I hadn´t tried the trimming tools until now and I made a mess of them.
I´d like to trim a curve the way you can see in the image below and I found that the trim with regions tool doesn´t work the way I thought: splitting the curve with each line not with each pair of lines.
the Region components all require closed curves because there needs to be an unambiguous inside/outside condition. It seems to me you want to split (not trim) the curve at the intersection points. Is that correct?
Splitting a curve at a number of points is best achieved with the Shatter Curve component I think. You'll have to create a list of splitting parameters, then you'll be able to get all the segments in one go.
Yes, you almost always need curve parameters (typically denoted "t") when you're dealing with curve evaluation. You can get curve parameters with the CurveCP component, or with the EvaluateLength component, or using any of the Curve Intersection components or, or, or...