I have a bunch of curves like this
that I want to be two different curves that meet at the endpoints.
I am struggling to find a way to do this.
The component Explode should do it
(Curves > Utilities > Explode)
Easy and probably what you need. But you can also use the Shatter component and provide a set of splitting parameters. You can create parameters at kinks and other discontinuities using the Discontinuity component.
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