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Designing Viae Globi: Master Geometry on a Sphere Project

Explore the innovative process of creating Viae Globi sculptures on a sphere using CAD tools and geometric principles. Learn how to model the Pax Mundi design and bring it to life through a detailed workflow.

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Designing Viae Globi: Master Geometry on a Sphere Project

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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. 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.

  3. 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   

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

  5. 2-period “Gabo Curve” • Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used (symmetry!).

  6. 4-period “Gabo Curve” Same construction as for as for 2-period curve

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

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

  9. 2-period Gabo sculpture Tennis ball – or baseball – seam used as sweep curve.

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

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

  12. 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.

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

  14. Many Different Viae Globi Models

  15. Maloja

  16. 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.

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

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

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

  20. 4 pieces make the whole sculpture Model of Master Part Made with FDM

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

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

  23. Subdivide into Two Master Segments

  24. Machined Master Pattern #2

  25. (Cut) Master  Silicone Rubber Mold

  26. Mold Several (4) Wax Copies

  27. Spruing the Wax Parts for Casting

  28. Ceramic Slurry Shell Around Wax Part

  29. Shell Ready for Casting

  30. Casting with Liquid Bronze

  31. The Freed Bronze Cast

  32. Assembling the Segments

  33. The “Growing” Ribbon

  34. The Single Support Point

  35. Grinding the Welded Seams,Polishing the Surface

  36. Applying Patina

  37. Ready for Shipping

  38. The Move Around the Building (Jan.18)

  39. Front Door H&R Block Building

  40. Steve Tightening the Bolts

  41. Brent Polishing Our Baby

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