  Let $ \Omega \subset R^2$ be a bounded piecewise smooth domain and
$\phi_\lambda$ be a Neumann (or Dirichlet) eigenfunction with eigenvalue
$\lambda^2$ and nodal set ${ N}_{\phi_{\lambda}} = {x \in \Omega;
\phi_{\lambda}(x) = 0}.$ Let $H \subset \Omega$ be an interior $C^{\omega}$
curve. Consider the intersection number $$ n(\lambda,H):= \# (H \cap
N_{\phi_{\lambda}} ).$$ We first prove that for general piecewise-analytic
domains, and under an appropriate "goodness" condition on $H$, $$ n(\lambda,H)
= {\mathcal O}_H(\lambda) (*)$$ as $\lambda \rightarrow \infty.$ We then prove
that the bound in $(*)$ is satisfied in the case of quantum ergodic (QE)
sequences of interior eigenfunctions, provided $\Omega$ is convex and $H$ has
strictly positive geodesic curvature.
