If you run the Axis lathe sim you can look at the tools in the tool 
table there is one defined for each orientation. The angles are for 
display only. The orientation and radius are used to define the control 
point. The control point and radius is used by G41/42 cutter compensation.

http://linuxcnc.org/docs/html/lathe/lathe-user.html#_lathe_tool_orientation_a_id_lathe_tool_orientation_a

The "angle" starts at the line parallel to Z+ and goes clockwise. Which 
one is the front angle and back angle are a mystery to me. Looking at 
the tool table for Axis lathe sim you can see even negative numbers are 
used to describe the angles.

JT

On 6/24/2015 4:03 PM, Tom Easterday wrote:
> 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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