cross-eye stereo pair
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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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Advantages of CAD of Sculptures

• Exploration of a larger domain
• Instant visualization of results
• Eliminate need for prototyping
• Create virtual reality pictures
• Making more complex structures
• Better optimization of chosen form
• More precise implementation
• Rapid prototyping of maquettes

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Sculpture Design Solar Arch

• branches 4
• storeys 11
• height 1.55
• flange 1.00
• thickness 0.06
• rim_bulge 1.00
• warp 330.00
• twist 247.50
• azimuth 56.25
• mesh_tiles 0
• textr_tiles 1
• detail 8
• bounding box
• xmax 6.01,
• ymax 1.14,
• zmax 5.55,
• xmin -7.93,
• ymin -1.14,
• zmin -8.41

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Competition in Breckenridge, CO
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SLA Maquette of Solar Arch
Back-lighting and photo by Philip Geller
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FDM Maquette of Solar Arch

• 2nd place

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We Can Try Again in L.A.
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or in Washington D.C.
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V-art
VirtualGlassScherkTowerwith MonkeySaddles Ja
ne Yen
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SFF Maquettes of Future Sculptures
Monkey- Saddle Cinquefoil
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Various Scherk-Collins Sculptures
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Fused Deposition Modeling (FDM)
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Looking into the FDM Machine
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Zooming into the FDM Machine
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Séquins Minimal Saddle Trefoil

• Stereo-lithography master

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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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Brent Collins Trefoil
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Family of Symmetrical Trefoils
W2
W1
B1 B2 B3
B4
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Higher-order Trefoils (4th order saddles)
W1
W2
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Exploring New Ideas

• 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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Brent Collins Pax Mundi
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Keeping up with Brent ...

• A warped Scherk tower is not able to describe
  a shape like Pax Mundi.
• Need a broader paradigm !
• Use the SLIDE modeling environment(developed at
  U.C. Berkeley by J. Smith)it provides a nice
  combination of procedural modeling and
  interactivity.

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SLIDE

• SLIDE Scene Language for Interactive Dynamic
  Environments
• Developed as a modular rendering pipelinefor our
  introductory graphics course.
• Primary Author Jordan Smith
• Based on OpenGL and Tcl/tk.
• Good combination of interactive 3D graphicsand
  parameterizable procedural constructs.

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SLIDE Example Klein Bottle

• Final Project CS 184, Nerius Landys Shad
  Roundy

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SLIDE Example Bugs Life

• Final Project CS 184, David Cheng and James Chow

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SLIDE as a Design Tool

• SLIDE is being enhanced currentlyto serve as a
  front-end for CyberBuild.
• Recently added
• Spline curves and surfaces
• Morphing sweeps along such curves
• 3D warping module (Sederberg, Rockwood)
• Many types of subdivision surfaces
• These are key elements for Sculpture Generator II

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3D Hilbert Curves (FDM)

• Hilbert64 and Hilbert512

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SLIDE-UI for Knot Generation
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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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Via Globi 5 (Gold)
Wilmin Martono
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Figure-8 Knot with C-Section
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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.

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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 artists inspiration.

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Questions ?
THE END
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SPARE

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Conclusions (3)

• What makes a CAD tool productive for this kind
  of work ?
• Not just virtual clay,
• partly procedural
• fewer parameters that need to be set.
• Keep things aligned, joined
• guarantee symmetry, regularity,
• watertight surfaces.
• Interactivity is crucial !

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Some of the Parameters in SC1
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AAAS 2001, San Francisco

• Procedurally Defined Geometrical Sculptures
  
• Carlo H. Séquin
• University of California, Berkeley
• Brent Collins
• Gower, Missouri