  We present a certified algorithm based on subdivision for computing an
isotopic approximation to any number of curves in the plane. Our algorithm is
based on the certified curve approximation algorithm of Plantinga and Vegter.
The main challenge in this algorithm is to correctly and efficiently identify
and isolate all intersections between the curves. To overcome this challenge,
we introduce a new and simple test that guarantees the global correctness of
our output. A main step in our algorithm for approximating any number of curves
is to correctly approximate a pair of curves. In addition to developing the
details of this special case, we provide complexity analyses for both the
number of steps and the bit-complexity of this algorithm using both worst-case
bounds as well as those based on continuous amortization.
