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I'm struggeling to get a (clean) intersection of the following profiles. It has to be this kind of arc stripe intersected with a rectangle.

enter image description here

I tried these nodes

enter image description here

Even though the shape looks like it could also just an arc segment, this is not what I'm looking for. I would also be happy with a solution which can construct the shape.

I want to construct the following geometry in the end.

enter image description here the missing faces are important

And finally I want to stack these. I'm also trying to get a clean mesh and I know stacking these and filling the curves and extruding the profiles in the end will also be very tidious, but these are things to come. It it important that the faces on the sides are missing because there I will add more geometries.

It it important that the faces on the sides are missing because there I will add more geometries

thank for you help

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You could use maths, but the way the title is phrased, there's no general mathematical solution (there is for cutting out an arc as presented in the question body).

The generalized solution would be to use Boolean. Fill curves, extrude, then boolean, and then keep only the bottom (because the filled curve extrudes up)

You could continue extruding, flipping etc. until you get as many levels as you need…

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