How to Make Custom Curvature Graph

Hi all,

I am trying to break a closed curve (lets call this c0) into a series of segments based on its curvature. I want to get the parameter where either of these two things happens:

1) The curvature has a sharp break

2) The Curvature "flips"

The curvature graph component creates exactly what I need, but unfortunately it only visualizes the new curve (lets call this c1), without actually making it usable. If it were usable, I could just test for curve-curve intersections, and discontinuities in (c1). I have more or less replicated the behavior of the curvature graph component, except that my imitation is too smooth (lets call my imitation curve c2). I attached two images to demonstrate what I mean.

Is there a way to get exactly what the Curvature graph makes? How is it creating c1? Is it just a much larger sampling of points? Or does it somehow operate (calculus?) on the underlying formula of the curve (c0)?

Any guidance is hugely appreciated.