When collapsing edges, it seems like we also introduce new edges on top of just deleting edges and triangles, such as the top two triangles that used to only connect at a point but now share an edge. In general is there a way to tell when such things would happen?
Why is it called an "atomic" operation?
What was the dominant reason for choosing this half-edge representation for our coding project? Was it the ease of implementation?
What are some examples of when we need to use these operations?
How do you choose which half-edge to start from when looping through half-edges to make a change?
Could you use halfedge-collapse uniformly over a mesh to generate lower poly / "resolution" versions of a mesh? If so, is this how mesh decimation would be performed in practice?
How would you preserve manifoldness in a half edge edit? Would you somehow have to check if the new mesh is manifold and then reject the edit if not, or is there an easier way of determining whether or not an operation is valid?
What are some real uses for these operations?