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.

翻译：我们提出一种基于细分法的认证算法，用于计算平面内两条曲线的同构逼近。该算法建立在Plantinga和Vegter的认证曲线逼近算法基础之上。该计算的主要挑战在于正确且高效地计算曲线交点。为解决这一问题，我们引入了一种简单的新检验方法，可确保输出结果的全局正确性。