  Point containment queries for regions bound by watertight geometric surfaces,
i.e., closed and without self-intersections, can be evaluated straightforwardly
with a number of well-studied algorithms. When this assumption on domain
geometry is not met, such methods are either unusable, or prone to
misclassifications that can lead to cascading errors in downstream
applications. More robust point classification schemes based on generalized
winding numbers have been proposed, as they are indifferent to these
imperfections. However, existing algorithms are limited to point clouds and
collections of linear elements. We extend this methodology to encompass more
general curved shapes with an algorithm that evaluates the winding number
scalar field over unstructured collections of rational parametric curves. In
particular, we evaluate the winding number for each curve independently, making
the derived containment query robust to how the curves are arranged. We ensure
geometric fidelity in our queries by treating each curve as equivalent to an
adaptively constructed polyline that provably has the same generalized winding
number at the point of interest. Our algorithm is numerically stable for points
that are arbitrarily close to the model, and explicitly treats points that are
coincident with curves. We demonstrate the improvements in computational
performance granted by this method over conventional techniques as well as the
robustness induced by its application.
