The curve of the links determines the roundness of the umbrella and how easy it is to open.
The photo shows the middle stitch (the process of sewing together the cut umbrella links).
If you look closely at the top, you can see that it is an isosceles triangle with a slight curve. (If it had a curve, it wouldn't be called an isosceles triangle...)
This curve gives the umbrella a rounded appearance when opened and makes it easier to open.
The type of curve that is drawn is apparently up to the individual craftsman's ingenuity.
I once saw a Western-style umbrella maker cutting fabric on television, and the curves he made looked very unique to me.
It would be interesting to line up pieces by various craftsmen...
The craftsmen repeatedly adjust the position and degree of this curve until they are satisfied with the result.
We're breathing life into it so that it becomes a good umbrella.
It's a work of art!