  Given points $P_1,P_2,\ldots,P_m$ in the complex plane, we are concerned with
the problem of finding an interpolating curve with minimal bending energy
(i.e., an optimal interpolating curve). It was shown previously that existence
is assured if one requires that the pieces of the interpolating curve be
s-curves. In the present article we also impose the restriction that these
s-curves have chord angles not exceeding $\pi/2$ in magnitude. With this setup,
we have identified a sufficient condition for the $G^2$ regularity of optimal
interpolating curves. This sufficient condition relates to the stencil angles
$\{\psi_j\}$, where $\psi_j$ is defined as the angular change in direction from
segment $[P_{j-1},P_j]$ to segment $[P_j,P_{j+1}]$. A distinguished angle
$\Psi$ ($\approx 37^\circ$) is identified, and we show that if the stencil
angles satisfy $|\psi_j|<\Psi$, then optimal interpolating curves are globally
$G^2$.
  As with the previous article, most of our effort is concerned with the
geometric Hermite interpolation problem of finding an optimal s-curve which
connects $P_1$ to $P_2$ with prescribed chord angles $(\alpha,\beta)$. Whereas
existence was previously shown, and sometimes uniqueness, the present article
begins by establishing uniqueness when $|\alpha |,|\beta |\leq\pi/2$ and
$|\alpha -\beta|<\pi$.
