Classic Subdivision Schemes Schemes CatmullClark 1978 DooSabin 1978

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 • Interpolating Scheme – New Vertex Rule

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

Scheme Classification

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

Subdivision Rules

Limit Surface

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

Subdivision Rules

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

Subdivision Rules

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

Subdivision Rules • Regular Vertices

Subdivision Rules • Near Extraordinary Vertex

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

Subdivision Rules

Mid-Edge Scheme

Comparison