this is more of a math question than an EMC question, but I need the
question for EMC so thought someone else might have run into it.

I'm trying to figure out how I can calculate whether an arc will go
outside the working area of my CNC.  Let's say I have an arc from the
following parameters:

x1,y1,x2,y2,radius,direction (CW or CCW)

and that my working area boundaries are: minX = -5, minY = -5, maxX =
5, maxY = 5

how can i tell if the arc will go outside the boundaries?

so, for example, an arc with these values would go outside the bounds:

G0 x-4.5 y0
G02 x-4.5 y4 r2

in fact, it's almost entirely outside the bounds. but if I change the
radius to 6, it won't. (or if I change the direction to ccw of course)

thanks for any help!!

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