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CS285

CS285. Designing Viae Globi ( Roads on a Sphere ) Carlo H. Séquin University of California, Berkeley Inspired by B rent Collins Gower, Missouri. “Hyperbolic Hexagon” by B. Collins. 6 saddles in a ring 6 holes passing through symmetry plane at ±45º

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CS285

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  1. CS285 Designing Viae Globi (Roads on a Sphere) Carlo H. Séquin University of California, Berkeley Inspired by Brent Collins Gower, Missouri

  2. “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 ?

  3. Closing the Loop straight or twisted

  4. “Sculpture Generator I”, GUI

  5. Base Geometry: One Scherk Story • Hyperbolic Slices ==> Triangle Strips • Pre-computed -- then warped into toroid

  6. Brent Collins “Hyperbolic Hexagon II”

  7. Hyper-Sculpture: Family of 12 Trefoils W=2 W=1 B=1 B=2 B=3 B=4

  8. Brent Collins’ Pax Mundi1997: wood, 30”diam. 2006: Commission from H&R Block, Kansas City to make a 70”diameter version in bronze. My task: to define the master geometry. CAD tools played important role.

  9. How to Model Pax Mundi ... • Already addressed that question in 1998: • Pax Mundicould not be done withSculpture Generator I • Needed a more general program ! • Used the Berkeley SLIDE environment. • First: Needed to find the basic paradigm   

  10. Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis- or base-ball;  2-period Gabo curve.

  11. 2-period “Gabo Curve” • Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used (symmetry!).

  12. 4-period “Gabo Curve” Same construction as for as for 2-period curve

  13. Pax Mundi Revisited • Can be seen as:Amplitude modulated, 4-period Gabo curve

  14. 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.

  15. SLIDE Example: Klein Bottle Final Project CS 184, Nerius Landys & Shad Roundy

  16. SLIDE Example Bug’s Life Final Project CS 184, David Cheng and James Chow

  17. 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

  18. SLIDE-UI for Knot Generation

  19. SLIDE-GUI for “Pax Mundi” Shapes Good combination of interactive 3D graphicsand parameterizable procedural constructs.

  20. 2-period Gabo sculpture Tennis ball – or baseball – seam used as sweep curve.

  21. Viae Globi Family (Roads on a Sphere) 2 3 4 5 periods

  22. Via Globi 5 (Virtual Wood) Wilmin Martono

  23. Sweep Curve Generator: Gabo Curves as B-splines Cross Section Fine Tuner: Paramererized shapes Sweep / Twist Controller Modularity of Gabo Curve Generator

  24. How do we orient, move, morph ...the cross section along the sweep path ? Sweep / Twist Control Natural orientationwith Frenet frame Torsion Minimization:Azimuth: tangential / normal 900° of twistadded.

  25. Extension: Free-form Curve on a Sphere Spherical Spline Path Editor (Jane Yen) Nice smooth interpolating curves through sparse data points

  26. Many Different Viae Globi Models

  27. Maloja

  28. 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.

  29. Paradigm Extension:Sweep Path is no longer confined to a sphere! Music of the Spheres (Brent Collins)

  30. Allows Knotted Sweep Paths Chinese Button Knot

  31. Really Free-form 3D Space Curves Figure-8 knot

  32. Using Another Cross Section Galapagos 6

  33. Target Geometry • Constraints: • Bronze, 70” diameter • Less than 1500 pounds • Less than $50’000 • Maintain beauty, strength • Minimize master geometry

  34. Use smoother quintic spline Make 4 identical parts(needs extra control point) Add a few “warp” parameters Emulation

  35. Use 4 copies. Emulation; Define Master Pattern • Master to make a mold from. Alignment tab

  36. 4 pieces make the whole sculpture Model of Master Part Made with FDM

  37. Joe Valasek’s CNC Milling Machine • Styrofoam milling machine

  38. Alignment tabs for easy assembly Design of Two-Part Master

  39. Subdivide into Two Master Segments

  40. Machined Master Pattern #2

  41. (Cut) Master  Silicone Rubber Mold

  42. Mold Several (4) Wax Copies

  43. Spruing the Wax Parts for Casting

  44. Ceramic Slurry Shell Around Wax Part

  45. Shell Ready for Casting

  46. Casting with Liquid Bronze

  47. The Freed Bronze Cast

  48. Assembling the Segments

  49. The “Growing” Ribbon

  50. The Single Support Point

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