CS285

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CS285

• Designing Viae Globi
• (Roads on a Sphere)
• Carlo H. Séquin
• University of California, Berkeley
• Inspired by
• Brent Collins
• Gower, Missouri

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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
• Discussion What 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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Sculpture Generator I, GUI
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Base Geometry One Scherk Story

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

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Brent Collins
Hyperbolic Hexagon II
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Hyper-Sculpture Family of 12 Trefoils
W2
W1
B1 B2 B3
B4
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Brent Collins Pax Mundi1997 wood, 30diam.
2006 Commission from HR Block, Kansas
City to make a 70diameter version in
bronze. My task to define the master
geometry. CAD tools played important role.
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How to Model Pax Mundi ...

• Already addressed that question in 1998
• Pax Mundi could not be done with Sculpture
  Generator I
• Needed a more general program !
• Used the Berkeley SLIDE environment.
• First Needed to find the basic paradigm ? ? ?

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Sculptures by Naum Gabo

• Pathway on a sphere
• Edge of surface is like seam of tennis- or
  base-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 (symmetry!).

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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-GUI for Pax Mundi Shapes
Good combination of interactive 3D graphicsand
parameterizable procedural constructs.
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2-period Gabo sculpture
Tennis ball or baseball seam used as sweep
curve.
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Viae Globi Family (Roads on a Sphere)
2 3 4
5 periods
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Via Globi 5 (Virtual Wood)
Wilmin Martono
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Modularity of Gabo Curve Generator

• Sweep Curve Generator
• Gabo Curves as B-splines
• Cross Section Fine Tuner
• Paramererized shapes
• Sweep / Twist Controller

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Sweep / Twist Control

• How do we orient, move, morph ...the cross
  section along the sweep path ?

Natural orientationwith Frenet frame
Torsion MinimizationAzimuth tangential /
normal
900 of twistadded.
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Extension Free-form Curve on a Sphere
Spherical Spline Path Editor (Jane Yen)
Nice smooth interpolating curves through sparse
data points
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Many Different Viae Globi Models
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Maloja
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Extending the Paradigm Aurora-M

• Simple path on sphere,
• but more play with the swept cross section.
• This is a Moebius band.
• It is morphed from a concave shape at the bottom
  to a flat ribbon at the top of the flower.

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Paradigm Extension Sweep Path is no longer
confined to a sphere!

• Music of the Spheres (Brent Collins)

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Allows Knotted Sweep Paths

• Chinese Button Knot

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Really Free-form 3D Space Curves

• Figure-8 knot

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Using Another Cross Section

• Galapagos 6

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Target Geometry

• Constraints
• Bronze, 70 diameter
• Less than 1500 pounds
• Less than 50000
• Maintain beauty, strength
• Minimize master geometry

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Emulation

• Use smoother quintic spline
• Make 4 identical parts(needs extra control
  point)
• Add a few warp parameters

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Emulation Define Master Pattern

• Master to make a mold from.

Alignment tab

• Use 4 copies.

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Model of Master Part Made with FDM

• 4 pieces make the whole sculpture

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Joe Valaseks CNC Milling Machine

• Styrofoam milling machine

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Design of Two-Part Master

• Alignment tabs for easy assembly

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Subdivide into Two Master Segments
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Machined Master Pattern 2
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(Cut) Master ? Silicone Rubber Mold
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Mold ? Several (4) Wax Copies
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Spruing the Wax Parts for Casting
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Ceramic Slurry Shell Around Wax Part
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Shell Ready for Casting
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Casting with Liquid Bronze
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The Freed Bronze Cast
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Assembling the Segments
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The Growing Ribbon
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The Single Support Point
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Grinding the Welded Seams,Polishing the Surface
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Applying Patina
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Ready for Shipping
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The Move Around the Building (Jan.18)
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Front Door

• HR Block Building

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Steve Tightening the Bolts
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Brent Polishing Our Baby
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