  An arrangement of $n$ curves in the plane is given. The query is a point $q$
and the goal is to find the face of the arrangement that contains $q$. A
data-structure for point-location, preprocesses the curves into a data
structure of polynomial size in $n$, such that the queries can be answered in
time polylogarithmic in $n$.
  We design a data structure for solving the point location problem queries in
$O(\log C(n)+\log S(n))$ time using $O(T(n)+S(n)\log(S(n)))$ preprocessing
time, if a polygonal subdivision of total size $S(n)$, with cell complexity at
most $C(n)$ can be computed in time $T(n)$, such that the order of the parts of
the curves inside each cell has a monotone order with respect to at least one
segment of the boundary of the cell. We call such a partitioning a
curve-monotone polygonal subdivision.
