Really simple. This is one of those ‘looks way harder’ than it really is moments.
Here is the blank being cut (Atlas/Patriot/Polaris). I stop the blade just a little before half way. It is at a 45 degree angle. And I have a stop block to ensure the segments are going to be even all the way around. Although I imagine you could vary the segment up and down the blank.
You will notice that, because I like my fingers I don’t cut the blank to size until the swirl cuts are done
My planer goes down exactly to 1/8”, so a 1/8” blade work perfect for using that size of segmentation.
Here is the finished “Swirl” blank with the segments in place.
And here is the finished product. Well almost, this is a different pen. The other pen is sold and I have no pictures of it.