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NDIST 2012

NDIST 2012. Shape Representation Carlo H. Séquin University of California, Berkeley. Focus of Talk. Shape representation issues at the start and conclusion of designing RP models. Focus on HCI difficulties and CAD problems, at the start and end of a design / modeling project:

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NDIST 2012

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  1. NDIST 2012 Shape Representation Carlo H. Séquin University of California, Berkeley

  2. Focus of Talk Shape representation issuesat the start and conclusion of designing RP models • Focus on HCI difficulties and CAD problems,at the start and end of a design / modeling project: • How to get started? How to get your ideas into the CAD system. • How to finish? How to get your model properly 3D printed.

  3. A designer for 30 years… CCD TV Camera Soda Hall RISC 1 Computer Chip Octa-Gear (Cyberbuild)

  4. Recent Designs and Models

  5. Talk Outline Start: Concept Input “Sculpture Generator I” “Viae Globi” Sculptures  Interactive Inverse 3D Modeling Finish: Obtaining Tangible Output Construction of “Pax Mundi” Slicing Imperfect .STL files

  6. Brent Collins “Hyperbolic Hexagon II”

  7. Brent Collins: Stacked Saddles All photos by Phillip Geller

  8. Scherk’s 2nd Minimal Surface Isolated core

  9. “ScherkTowers” (2nd and 3d order) Normal “biped” saddles Generalization to higher-order saddles(“monkey saddles”) “Scherk Tower”

  10. “Hyperbolic Hexagon” by B. Collins • 6 saddles in a ring • = “wound up” 6-story Scherk tower • 6 holes passing through symmetry plane at ±45º • Discussion: What if … • we added more stories ? • or introduced a twist before closing the ring ?

  11. Closing the Loop straight or twisted “Scherk Tower” “Scherk-Collins Toroids”

  12. “Hyperbolic Heptagon” - Paper Skeleton

  13. Brent Collins’ Prototyping Process Mockup for the Saddle Trefoil Armature for the Hyperbolic Heptagon Time-consuming ! (1-3 weeks)

  14. Sculpture Generator I, GUI

  15. Some of the Parameters in “SC1”

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

  17. Generated Scherk-Collins Shapes

  18. Shapes from Sculpture Generator I

  19. A Simple Scherk-Collins Toroid Parameters:(genome) • branches = 2 • stories = 1 • height = 5.00 • flange = 1.00 • thickness = 0.10 • rim_bulge = 1.00 • warp = 360.00 • twist = 90 • azimuth = 90 • textr_tiles = 3 • detail = 8

  20. A Scherk Tower (on its side) • branches = 7 • stories = 3 • height = 0.2 • flange = 1.00 • thickness = 0.04 • rim_bulge = 0 • warp = 0 • twist = 0 • azimuth = 0 • textr_tiles = 2 • detail = 6

  21. V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen

  22. Collins’ Fabrication Process Wood master patternfor sculpture Layered laminated main shape Example: Vox Solis

  23. “Vox Solis” by Brent Collins

  24. Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%

  25. Shaded STL-file SSL-slices SSL Contours from QuickSlice

  26. Shaded STL-file SSL-slices SSL Contours from QuickSlice SML-roads in one of the central slices

  27. Profiled Slice through “Heptoroid” • One thick slicethru sculpture,from which Brent can cut boards and assemble a rough shape. • Traces represent: top and bottom,as well as cuts at 1/4, 1/2, 3/4of one board.

  28. Emergence of the Heptoroid (1) Assembly of the precut boards

  29. Emergence of the Heptoroid (2) Forming a continuous smooth edge

  30. Emergence of the Heptoroid (3) Smoothing the whole surface

  31. The Finished Heptoroid • at Fermi Lab Art Gallery (1998).

  32. Part 1b: VIAE GLOBI A completely different paradigm . . .

  33. Brent Collins’“Pax Mundi”1997: 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.

  34. 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   

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

  36. 2-period “Gabo Curve” • Approximation with quartic B-splinewith 8 control points per period;but only 3 DOF are used (symmetry!).

  37. 4-period “Gabo Curve” Same construction as for as for 2-period curve

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

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

  40. Many Different Viae Globi Models

  41. 1c: Interactive Inverse 3D Modeling How to generalize this approach. Important: Include the designer in the reverse-engineering loop!

  42. Example Design Scenario Kitchen appliances “With a Heart”

  43. Modular Reverse Engineering • Extract parameterized descriptions, module by module. • In each case choose a representation that best enables the intended re-design. • Use plausible, commonly used CAD constructs: • CSG • Quadrics • Extrusions • Rotational Sweeps • Progressive Sweeps

  44. Interactive Inverse 3D Modeling ( Jimmy Andrews’ PhD thesis) Redesigns enabled by different imposed structure Initial artifact Let the user select a high-level model structurethat is most useful for immediate re-design.

  45. Option 1: Varying Rotational Symmetry 3 fold 4 fold 20 fold Extract one sector; collapse/expand in polar coordinates.

  46. Opt.2: Editing as Surface of Revolution Mesh is rotationally collapsed to yielda compound “cross-section”; This cross-sectioncan then be edited,and this will affectthe whole mesh.

  47. Opt.3: Extraction as a Progressive Sweep 20-story Scherk chain Revised trefoil sweep path

  48. User-Guided Fitting Modules • Stationary sweeps: (Surfaces of revolution, helices, etc) • Progressive sweeps: • Quadrics: • Freeform surfaces: • CSG modules: …

  49. Stationary Sweeps Defined by a simple sweep motion, with a fixed axis (e.g. revolution, helix, spiral) (simple motion) (simple velocity field) If normal is perpendicular to velocity field: … then assume point belongs to sweep.

  50. Fitting Algorithm: • Find velocity field that fits marked data points:Minimize (subject to constraint): • Grow the region by adding more fitting points • Repeat (typically converges in 2-3 iterations) [ Pottmann, Lee, and Randrup, 98 ]

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