I'm not sure why intersection gives this result, but I did find a workaround. The 'Cut Paths' tool splits lines correctly at the shape boundary. One still has to go through and manually delete the lines outside the shape, but at least the nodes get placed correctly at the shape boundary. Cut Path ex...

I have a complicated line drawing consisting of a lot of open paths. I would like to intersect this drawing with a shape. I am hoping for an effect similar to masking the lines with the shape, but I need to reduce to simple paths due to restrictions in the downstream software consuming the SVG. I've...