Faced the following problem a few months back: Have two sets of curves in Cartesian coordinates, want to find if they intersect and where?
No straight forward solution was available, could find various solution using functions but none available with x, y coordinates.
Solution, found a matlab implementation that did just that, ported it to python. This is a pure python numpy implementation of interaction of two curves.
Produces the picture at the start of this post. As always the entire code freely available at this github repo.