Good day,
Is there a way to control the squirliness of this edge loop, or is it just a result of the irregular mesh that I can’t really correct for?
I don’t think that there will be any difference visually - the bottom of this glass is flat against Z.
Thanks!
Use Looptools Circle option?
Thats what your subdivision modifier does with tri’s. Subdivision turns tris to diamond quads, you dont get a smooth circular edge loop.
There is a simple way to get a nice clean circular edge there. Just add an edge loop around the pole.
Ah… I misunderstood and didn’t look close enough at the image. Just ignore the way it’s displayed - or turn off the Adjust Edit Cage to Modifier Result icon.
turn off the Edit modifier (Triangle with vertices icon highlighted in blue on your Subsurf modifier tab)
Thank you! 
