  This paper presents the first purely numerical (i.e., non-algebraic)
subdivision algorithm for the isotopic approximation of a simple arrangement of
curves. The arrangement is "simple" in the sense that any three curves have no
common intersection, any two curves intersect transversally, and each curve is
non-singular. A curve is given as the zero set of an analytic function
$f:\mathbb{R}^2\rightarrow \mathbb{R}^2$, and effective interval forms of $f,
\frac{\partial{f}}{\partial{x}}, \frac{\partial{f}}{\partial{y}}$ are
available. Our solution generalizes the isotopic curve approximation algorithms
of Plantinga-Vegter (2004) and Lin-Yap (2009).
  We use certified numerical primitives based on interval methods. Such
algorithms have many favorable properties: they are practical, easy to
implement, suffer no implementation gaps, integrate topological with geometric
computation, and have adaptive as well as local complexity.
  A version of this paper without the appendices appeared in Lien et al.
(2014).
