What does it mean when it says we "split edges of original mesh in any order"? Like we randomly split the edges?
Mehvix
The order we split doesn't matter as the flip rule ensures we obtain the same result (even if we randomly chose the order to split edges)
Alescontrela
Why do we flip edges? is it to make sure we don't add too many degrees to any particular vertex?
0-0-00-0
In splitting, we just add a midpoint to each of the old edges, and randomly choose a vertex (old or new) to connect it with.Then we flip every new edge that touches exactly one old and one new vertex. Is my understanding correct?
0-0-00-0
If the edges are randomly added, how do you make sure that the edges don't cross over each other?
stephanie-fu
From my understanding, once you make the first split, the other two splits will stay on their "side" of the bisection since they are attending to different triangle edges. So no matter your subdivision order, you won't get edges that cross each other.
andreisito
During the split edge stage, after adding new vertices, how do we know where to draw the new edges?
mark-nguyen1
From the picture, I think the first edge, edge_f, can start from any of the midpoints, but it should connect to the opposite black edge. From there, the two other new midpoints from the same triangle will connect to edge_f.
angelajyzhang
From the pictures, this algorithm makes sense, but I wonder what the proof is behind why this works so efficiently and that it ensures there is no crossing of any edges or that it won't create other subshapes.
What does it mean when it says we "split edges of original mesh in any order"? Like we randomly split the edges?
The order we split doesn't matter as the flip rule ensures we obtain the same result (even if we randomly chose the order to split edges)
Why do we flip edges? is it to make sure we don't add too many degrees to any particular vertex?
In splitting, we just add a midpoint to each of the old edges, and randomly choose a vertex (old or new) to connect it with.Then we flip every new edge that touches exactly one old and one new vertex. Is my understanding correct?
If the edges are randomly added, how do you make sure that the edges don't cross over each other?
From my understanding, once you make the first split, the other two splits will stay on their "side" of the bisection since they are attending to different triangle edges. So no matter your subdivision order, you won't get edges that cross each other.
During the split edge stage, after adding new vertices, how do we know where to draw the new edges?
From the picture, I think the first edge, edge_f, can start from any of the midpoints, but it should connect to the opposite black edge. From there, the two other new midpoints from the same triangle will connect to edge_f.
From the pictures, this algorithm makes sense, but I wonder what the proof is behind why this works so efficiently and that it ensures there is no crossing of any edges or that it won't create other subshapes.