Finding all intersections between planar curves

This article proposes a new algorithm for finding all intersections between two planar curves within a given domain. The algorithm is a hybrid between subdivision and iterative methods. We use a test based on Kantorovich´s theorem to detect the starting point where Newton´s method converges quadratically and the subdivision scheme to exclude certain regions that do not contain any intersections. Our algorithm is guaranteed to detect all intersections in the domain for nondegenerate and non-illposed cases. We implement the algorithm in Matlab and run it on some test problems. The computed solutions and the efficiency of the algorithm are shown.