Split Curve at Points Where Slope Changes Direction

Hello everyone!

Thanks for everyone's help. This forum is a great resource.

So, I'm quite new to this grasshopper thing. I have read a few and watched several tutorials, but I am still not very proficient at all. In my head, I feel that I know how to go about solving a problem, but I don't know the components well enough sometimes, and other times I don't understand how to work with their inputs. I still need to learn graft, dispatch, and many others. Any suggestions on the best learning resources, such as tutorials which utilize a wide range of components, would be helpful so I can get a bit more of this done on my own.

Anyway, what I'm trying to do is take a closed curve, and split it into several segments based on whether the slope of the curve is positive or negative. I have a CNC machine, and certain woods are prone to tearout if they are not cut in the correct direction. So, rather than manually splitting every curve that I want to mill, I figured a Grasshopper definition would be useful.

As you can see in the image above, the portions of the curve which have a positive slope need to be climb cut, and those with negative need to be cut conventionally (before doing the entire profile conventionally).

Is there a way to find the points where the slope polarity(?) changes? I know that I will need to use shatter, and I was considering flipping every other segment, but sorting them into 2 separate groups would work as well.

Thanks so much for the help,

Justin