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Classic Subdivision Schemes

Classic Subdivision Schemes. Schemes. Catmull-Clark (1978) Doo-Sabin (1978) Loop (1987) Butterfly (1990) Kobbelt (1996) Mid-edge (1996 / 1997). Classification Criteria. Refinement Rules / Mesh Types. Reconstruction Basis. Approximating Scheme New Vertex Rule Old Vertex Rule

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Classic Subdivision Schemes

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  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 • C2 regular regions • C1 extraordinary vertices • Primal Triangular Quadrisection

  9. Subdivision Rules

  10. Limit Surface

  11. Butterfly Scheme • Interpolating Scheme • General Scheme • Continuity • C1 regular regions and extraordinary vertices • Primal Triangular Quadrisection

  12. Subdivision Rules

  13. Catmull-Clark Scheme • Approximating Scheme • Tensor Product Bicubic B-spline • Continuity • C2 regular regions • C1 extraordinary vertices • Primal Quadrilateral

  14. Subdivision Rules

  15. Kobbelt Scheme • Interpolating Scheme • Tensor Product 4-Point Scheme • Continuity • C1 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 • C1regular regions and extraordinary vertices • Dual Quadrilateral

  19. Subdivision Rules

  20. Mid-Edge Scheme

  21. Comparison

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