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I saw the VERY COOL solution that JoeGadget assembled for cutting segmented-bowl pieces on the laser engraver =>

https://www.instructables.com/id/Segmented-Turning-Blank-for-bowls-and-cups/

I reproduced his work, then proceeded to cut a few strips of cherry and birch using his method...

I make my stuff at TechShop in San Jose...

I saw that cutting was taking more time than needed.  Since Laser time is at a premium, I decided to modify the drawing and minimize the number of times the laser has to make cuts. 

I also wanted to minimize "dead travel time" - when the laser is just traveling and not doing any work.

So I went for some Serpent action...

I'm attaching a snippet of the Corel file that enables the Serpent.

The Laser driver's algorithm is a bit confusing, but overall I saved a great deal of time, since the intersecting faces only needed to be cut once for two 'puzzle' pieces.

I am making my segmented cylinders for a coffee mug.  Here are some of the woods I'm using - Cherry, Birch, and Walnut.

Thank you, JoeGadget, once again, for the insight on making this happen.

I make my stuff at TechShop in San Jose...