Assume we have a mesh represented as a half edge datastructure.
We want to subdivide faces without introducing unnecessary vertices (i.e the new number of vertices must be exactly V + E where V is the old number of vertices and E is the old number of edges).
Clearly this is wrong.
If instead I iterate over the faces I get the following pattern:
This is happening because at every step I am trying to to:
- Focus on only one simplex at a time,
- Maintain the connectivity information of the mesh in a valid state (every edge has <2 faces, vertices only exist at the end of edges, faces only have 3 Half edges...), like for example, I am avoiding getting into this state: