cs285 designing viae globi (roads on a sphere) carlo h. séquin university of california, berkeley...
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CS285CS285Designing 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. CollinsHyperbolic 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 LoopClosing the Loop
straight
or
twisted
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““Sculpture Generator I”, GUI Sculpture Generator I”, GUI
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Base Geometry: One Scherk StoryBase Geometry: One Scherk Story
Hyperbolic Slices ==> Triangle Strips
Pre-computed -- then warped into toroid
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Brent CollinsBrent Collins
“Hyperbolic Hexagon II”
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Hyper-Sculpture: Hyper-Sculpture: Family of 12 TrefoilsFamily of 12 Trefoils
W=2
W=1
B=1 B=2 B=3 B=4
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Brent Collins’ Brent Collins’ Pax MundiPax Mundi
1997: wood, 30”diam.1997: wood, 30”diam.
2006: Commission from H&R Block, Kansas Cityto make a 70”diameter version in bronze.
My task: to define the master geometry.
CAD tools played important role.
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How to Model How to Model Pax MundiPax 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 GaboSculptures 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”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”4-period “Gabo Curve”
Same construction as for as for 2-period curve
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Pax MundiPax Mundi Revisited Revisited
Can be seen as:
Amplitude modulated, 4-period Gabo curve
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SLIDESLIDE
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 BottleSLIDE Example: Klein Bottle
Final Project CS 184, Nerius Landys & Shad Roundy
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SLIDE Example Bug’s LifeSLIDE Example Bug’s Life
Final Project CS 184, David Cheng and James Chow
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SLIDE as a Design ToolSLIDE 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 GenerationSLIDE-UI for Knot Generation
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SLIDE-GUI for “SLIDE-GUI for “Pax MundiPax Mundi” Shapes” ShapesGood combination of interactive 3D graphicsand parameterizable procedural constructs.
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2-period Gabo sculpture2-period Gabo sculpture
Tennis ball – or baseball – seam used assweep curve.
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Viae Globi Viae Globi Family Family (Roads on a Sphere)(Roads on a Sphere)
2 3 4 5 periods
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Via Globi 5Via Globi 5 (Virtual Wood) (Virtual Wood)
Wilmin Martono
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Modularity of Modularity of Gabo Curve GeneratorGabo 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 ControlSweep / Twist Control
How do we orient, move, morph ...the cross section along the sweep path ?
Natural orientationwith Frenet frame
Torsion Minimization:Azimuth: tangential / normal
900° of twistadded.
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Extension:Extension: Free-form Curve on a Sphere 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 Many Different Viae GlobiViae Globi Models Models
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MalojaMaloja
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Extending the Paradigm:Extending the Paradigm: Aurora-MAurora-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:Paradigm Extension: Sweep Path Sweep Path is no longer confined to a sphere!is no longer confined to a sphere!
Music of the Spheres (Brent Collins)
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Allows Knotted Sweep PathsAllows Knotted Sweep Paths
Chinese Button Knot
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Really Free-form 3D Space CurvesReally Free-form 3D Space Curves
Figure-8 knot
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Using Another Cross SectionUsing Another Cross Section
Galapagos 6
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Target GeometryTarget Geometry
Constraints:• Bronze, 70” diameter• Less than 1500 pounds• Less than $50’000• Maintain beauty, strength• Minimize master geometry
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EmulationEmulation
Use smoother quintic spline
Make 4 identical parts(needs extra control point)
Add a few “warp” parameters
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Emulation; Define Master PatternEmulation; Define Master Pattern
Use 4 copies.
Master to make a mold from.
Alignment tab
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Model of Master Part Made with FDMModel of Master Part Made with FDM
4 pieces make the whole sculpture
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Joe Valasek’s CNC Milling MachineJoe Valasek’s CNC Milling Machine
Styrofoam milling machine
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Design of Two-Part MasterDesign of Two-Part Master
Alignment tabs for easy assembly
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Subdivide into Subdivide into TwoTwo Master Segments Master Segments
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Machined Master Pattern #2Machined Master Pattern #2
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(Cut) Master (Cut) Master Silicone Rubber Silicone Rubber MoldMold
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MoldMold Several (4) Wax Copies Several (4) Wax Copies
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SpruingSpruing the the Wax PartsWax Parts for Casting for Casting
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Ceramic Slurry ShellCeramic Slurry Shell Around Wax Around Wax PartPart
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ShellShell Ready Ready for Castingfor Casting
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Casting with Casting with Liquid BronzeLiquid Bronze
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The Freed The Freed Bronze CastBronze Cast
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Assembling the SegmentsAssembling the Segments
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The “Growing” RibbonThe “Growing” Ribbon
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The Single Support PointThe Single Support Point
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Grinding the Welded Seams,Grinding the Welded Seams,Polishing the SurfacePolishing the Surface
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Applying PatinaApplying Patina
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Ready for ShippingReady for Shipping
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The Move Around the Building (Jan.18)The Move Around the Building (Jan.18)
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Front DoorFront Door
H&R Block Building
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Steve Tightening the BoltsSteve Tightening the Bolts
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Brent Polishing Our BabyBrent Polishing Our Baby
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