Another thing complicating CNC on a pattern torch (like this 
onehttp://www.hellotrade.com/esab-usa/ultra-graph-single-torch-pattern-cutter.html
 ) is the maximum work envelope the arm can reach isn't a quadrilateral.

As the arm end gets close to the column the range of motion is very restricted 
and at maximum reach it describes an arc.

I figure the best compromise would be to define a quadrilateral that the torch 
can reach and just go with it.

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