1. Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision Surfaces

2. computer graphics & visualization Manuel Mesters - Subdivision Surfaces At a glance Refinement 1Refinement 2 Refinement ∞

3. computer graphics & visualization Manuel Mesters - Subdivision Surfaces At a glance

4. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

5. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

6. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Making of Geri‘s Game

7. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Geri’s Game - 1st animation using Subdivision Surfaces - Playground for new technologies - Best Animated Short (1997)

8. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Draft - 1000s of drawings

9. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Clay Models - Double Life Size Model: - Head - Hands

10. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Digitizing - Laserscanner -> Point Cloud

11. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Mesh - Point Cloud -> Mesh - Controls for facial movements (manual insertion)

12. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Animation Process - Using Pixar’s RenderMan: - Animate Mesh - Call Controls / Subdivide

13. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Cloth Dynamics - Dynamic flexible mesh - Energy functions - Many equations...

14. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Watch Geri’s Game

15. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

16. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Definition Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements

17. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Definition Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements - Start: Control Mesh - Process: Apply refinement rules (many times) - Result: Smooth curve/surface

18. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve Start: Polygon Apply refinement rule Result: Smooth curve

19. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve - Rules

20. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve

21. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Different Algorithms - Different Results Loop Catmull-Clark Butterfly Doo-Sabin

22. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Different Algorithms - Different Results Loop Catmull-Clark Butterfly Doo-Sabin

23. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

24. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision

25. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision original vertex v3 v1v2 v4

26. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision edge point (ep): constructed on each edge original vertex v3 v1v2 v4 ep

27. computer graphics & visualization Manuel Mesters - Subdivision Surfaces vertex point  constructed for each old (original) vertex Loop Subdivision edge point original vertex

28. computer graphics & visualization Manuel Mesters - Subdivision Surfaces vertex point: constructed for each old (original) vertex Loop Subdivision A given vertex has n neighbor vertices. The new vertex point: For n = 3 For n > 3 v v

29. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop - Local Subdivision - Exclude some edges from Subdivision - More details later...

30. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

31. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision

32. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE

33. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE

34. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE VERTEX

35. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Sharp creases - Subdivision produces smooth surfaces 1.Tag Edges as “sharp” or “not-sharp” During Subdivision, 2.if an edge is “sharp”, use sharp subdivision rules. 3.If an edge is “not-sharp”, use normal smooth subdivision rules.

36. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Infinitely Sharp Creases - Tag Control vertices and edges as sharp - Face points: same as smooth rule - Edge points: place at midpoint of edge - Vertex points - One sharp incident edge (dart): same as smooth rule - Two sharp edges (crease): (e 1 + 6v i + e 2 ) / 8 - Three or more sharp edges (corner): do not modify point

37. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Sharp rules FACE (unchanged) EDGE VERTEX crease dart corner >2 2 0,1 # adj. Sharp edges

38. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Semi-sharp creases 1.Tag Edges as “sharp” or “not-sharp” n = 0 : “not sharp” n > 0 : sharp During Subdivision, 2.if an edge is “sharp”, use sharp subdivision rules. Newly created edges, are assigned a sharpness of n-1. 3.If an edge is “not-sharp”, use normal smooth subdivision rules.

39. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Sharpness!

40. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

41. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary Take home message

42. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements

43. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary

44. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - There are different Algorithms - Mesh Type - Rules

45. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - Loop - Catmull-Clark

46. computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - Subdivision - Standard rules -> smoothness - Additional rules -> sharpness - Sharpness parameter -> flexibility

47. computer graphics & visualization Manuel Mesters - Subdivision Surfaces The End Thank you for your attention