What do you exactly mean?
I tried to follow your suggestion, but I could not make it ‘redraw border/perimeter.’
Chris’ one made it possible for me to create the quads.
But, your suggestion, your suggestion made me believe to go even further with quads (see image) below, however, I was not able to make it.
I thought from your description that I could do ‘discontinuity’ and ‘shatter’ to get the points and edges; and with a normal surface mesh extracting the vertices; combine everything and get a very smooth quad semi triangle mesh. That is what you meant right?
EDIT: see latest file below this post (my response to Mr. Chanley)
20181031 problem mesh quads 03.gh (71.5 KB)