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Objective of Subdivision surface
Keep advantages from
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- general topology of meshes
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- smoothness of parametric splines
Example on curves
\[ \left( \begin{array}{l} p^{n+1}_{2k} \\ p^{n+1}_{2k+1} \end{array} \right) = \left( \begin{array}{ll} 1/3 & 2/3 \\ 2/3 & 1/3 \end{array} \right) \left( \begin{array}{l} p^{n+1}_{k} \\ p^{n+1}_{k+1} \end{array} \right) \]
For surfaces: 2D subdivision mask
