well you culd modify things a bit
My first stupid solution: Calculate the intersection curve of two nurbs surfaces
Ok this works, instead of a small tube tough make the surface a simle extrude of a line thet starts at your curve. Thsiway you can jsut ask for the location of the vertex 0. Should save you some nodes.
BUT i don't get informations about the normals of the object and it's not really fast.
But the normal has nothing to do with your question that is a difrferent ballgame alltogether, Just feed the uv position to a surface info node.
i don't know how to calculate the intersection with a defined linear curve
ahh so the curve is linear. In thatcase you should try to use the ray intersect plugin.