Subdivision Surface
Subdivision repeatedly splits each element of a surface into smaller pieces and replaces vertex positions with weighted average of neighbors.
Main considerations:
- interpolating vs. approximating
- limit surface continuity (C^1, C^2, …) (derivative)
- behavior at irregular vertices
There are a lot of subdivision schemes. For quad meshes, the most common scheme is Catmull-Clark. And for triangle meshes, there are several popular schemes such as Loop, Butterfly, or Sqrt(3).