Grasshopper surface-surface intersection problem

Hello people. I have a (i assume) very basic question.

I’m trying to construct the hull surface of a boat based on some numerical data. I am also supposed to obtain the same numerical data from the same constructed surface as if i do not have the initial numerical data as the second step.

I have managed to do the first main step, constructing the lines and creating a network surface. Problem starts at the second step.

I want to find intersection lines of one surface and a series of surfaces to obtain some lines. After that i need to do the same thing based on the same main surface and a different series of surfaces which belong to a different plane to obtain some other lines. At the end i need to get the intercetion points of the two curve sets which should be obtained from surface intersections.

Where i get stuck is actually the first step. I cannot obtain the intersection lines. I might be trying some pointless hard way, i’m not sure. I think maybe the points can be obtained directly by finding the intersection points of three surfaces (hull surface, xy plane surface series and yz plane surface series).

I’m sharing the basic hull surface, first and second series of surfaces that i want to intersect, and the curves i am supposed to obtain.

Any help would be appreciated.