In this document http://linuxcnc.org/docs/html/lathe/lathe-user.html 
<http://linuxcnc.org/docs/html/lathe/lathe-user.html> section "3. Lathe Tool 
Orientation" there is a diagram of tools and their positions.  I have a tool in 
position 3 (315deg) that has an 80 degree angle on it.  So I assume one angle 
is 315-40=275 and one angle is 315+40=355.  But which is frontangle and which 
is backangle?  Above the diagram is says “The FRONTANGLE and BACKANGLE are 
clockwise starting at a line parallel to Z+.”  But if that is true then the 
tools at position 5 and 7 are marked wrong because it shows their  BACKANGLE 
first and FRONTANGLE second (if clockwise from that parallel line).

Secondly, what are these angles used for in actual cutting, since the radius of 
the nose of the tool is what is engaging the workpiece?

-Tom

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