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I think you misinterpreted my design meaning, I mean put the tools outside along the y axis.

 

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github.com/grandixximo/Linuxcnc-G-code
gcode formatter for anyone who writes gcode subroutines by hand

Hi,

I thought, mabye just start coding a clothoid lib. And try to
understand how 3d clothoids work.

I followed this paper, the same as Andrew used : 2d clothoid
Then coded chapter 4 into c code.
Was also able to look into Andrews clothoid code from where i
borrowed the gaus legendre.

With a little assistance of DeepSeek i was able to get a single 2d clothoid
running and plotted with gnu plot.

Then i turned on my experimental mode and tried to expand the signle 2d clothoid
to a single 3d clothoid.

The 3d clothoid uses torsion. To keep it simple i used simple names in the c code.

theta0 & kappa0 -> xy
theta1 & kappa1 -> z

I think the hard part is really the bi-clothoid fitting, wich has to be coded yet.

Code so far:
libclothoid

Gnu plot of single 3d clothoid: