How to smooth a curved surface without it looking like a paper plate? I have always had issues with curved surfaces, like the foot of a wine glass, for instance, but I have found that with smoothing them, it makes them to look like either a pancake or a paperplate, here is a fine example of this cylinder that I used the subserf modifier on:



It's just a simple cylinder:


And when I subsurf it, it makes like these ridges in the middles of what would be the tris.
You will automatically have these artifacts with this kind of topology (if you leave the top without any edge loop along the rim), because the subsurf won't leave enough faces to interpolate correctly between the slice and the top. So create a bevel or at least an inset to fix the problem: