Resize a ring outside diameter?

[toy4x4]

I have a ring as shown. I want to shrink the outside portion of the ring while leaving the inside diameter the same. I played withthe donut tool but never got where the design would "squish" inside the ring portion. Any ideas?

[user_0815]

Hmmm. The only thing that comes to my mind spontaneously is using a mesh layer. But that is eyeballing.  Set four points on each side both inside and outside, then move the points as needed. Adjust the roundness with the handles. Perhaps place a donut below to match your desired result. 

[NotMyFault]

If you have designer:

1. create a custom brush with the Greek pattern.
2. use a circle of suitable diameter to get exactly the inner and outer diameter. The stroke width is the difference between inner and outer. The circle diameter is the average of both.

If you have Photo:

1. get a perfect quadratic crop of the circle
2. use polar to rectangular filter
3. adjust height as needed (use marks on the source layer)
4. use rectangular to polar filter