CS285

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CS285

• Sculpture Generator I
• Carlo H. Séquin
• University of California, Berkeley
• In Collaboration with
• Brent Collins
• Gower, Missouri

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Brent Collins

• Genesis Brent Collins at BRIDGES 2000

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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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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.
• A key problem is making the sculpture look good
  from all sides !

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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
Wood master patternfor sculpture
Layered laminated main shape
Example Vox Solis
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The Need for a Prototyping Tool

• Intriguing Conceptual Idea Turn the
  Hyperbolic Hexagon into a Heptagon
• Goals Give it more variety
• Make different hole-angles visible from one
  direction by adding twist before closure.
• Results Surface becomes single-sided
• The four separate edges join into a torus knot.
• Question Will it look beautiful ?
• What can we do if it doesn t ?
• Perhaps more twist can save it ?
• What is the best size for the holes, the flanges
  ?
• How can we find out quickly ?

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Sculpture Generator I

• Prototyping 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.

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Generated Scherk-Collins Shapes
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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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Sculpture Generator, GUI
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Some of the Parameters in SC1
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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.
• ? Use closed-form hyperbolic approximation.

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Base Geometry One Scherk Story

• Hyperbolic Slices gt Triangle Strips
• Pre-computed -- then warped into toroid

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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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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

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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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How to Obtain a Real Sculpture ?

• Prepare a set of cross-sectional blue printsat
  equally 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)
Brent Collins
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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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Heptoroid
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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

• 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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FDM Maquette of Solar Arch
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Breckenridge Competition

• 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(R
adiance 40 hours) Jane Yen
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SFF (Solid Free-form Fabrication)
Monkey- Saddle Cinquefoil
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Various Scherk-Collins Sculptures
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Fused Deposition Modeling (FDM)
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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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New Possibilities
Developing Parameterized, Procedurally Generated
Sculpture Families
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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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Inspiration Brent Collins Pax Mundi
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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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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 as for 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

• 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 originally a modular rendering tool.
• Later enhanced to serve as a CAD tool
• Spline curves and surfaces
• Morphing sweeps along such curves
• 3D warping module (Sederberg, Rockwood)
• Many types of subdivision surfaces
• These are key elements for a 2nd Generation
  Sculpture Generator

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SLIDE-UI for Knot Generation
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SLIDE-UI for Pax Mundi Shapes
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Via Globi 5 (Gold)
Wilmin Martono
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Via Globi 3 (Stone)
Wilmin Martono
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Viae Globi Family (Roads on a Sphere)
L2 L3 L4
L5
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Conclusions (1)

• Procedural thinking about some art object adds a
  new and promising dimension.It allows the artist
  to increase the complexity, precision, and
  optimality of a particular piece of art.
• The computer must be seen as yet another
  power-tool at the artists disposition, --
  supplementing the pneumatic chisel, the
  airbrush, and the welding machine.

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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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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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Conclusions (4)

• Rapid prototyping (layered fabrication)must now
  be considered a new facetin the spectrum of MM
  technologies.
• It provides tangible (high-quality haptic)output
  for objects with which usersmay want to
  interact.
• Even for sculptures(intended primarily for
  visual enjoyment)the physical maquette
  disclosessubtle geometrical features that
  arenot visible in the virtual rendering.

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Questions ?
THE END