Post on 21-Dec-2015
CS285CS285Designing Viae Globi
(Roads on a Sphere)
Carlo H. Séquin
University of California, Berkeley
Inspired by
Brent Collins
Gower, Missouri
““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 ?
Closing the LoopClosing the Loop
straight
or
twisted
““Sculpture Generator I”, GUI Sculpture Generator I”, GUI
Base Geometry: One Scherk StoryBase Geometry: One Scherk Story
Hyperbolic Slices ==> Triangle Strips
Pre-computed -- then warped into toroid
Brent CollinsBrent Collins
“Hyperbolic Hexagon II”
Hyper-Sculpture: Hyper-Sculpture: Family of 12 TrefoilsFamily of 12 Trefoils
W=2
W=1
B=1 B=2 B=3 B=4
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.
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
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.
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!).
4-period “Gabo Curve”4-period “Gabo Curve”
Same construction as for as for 2-period curve
Pax MundiPax Mundi Revisited Revisited
Can be seen as:
Amplitude modulated, 4-period Gabo curve
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.
SLIDE Example: Klein BottleSLIDE Example: Klein Bottle
Final Project CS 184, Nerius Landys & Shad Roundy
SLIDE Example Bug’s LifeSLIDE Example Bug’s Life
Final Project CS 184, David Cheng and James Chow
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
SLIDE-UI for Knot GenerationSLIDE-UI for Knot Generation
SLIDE-GUI for “SLIDE-GUI for “Pax MundiPax Mundi” Shapes” ShapesGood combination of interactive 3D graphicsand parameterizable procedural constructs.
2-period Gabo sculpture2-period Gabo sculpture
Tennis ball – or baseball – seam used assweep curve.
Viae Globi Viae Globi Family Family (Roads on a Sphere)(Roads on a Sphere)
2 3 4 5 periods
Via Globi 5Via Globi 5 (Virtual Wood) (Virtual Wood)
Wilmin Martono
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
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.
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
Many Different Many Different Viae GlobiViae Globi Models Models
MalojaMaloja
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.
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)
Allows Knotted Sweep PathsAllows Knotted Sweep Paths
Chinese Button Knot
Really Free-form 3D Space CurvesReally Free-form 3D Space Curves
Figure-8 knot
Using Another Cross SectionUsing Another Cross Section
Galapagos 6
Target GeometryTarget Geometry
Constraints:• Bronze, 70” diameter• Less than 1500 pounds• Less than $50’000• Maintain beauty, strength• Minimize master geometry
EmulationEmulation
Use smoother quintic spline
Make 4 identical parts(needs extra control point)
Add a few “warp” parameters
Emulation; Define Master PatternEmulation; Define Master Pattern
Use 4 copies.
Master to make a mold from.
Alignment tab
Model of Master Part Made with FDMModel of Master Part Made with FDM
4 pieces make the whole sculpture
Joe Valasek’s CNC Milling MachineJoe Valasek’s CNC Milling Machine
Styrofoam milling machine
Design of Two-Part MasterDesign of Two-Part Master
Alignment tabs for easy assembly
Subdivide into Subdivide into TwoTwo Master Segments Master Segments
Machined Master Pattern #2Machined Master Pattern #2
(Cut) Master (Cut) Master Silicone Rubber Silicone Rubber MoldMold
MoldMold Several (4) Wax Copies Several (4) Wax Copies
SpruingSpruing the the Wax PartsWax Parts for Casting for Casting
Ceramic Slurry ShellCeramic Slurry Shell Around Wax Around Wax PartPart
ShellShell Ready Ready for Castingfor Casting
Casting with Casting with Liquid BronzeLiquid Bronze
The Freed The Freed Bronze CastBronze Cast
Assembling the SegmentsAssembling the Segments
The “Growing” RibbonThe “Growing” Ribbon
The Single Support PointThe Single Support Point
Grinding the Welded Seams,Grinding the Welded Seams,Polishing the SurfacePolishing the Surface
Applying PatinaApplying Patina
Ready for ShippingReady for Shipping
The Move Around the Building (Jan.18)The Move Around the Building (Jan.18)
Front DoorFront Door
H&R Block Building
Steve Tightening the BoltsSteve Tightening the Bolts
Brent Polishing Our BabyBrent Polishing Our Baby