Certified simultaneous isotopic approximation of pairs of curves via subdivision

We present a certified algorithm based on subdivision for computing an isotopic approximation to a pair of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main challenge in this computation is to correctly and efficiently compute the intersections of the curves. To address this issue, we introduce a new, but simple test that guarantees the global correctness of our output.