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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).

This is what a single subdivided triangle looks like: enter image description here

If I naively try to iterate over every edge and reconnect faces I get the following sequence enter image description here enter image description here enter image description here

Clearly this is wrong.

If instead I iterate over the faces I get the following pattern:

enter image description here

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:

enter image description here

Any suggestions?

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No one answered so I will. The solution is to do the subdivision in 2 passes, first generating new triangles as I showed in the question.

Then on the second pass you flip them.

enter image description here

As described there: https://github.com/cmu462/Scotty3D/wiki/Loop-Subdivision

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