1. Sketching Complex Generalized Cylinder Spines ● Bartosz Fabianowski · John Dingliana ● Trinity College, Dublin, Ireland

2. Generalized Cylinders

3. cross-sections

4. Generalized Cylinders cross-sections spine

5. Generalized Cylinders ● Cross-sections:2D, easy to sketch cross-sections spine

6. Generalized Cylinders ● Cross-sections:2D, easy to sketch ● Spine:3D, difficult to sketch cross-sections spine

7. A Tricky Case

9. ● How to handle overlapping and looping spines?

10. A Tricky Case ● How to handle overlapping and looping spines? ● How to avoid self-intersections?

11. Related Work ● Kallio: 3D6B Editor: Projective 3D Sketching with Line-Based Rendering, SBIM 2005  Multiple input devices

12. Related Work ● Kallio: 3D6B Editor: Projective 3D Sketching with Line-Based Rendering, SBIM 2005  Multiple input devices ● Okabe, Owada, Igarashi: Interactive Design of Botanical Trees using Freehand Sketches and Example-based Editing, CGF 24(3) 2005  Domain-specific heuristics

13. Related Work ● Kallio: 3D6B Editor: Projective 3D Sketching with Line-Based Rendering, SBIM 2005  Multiple input devices ● Okabe, Owada, Igarashi: Interactive Design of Botanical Trees using Freehand Sketches and Example-based Editing, CGF 24(3) 2005  Domain-specific heuristics ● Cordier, Seo: Free-Form Sketching of Self- Occluding Objects, IEEE CGA 27(1) 2007  Heuristics from outline

14. Related Work ● Kara, Shimada: Construction and Modification of 3D Geometry Using a Sketch-based Interface, SBIM 2006  Projection onto auxiliary geometry

15. Related Work ● Kara, Shimada: Construction and Modification of 3D Geometry Using a Sketch-based Interface, SBIM 2006  Projection onto auxiliary geometry ● Cohen, Markosian, Zeleznik, Hughes, Barzel: An Interface for Sketching 3D Curves, I3D 1999  Fusion of curve and shadow

16. Related Work ● Kara, Shimada: Construction and Modification of 3D Geometry Using a Sketch-based Interface, SBIM 2006  Projection onto auxiliary geometry ● Cohen, Markosian, Zeleznik, Hughes, Barzel: An Interface for Sketching 3D Curves, I3D 1999  Fusion of curve and shadow ● Karpenko, Hughes, Raskar: Epipolar methods for multi-view sketching, SBIM 2004  Fusion of multiple views

17. Our Idea ● Step 1: Sketch overhead view

18. Our Idea ● Step 1: Sketch overhead view ● Pressure controls ordering of overlapping sections

19. Our Idea ● Step 2: Interactively adjust z coordinate

20. Our Idea ● Step 2: Interactively adjust z coordinate ● Advantages:

21. Our Idea ● Step 2: Interactively adjust z coordinate ● Advantages: ● Minimal, intuitive input

22. Our Idea ● Step 2: Interactively adjust z coordinate ● Advantages: ● Minimal, intuitive input ● Full control over all 3 coordinates

23. Our Idea ● Step 2: Interactively adjust z coordinate ● Advantages: ● Minimal, intuitive input ● Full control over all 3 coordinates ● Automatic prevention of self-intersections

24. Representation

25. ● Spine:Polyline

26. Representation ● Spine:Polyline ● Generalized cylinder:Capsules

27. Representation

28. ● Generalized cylinder:Swept-sphere volume

29. Representation ● Generalized cylinder:Swept-sphere volume ● Spine:Polyline

30. Constraints: Step 1

31. ● Overlapping capsule pairs

32. Constraints: Step 1 ● Problem: Inconsistencies

33. Constraints: Step 1 ● Overlapping sections

34. Constraints: Step 2 ● One z coordinate per manually positioned node

35. Optimization ● Iteratively adjusts z coordinates ● Never moves manually positioned nodes

36. Internal Forces

37. ● Apply Laplacian smoothing: ● Move nodes toward interpolation of neighbors

38. Internal Forces ● Apply Laplacian smoothing: ● Move nodes toward interpolation of neighbors ● Attenuated over time

39. Internal Forces ● Apply Laplacian smoothing: ● Move nodes toward interpolation of neighbors ● Attenuated over time

40. External Forces

41. ● Correct constraint violations: ● Move apart section coming into contact

42. External Forces ● Correct constraint violations: ● Move apart section coming into contact

43. Coarse Pass ● Nodes: ● Manually positioned spine nodes

44. Coarse Pass ● Nodes: ● Manually positioned spine nodes ● Two nodes representing each overlapping section pair

45. Coarse Pass ● Nodes: ● Manually positioned spine nodes ● Two nodes representing each overlapping section pair ● Internal force: ● Moves node toward interpolation of neighbors

46. Coarse Pass ● Nodes: ● Manually positioned spine nodes ● Two nodes representing each overlapping section pair ● Internal force: ● Moves node toward interpolation of neighbors ● External force: ● Ensures overlapping sections are at least one radius apart

47. Fine Pass ● Nodes: ● Actual spine nodes

48. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results

49. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results ● Internal force: ● Moves node toward interpolation of neighbors

50. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results ● Internal force: ● Moves node toward interpolation of neighbors ● Moves neighbors in opposite direction with halved strength

51. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results ● Internal force: ● Moves node toward interpolation of neighbors ● Moves neighbors in opposite direction with halved strength

52. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results ● Internal force: ● Moves node toward interpolation of neighbors ● Moves neighbors in opposite direction with halved strength ● External force: ● Collision detection between capsules

53. Fine Pass ● Nodes: ● Actual spine nodes ● Positions initialized by interpolation of coarse results ● Internal force: ● Moves node toward interpolation of neighbors ● Moves neighbors in opposite direction with halved strength ● External force: ● Collision detection between capsules ● Complex interactions handled over multiple iterations

54. Special Case: Loops ● Overlapping sections

55. Special Case: Loops ● Red section has reached its own start

56. Special Case: Loops ● A new winding is begun

57. Special Case: Loops ● First and last windings: ● Pressure controls ordering ● Arranged multiple radii apart in coarse pass

58. Results

63. A General Finding ● Sketch-based input is more than just position

64. A General Finding ● Sketch-based input is more than just position ● Up to six degrees of freedom: ● Position

65. A General Finding ● Sketch-based input is more than just position ● Up to six degrees of freedom: ● Position ● Pressure

66. A General Finding ● Sketch-based input is more than just position ● Up to six degrees of freedom: ● Position ● Pressure ● Pen tilt

67. A General Finding ● Sketch-based input is more than just position ● Up to six degrees of freedom: ● Position ● Pressure ● Pen tilt ● Pen rotation

68. A General Finding ● Sketch-based input is more than just position ● Up to six degrees of freedom: ● Position ● Pressure ● Pen tilt ● Pen rotation ● Let's find novel uses in sketch-based modeling

69. Sketching Complex Generalized Cylinder Spines ● Bartosz Fabianowski · John Dingliana ● Trinity College, Dublin, Ireland

70. Questions?