1. Classic Subdivision Schemes

2. Schemes Catmull-Clark (1978) Doo-Sabin (1978) Loop (1987) Butterfly (1990) Kobbelt (1996) Mid-edge (1996 / 1997)

3. Classification Criteria

4. Refinement Rules / Mesh Types

5. Reconstruction Basis Approximating Scheme –New Vertex Rule –Old Vertex Rule Interpolating Scheme –New Vertex Rule

6. Smoothness Based on Box Splines –Extraordinary Vertices General Schemes –Regular Convergence –Extraordinary Vertices

7. Scheme Classification

8. Loop Scheme Approximating Scheme Three Directional Box-Spline Continuity –C 2 regular regions –C 1 extraordinary vertices Primal Triangular Quadrisection

9. Subdivision Rules

10. Limit Surface

11. Butterfly Scheme Interpolating Scheme General Scheme Continuity –C 1 regular regions and extraordinary vertices Primal Triangular Quadrisection

12. Subdivision Rules

13. Catmull-Clark Scheme Approximating Scheme Tensor Product Bicubic B-spline Continuity –C 2 regular regions –C 1 extraordinary vertices Primal Quadrilateral

14. Subdivision Rules

15. Kobbelt Scheme Interpolating Scheme Tensor Product 4-Point Scheme Continuity –C 1 regular regions and extraordinary vertices Primal Quadrilateral

16. Subdivision Rules Regular Vertices

17. Subdivision Rules Near Extraordinary Vertex

18. Doo-Sabin Scheme Approximating Scheme Tensor Product Quadratic B-Spline Continuity –C 1 regular regions and extraordinary vertices Dual Quadrilateral

19. Subdivision Rules

20. Mid-Edge Scheme

21. Comparison