1. Jeff Ballard Nick Rasmussen
Subdivision Surfaces
Jeff Ballard
Nick Rasmussen
Jeff

2. Overview Motivation for Subdivision Surfaces Subdivision Schemes
Interesting Properties
Discussion of Papers
Jeff

3. Traditional Modeling Techniques
Polygons
Splines
Implicit Surfaces

4. Polygons - Pro
Fast
Arbitrary Topology
Easy Stitching

5. Polygons - Con C0 Continuity High Counts for Complex Surfaces
Edits Hard to do Globally

6. B-Splines - Pro
Mathematically Elegant
Well Understood
C2 Everywhere

7. B-Splines - Con Needs ‘Socking’ to Prevent Cracks
Sharp/Curved Edges Hard
High CV Count Creatures

8. NURBS - Pro CV Weights => Sharp Edges, Finer Control Trim Curves
Widespread Support (sort-of :)

9. NURBS - Con Trim Curves Susceptible to Numerical Error
Very Hard to Sock with Trim Curves
Difficult to Implement
Greater Sophistication Needed for Modeling Tools

10. Implicit Surfaces - Pro
‘Blobby’ Objects
Mathematically Trivial

11. Implicit Surfaces - Con
Poor Control
Hard to Model Details
Achieving Correct Polyginization

12. Why Subdivision Surfaces?
Single Surface for All Modeling Operations
Multi-Resolution Edits
Extensions to Support Sharp Edges
Arbitrary Topology
No Cracks

13. Subdivision Terminology
Vertices:
Regular/Extraordinary
Odd/Even
Face/Edge
Edges:
Boundaries and Creases
Control Mesh

14. Overview Of Subdivision Schemes
Corner Cutting
Vertex Insertion
Interpolating
Approximating

15. Corner Cutting Old Vertices are Discarded Common Schemes: Doo-Sabin
Mid-Edge
2 steps
4 steps

16. Interpolating Even Vertices Remain Stationary
‘Inflates’ Out to Limit Surface (bad)
Common Schemes:
Modified Butterfly (triangle based)
Kabbelt (quad based)

17. Approximating Even Vertices are Moved Converges in to Limit Surface
Convergence Faster than Interpolating Schemes
Better Mathematical Properties
Common Schemes:
Loop (triangle based)
Catmull-Clark (quad based)

18. Subdivision Example: Catmull-Clark
Quad-Based
Approximating Subdivision Surface
Isomorphic to B-Spline Patch Around Regular Vertices

19. Catmull-Clark Demonstration

20. Interesting Properties
Explicit Evaluation
Subdivide Scalar Parameters
‘Snap’ to Limit Surface

21. Big ‘Wins’
No Cracks

22. Big ‘Wins’ (cont.) View-Dependant Mesh Refinement
Operate on only one Geometry
Polygon Reduction on Control Mesh
‘Pawn’ Geometry

23. Papers Interactive Multiresolution Mesh Editing
Zorin et. al.
Non-Uniform Recursive Subdivision Surfaces
Sederberg et. al.
Exact Evaluation of Loop Subdivision Surfaces
Jos Stam

24. Papers (cont.) Exact Evaluation of Catmull-Clark Subdivision Surfaces
Jos Stam
Subdivision Surfaces in Character Animation
DeRose et. al.

25. Interactive Multiresolution Mesh Editing
Uniform Editing On All Detail Levels
Edit At One Resolution and Propagate Changes

26. Interactive Multiresolution Mesh Editing (cont.)
Subdivide Surfaces Only Where it Matters

27. Non-Uniform Recursive Subdivision Surfaces
Interesting, But Missed the Ball
NURSSes:NURBS as Catmull-Clark:B-Splines
We Don’t Want/Need NURBS

28. Exact Evaluation of Catmull-Clark Subdivision Surfaces
Subdivision Surfaces Without Subdividing
Precompute Eigenbasis Functions
Produce the Limit Surface Directly

29. Subdivision Surfaces in Character Animation
Wonderful Overview of Subdivision Surfaces
The Right Way to do Edge Weights
Fits Well With RenderMan

30. Subdivision in Action…

31. A Bug’s Life

32. Geri’s Game

33. Conclusions