I wanted to make a prettier Voronoi pattern for my unique ring.
A ring is revolved surface has a seam and I wanted to map the continuous Voronoi pattern on the surface.
After a lot of thought and research, I found a pretty good principle.
The more users know, the happier! haha 
---------- Let me summarize two important things. -----------
1. It should have a data structure with rows and columns.
You can create the random points has a data structure by using the way I introduced in my pre-post about Voronoi transform.
(Remember that it is important to make a point half of a column/row a distance from the surface boundary from the beginning so that the start and end of the iteration are evenly spaced.)
2. Copy the first and last columns (rows) and paste to add them to the other side end column (rows).
These added points will guide the direction of the Voronoi infinite lines.
This is the right key point!
After getting Voronoi polygons by expansion points, the next step is filtering the polygons intersected with original Voronoi cell points.
Here are my scrip and full video about how did I work it out. Enjoy 
PART1: Restricted Random Points ~ Voronoi (0:00:32)
PART2: Expansion to Repeated Points (0:05:27)
PART3: Development into Repeated Voronoi (0:10:05)
PART4: Map to Donut (0:18:43)
VoroRepeat-3_share.dyn (73.1 KB)
