A hybrid method for computing the intersection and tangency points of plane curves

摘要

In this paper we present a symbolic-numeric (hybrid) method for computing the intersection and tangency points of given plane curves. The whole procedure involves three phases: (i) implicitization, (ii) root specification, and (iii) inversion. For each one of these phases we propose an appropriate algorithm fully documented regarding its complexity and stability. A comparison with other existing methods is also provided. All the proposed methods are illustrated through examples.