Find a coordinate from a polycurve to cut a surface

Hi, I’m trying to cut different shape of surfaces to generalize shape in dynamo to move on to next procedure.
Here are examples,I could find coordinates from edges and reoder the list by clockwise,and tried to find red points in different shapes with vactor values but I can’t fix any rules to find a red point in different shapes,Is there any Ideas for this?

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@jaeho ,

thats one variation. I think you can also use start and endpoint… you have to search for something specific in the geometry.